Burkhard, R. A. (2004, July). Learning from architects: the difference between knowledge visualization and information visualization. In Information Visualisation, 2004. IV 2004. Proceedings. Eighth International Conference on (pp. 519-524). IEEE.

Burkhard, R. A. (2004, July). Learning from architects: the difference between knowledge visualization and information visualization. In Information Visualisation, 2004. IV 2004. Proceedings. Eighth International Conference on(pp. 519-524). IEEE.

information visualization

視覺表示能夠應用於說明關係(to illustrate relations)、確認模式(to identify patterns)、呈現概觀與細節(to present both an overview and details)、支援問題解決(to support problem solving)以及傳播不同知識類型(to communicate different knowledge types)等任務，具有激勵人們(to motivate people)、提出新觀點(to present new perspectives)、增強記憶(to increase remembrance)、支援學習的過程(to support the process of learning)、集中觀看者的注意力(to focus the attention of the viewer)和組織與協調通訊(to structure and coordinate communication)等優點(Eppler [16])。本研究區別資訊視覺化(information visualization)和知識視覺化(knowledge visualization)，將資訊視覺化定義為利用視覺化方法與過程，探索抽象的資料，產生新的洞見(insight)，如Card et al. [2]所定義的「使用電腦支援、互動與視覺表達資料資料，藉以增強認知」；而知識視覺化則是利用視覺表示來改善人或群體間的知識移轉(knowledge transfer)。知識視覺化可以幫助管理者減少資訊過荷(information overload)、誤解(misinterpretation)和誤用(misuse)等問題。

由於知識移轉需要解決資訊深度(information depth)、有限時間(limited time)、不同認知背景(difference cognitive background)和資訊相關性(information relevance)等困難。不同的任務需要不同的視覺化方法，整合多種方法可以達到互補的效用，增進知識移轉的效能與動機等品質、增進接收者的注意力、減少資訊過荷、改善決策。因此，本研究認需要提供管理者一個架構(framework)，幫助他們針對個別任務發現最有希望的視覺化方法。本研究根據知識類型(knowledge type)、接收者類型(recipient type)、視覺化類型(visualization type)等三個觀點提出知識視覺化的架構。知識類型在於考慮需要移轉的知識為何種類型，例如陳述性知識(declarative knowledge)、程序性知識(procedural knowledge)、實驗性知識(experimental knowledge)、方位性知識(orientational knowledge)、個人知識(individual knowledge)。接收者類型的目的在確認目標族群以及接收者的情境脈絡(context)和認知背景。

The transfer of knowledge is a core process and difficult to manage [1]. For the transfer of knowledge the following difficulties need to be solved:

• Information depth: Trade off between an overview and details that need to be communicated.

• Limited time: Limited time, attention and capacity of the recipients.

• Different background: Different cognitive backgrounds and difficulties of decision makers to understand the novel information visualization tools.

• Relevance: Providing the relevant information to different stakeholders.

What is missing, is a mediating framework for the use of visualization methods for different tasks that concern managers; starting from information exploration and ending with the transfer of knowledge. The methods should be customized to the recipients' cognitive background and information need. This missing framework would help managers to find the most promising visualization method for the individual task.

Knowledge visualization examines methods to reduce the predominant problems of managers:

• Information overload: Decision Makers cannot identify the relevant information.

• Misinterpretation: Decision makers cannot understand, evaluate and interpret the information.

• Misuse: Decision makers cannot use or misuse the information for decision making.

In an analysis on the way how architects use visual representation for the transfer of knowledge we found a simple but important insight: Architects combine different visualization types that complement one another to illustrate different levels of details. Combining traditional visualizations with novel information visualizations is a promising approach that increases the knowledge transfer quality (effectiveness, motivation) and the attention of recipients, reduces the information overload and as a consequence improves decision making.

Several empirical studies show that visual representations are superior to verbal-sequential representations in different tasks, i.e. to illustrate relations, to identify patterns, to present both an

overview and details, to support problem solving and to communicate different knowledge types [12-14].

The use of visual metaphors is effective for the transfer of knowledge [15]. Eppler [16] describes six advantages: (1) to motivate people, (2) to present new perspectives, (3) to increase remembrance, (4) to support the process of learning, (5) to focus the attention of the viewer and (6) to structure and coordinate communication.

Information visualization is a rapidly advancing field of study [2-6].Card et al. [2] define it, as "... the use of computer-supported, interactive, visual representations of abstract data to amplify cognition".

We define knowledge visualization as: Knowledge visualization examines the use of visual representations to improve the transfer of knowledge between at least two persons or group of persons.

Information visualization and knowledge visualization are both exploiting our innate abilities to effectively process visual representations. But the way of using these abilities differs: Information visualization aims to explore abstract data and to create new insights. Knowledge visualization in contrast aims to improve the transfer of knowledge between at least two persons or groups of persons.

Bertin [5] created a semiology of graphic representation methods.

Lohse et al. [31] report a structural classification of visual representations. It focuses on the classification of visual representations into hierarchically structured categories. Six groups were introduced: graphs, tables, maps, diagrams, networks and icons.

Shneiderman [32] proposes a type by task taxonomy of information visualization where he sorts out the design prototypes to guide researchers to new visualization approaches.

For an effective transfer of knowledge three perspectives are important: a Knowledge Type Perspective, a Recipient Type Perspective and a Visualization Type Perspective.

The Knowledge Type Perspective aims to identify the type of knowledge that needs to be transferred. Different types of knowledge are described in knowledge management literature. For our framework we distinguish five types of knowledge: Declarative knowledge (Know-what), procedural knowledge (Know-how), experimental knowledge (Know-why), orientational knowledge (Know-where), individual knowledge (Know-who).

The Recipient Type Perspective aims to identify the target group and the context of the recipient. The recipient can be an individual, a team, a whole organization or a network of persons. Knowing the context and the cognitive background of the recipient is essential for finding the right visualization method for the transfer of knowledge.

The Visualization Type Perspective aims to establish a simple taxonomy that is able to structure the existing visualization methods.

In contrast to information visualization, which exploits our innate abilities to effectively process visual representation to explore information, knowledge visualization uses these abilities to improve the transfer of knowledge between at least two persons or group of persons.

A sketch as seen in Figure 2 outlines a first rough or incomplete draught or plan. It represents the main idea and key features of a preliminary study. Sketches are atmospheric, fast and universally accessible. Sketches help to quickly visualize an idea with the flexibility to handle any shape one imagines.

Garland defines a diagram as a “visual language sign having the primary purpose of denoting function and/or relationship” [28]. ... For the transfer of knowledge in organizations diagrams help to reduce complexity and amplify cognition. Visualizing a complex situation with boxes and arrows, helps in understanding causal relationships. Diagrams help to categorize and structure information to improve decision making. In contrast to sketches they are precise and determined.

Kemp defines an image (Figure 3) as: “Images are representations which are primarily concerned with impression, expression, or realism.” [29]. An image can among others be a rendering, a photograph or a painting.  ... For the transfer of knowledge in organizations images help to get attention, inspire recipients, to anchor a message through addressing emotions, to improve recall or to provoke discussions.

Physical objects or architectural models bring together plans and sections, help to imagine a spatial
composition and enables to see a project from different viewpoints. They can be abstract or realistic. Physical objects are haptic and allow to experience materials. Architectural models allow to control difficult details. ... For the transfer of knowledge in organizations objects help to get the attention, to initiate discussions, present different views, to improve learning through constant presence or to integrate digital interfaces.

Interactive visualizations are computer-based electronic visualizations that allows the user to control, combine, and manipulate different types of information or media. ... For the transfer of knowledge in organizations interactive visualizations help for example to fascinate recipients, to enable interactive collaboration, to reveal unforeseen relationships and to present complex data.

Rodrigues, J. F., Traina, A. J., & de Oliveira, M. C. F. (2006, July). Reviewing data visualization: an analytical taxonomical study. In Information Visualization, 2006. IV 2006. Tenth International Conference on (pp. 713-720). IEEE.

Rodrigues, J. F., Traina, A. J., & de Oliveira, M. C. F. (2006, July). Reviewing data visualization: an analytical taxonomical study. In Information Visualization, 2006. IV 2006. Tenth International Conference on (pp. 713-720). IEEE.

information visualization

資料視覺化(data visualization)希望當將圖形資訊呈現給使用者時，使用者便能夠立即理解，提供較快速而的資料分析機制。目前已經有許多針對資料視覺化技術的分類架構(classification schemes)提出。Keim[13]以進行視覺化的資料類型(data type)、視覺化技術(visualization technique)以及應用的互動/扭曲技術(interaction/distortion technique applied)為分類架構(taxonomy)的三個面向，來將視覺化技術與系統加以歸類(categorize)。Schneiderman [27]的分類學則則是一個成對的系統(a pair wise system)，包含分析的資料類型以及一組分析的任務，任務例如概觀(overview)、放大縮小(zoom)、過濾(filter)、選取詳細訊息(details-on-demand)等等。Chi [4]的分類法根據一個特定的視覺化模型中不同的性質，詳細地說明視覺化技術，包含資料、抽象(abstraction)、轉換和映射(transformation和mapping)、呈現(presentation)以及互動(interaction)。Tory and Möoller [29]根據視覺塑模(visual modeling)的直覺知覺，將科學視覺化(scientific visualization)和資訊視覺化(information visualization)分別定義為連續及離散類型 。Wiss and Carr [34]在探討3-D技術時則提出了一個考慮注意(attention)、抽象化(abstraction)以及互動支持性(interaction affordance)等的認知為基礎的分類法 。這些分類架構大多僅針對視覺化過程(visualization process)中的某一面向，然而還存在許多有待解決的問題，例如：視覺探索場景(visual exploration scene)的基礎構件(building blocks)是什麼？互動機制如何連結到事實？

本研究根據視覺化技術的機制和視覺知覺理論(visual perception theory)，以解釋視覺化場景如何構成以及它們的構成部分如何有助於視覺理解，做為分析模型。本研究認為視覺化是利用空間化(spatialization)的方式讓資料得以空間性的被感知，並以位置(position)、形狀(shape)和顏色(color)等視覺刺激(visual stimuli) 來代表資料項目或特徵，將可以注意到的差異(noticeable differences)極大化(Ware [32])，空間化後的資料才能夠在知覺注意(conscious attention)前確認事物，能夠立即與容易地引發注意，提昇與加速資料理解。Figure 1表現出這樣的分類法概念。

進一步而言，資料的空間化是將資料從難以說明的原始形式轉換為可視的空間形式，空間化的程序有結構展現(structure exposition)、投射(projection)、樣式定位(patterned positioning)以及 再製(reproduction)等。結構展現是指資料可以嵌入階層或關係網絡等內在結構(intrinsic structures)，可以大抵體現出資料的意義，也就是使得相關的資料結構能夠視覺化地覺察，例如樹狀地圖(treemaps) [28] 或力導向圖式布局(force directed graph structures) [8] 都屬於結構展現。樣式定位是根據一個或多個方向、直線、圓，甚至特定模式，依序安排個別資料項目的設定，意圖填滿整個投射空間，有時稱之為密集向素呈現(dense pixel displays)，這樣的空間化技術有像素長條圖(pixel bar charts) [15]，圓餅圖(pie charts)也屬於這類。在投射這類空間化技術的呈現上，資料項目的位置由一個已知或內涵的數學函數來定義，著名的案例有平行座標(parallel coordinates)與星狀座標(star coordinates) [11]。在再製(reproduction)的呈現上，資料的定位是事先已知的，並且從資料蒐集的系統來決定。

在視覺化場景中，位置是前注意知覺(pre-attention perception)的主要部分，而且它和空間化非常有關。位置包括排列(arrangement)、對應(correspondence)、參考(referential)等三種型式，分別由空間化的各種機制所產生。結構展現產生排列，特定的排列能描述結構、階層或其他整體特性(global property)等資訊，資訊可以從局部的個別元素間相互位置或是整體的景觀概況上察覺，例如樹狀地圖表現資料項目間的階層關係。樣式定位會產生位置上的對應，資料項目的位置決定它的對應特性。投射與再製運用函數或明確的參考來源(explicit referewnce)決定資料的位置，提供使用者得以了解。

形狀可以表達的資訊，包含差異(differentiation)、對應(correspondence)、意義(meaning)和關係(relationship)等。差異是指以呈現的形狀區別這些項目，來提供近一步的詮釋。對應則是利用每一種引人注目的形狀對應一種資訊特徵，例如大小比例便是常用的方式。意義是指呈現的形狀本身便帶有意義，這種方式依賴使用者的知識與過去經驗，例如箭頭。關係：線條、外廓或表面可以利用來表現一組資料項目間的關係。

顏色可以傳遞資料項目間的差異和對應。在差異方面，顏色用來表示資料特徵上的相等(或不相等)，對應上則可表現離散資料的類別、層級或連續資料的值大小。

互動模式則有參數的(parametric)、視景轉換(view transformation)、過濾(filtering)、揀選細節(details-on-demand)、變形(distortion)。參數的互動是指變更位置、形狀和顏色等參數。視景轉換以縮放、旋轉、翻轉等，對視景提供物理性接觸。過濾透過顏色或形狀等方式，視覺性地選取一部份的資料。揀選細節是指資料的詳細資訊可以被隨時檢索出，並呈現在場景上。變形提供投射的視覺化結果，讓不同的觀點可以同時被觀察與定義。

These efforts are generically known as (data) Visualization, which provides faster and user-friendlier mechanisms for data analysis, because the user draws on his/her comprehension immediately as graphical information comes up to his/her vision.

Several classification schemes have been proposed for visualization techniques, each one focusing on some aspect of the visualization process.

However, many questions remain unanswered.

What are the building blocks of a visual exploration scene?

How interaction mechanisms relate to these facts?

In this work, we discuss these issues and analytically find answers to them based on the very mechanisms of the visualization techniques and on visual perception theory.

In this paper we discuss the subjective nature of visualization by proposing a discrete model that can better explain how visualization scenes are composed and formed, and how their constituent parts contribute to visual comprehension.

It (Keim [13]) maps visualization techniques within a three dimensional space defined by the following discrete axes: the data type to be visualized (one, two, multi-dimensional, text/web, hierarchies/graphs and algorithm/software), the visualization technique (standard 2D/3D, geometrical, iconic, dense pixel and stacked), and the interaction/distortion technique applied (standard, projection, filtering, zoom, distortion and link & brush).

This taxonomy is suitable to quickly reference and categorize visualization techniques, but it is not adequate to explain their mechanisms.

A simpler taxonomy was earlier presented by Schneiderman [27]. It delineates a pair wise system based on a set of data types to be explored, and on a set of exploratory tasks to be carried out by the analyst. This taxonomy, known as task (overview, zoom, filter, details-on-demand, relate, history and extract) by data type (one, two, three, multidimensional, tree and network) taxonomy, was pioneer in analytically delineating visualization techniques.

Another interesting classification is presented by Chi [4], a quite analytical approach, which details visualization techniques through various properties related to a specific visualization model. The taxonomy embraces data, abstraction, transformation and mapping tasks, presentation and interaction.

Tory and Möoller [29] define Scientific Visualization and Information Visualization, respectively, as continuous ([one, two, three, multi-dimensional] versus [scalar, vector, tense, multi-variate]) and discrete (two, three, multidimensional and graph & tree) classes, according to the intuitive perception of their visual modeling.

Wiss and Carr [34] describe a cognitive based taxonomy that considers attention, abstraction and (interaction) affordance in order to discus 3-D techniques.

Visualization can be understood as data represented visually. That is, it takes advantage of spatialization to allow data to be visually/spatially perceived and it relies on visual stimuli to represent data items or data attributes/ characteristics.

Spatialization of data refers to its transformation from a raw format that is difficult to interpret into a visible spatial format.

In fact, Rohrer et al. [25] state that visualizing the non-visual requires mapping the abstract into a physical form, and Rhyne et al. [23] differentiate Scientific visualization and Information visualization based on whether the spatialization mechanism is given or chosen, respectively.

Semiotic theory is the study of signs and how they convey meaning. According to semiotic theory, the visual process is comprised of two phases, the parallel extraction of low-level properties (called pre-attentive processing) followed by a sequential goal-oriented slower phase.

Pre-attentive processing plays a crucial role in promoting visualization’s major gain, that is, improved and faster data comprehension [30].

The work described by Ware [32] identifies the categories of visual features that are pre-attentively processed. Position (2D position, stereoscopic depth, convex/concave shading), Shape (line orientation, length, width and line collinearity, size, curvature, spatial grouping, added marks, numerosity) and Color (hue, saturation) are considered and, according to Pylyshyn et al [21], specialized areas of the brain exist to process each of them (Figure 2).

Visualizing data demands a maximization of just noticeable differences. To satisfy this need, visualizations rely on pre-attentive stimuli - characteristics inherent to visual/spatial entities. Therefore, the data must first be mapped to the spatial domain (spatialized) in order to be pre-attentively perceived.

In this section we identify a set of procedures for data spatialization: Structure exposition, Projection, Patterned positioning and Reproduction.

Structure exposition: data can embed intrinsic structures, such as hierarchies or relationship networks (graph-like), that embody a considerable part of the data significance.

This class comprises visualization techniques that rely on methods to adjust data presentation so that the underlying data structure can be visually perceived. Examples are the TreeMap technique [28], illustrated in Figure 3(a), and force directed graph layouts [8], such as the one illustrated
in Figure 3(b);

Patterned: this is the simplest positioning procedure, with the set of individual data items arranged sequentially (ordered or not) according to one or more directions, linear, circular or according to specific patterns.

Patterned techniques tend to fully populate the projection area and sometimes are referred to as dense pixel displays. Examples include Pixel Bar Charts [15], showed in Figure 4(a), pie charts (circular disposition), depicted in 4(b) and pixel oriented techniques in general [12].

Projection: stands for a data display modeled by the representation of functional variables. That is, the position of a data item is defined by either a well-known or an implicit mathematical function.

In a projection, the information given is magnitude and not order, as in a patterned spatialization. Examples are Parallel Coordinates (one projection per data dimension), Star Coordinates [11] and conventional graph plots, as illustrated in Figure 5;

Reproduction: data positioning is known beforehand and is determined by the spatialization of the system from where data were collected, as exemplified in Figures 6(a) and 6(b).

In reproduction, the data inherits positioning from its original source.

Position is the primary component for pre-attention perception in visualization scenes and it is strictly related to the spatialization process. So, while spatialization is the cornerstone for enabling visual data analysis (as it maps data to the visual/spatial domain), it also dictates the mechanism for pre-attentive positional perception.

Thus, positional pre-attention occurs in the form of Arrangement, Correspondence and Referential, explained in the following paragraphs. These classes derive, respectively, from spatializations Structure Exposition, Patterned and Projection/ Reproduction.

Structure Exposition → Arrangement: specific arrangements can depict structure, hierarchy or some other global property. Without an explicit referential, information is perceived locally through individual inter-positioning of elements and/or globally through a scene overview. For instance,
TreeMap (Figure 3(a)) presents the hierarchy of the data items, and a graph layout (Figure 3(b)) presents network information.

Patterned → Correspondence: the position of an item, either discrete or continuous, determines its corresponding characteristic without demanding a reference. For example, see Figure 10(b) where each of the four line positions maps one data attribute. Other examples are Parallel Coordinates and Table Lens [22], techniques that define an horizontal sequence for placing data attributes;

Projection → Referential: this is the most obvious relation between spatialization and positional pre-attention. Projections have a supporting function whose intervals define referential scales suited to analogical comprehension.

Reproduction → Referential: the position of an element, discrete or continuous, is given relative to an explicit reference, such as a geographical map (Figure 6(b)), a meaningful shape (Figure 7(a)) or a set of axes (Figure 7(b));

In particular, the Shape stimulus embraces the largest number of possibilities to express information: Differentiation, Correspondence, Meaning and/or Relationship.\

Differentiation: the shape displayed discriminates the items for further interpretation, as in Figures 8(a), 9(a) and 10(a);

Correspondence: discrete (Figure 8(a)) or continuous (Figure 8(b)), each noticeable shape corresponds to one informative feature. Proportion (variable sizing) is the most used variation for this practice;

Meaning: the shape displayed carries meaning, such as an arrow, a face or a complex shape (e.g. text), whose comprehension may depend on user’s knowledge and previous experience, as depicted in Figures 7(b) and 8(b);

Relationship: shapes, such as lines, contours or surfaces, denote the relationship between a set of data items, e.g., in Parallel Coordinates, 3D plots and paths in general, illustrated in Figures 5(a) and 7(a).

Color conveys information by Differentiation and/or Correspondence of data items:

Differentiation: colors have no specific data correspondence, they just depict equality (or inequality) of some data characteristic, as it may be observed in the visualizations depicted in Figures 9(a) and 9(b). The coloring of the items, either discrete or continuous, is data dependent or user input dependent;

Correspondence: discrete or continuous, as observed in Figures 7(a) and (b). In the discrete case each noticeable color maps one informative feature, usually a class, a level, a stratum or some predefined correspondence. In the continuous case, the variation of tones maps a set of continuous data values.

Therefore, we must clarify the role of interaction techniques in the visualization scene. We define two conditions for identifying an interaction technique:

1. An interaction technique must enable a user to define/redefine the visualization by modifying the characteristics of pre-attentive stimuli;
2. An interaction technique, with appropriate adaptations, must be applicable to any visualization technique.

The first condition arises from the direct assumption that interaction techniques alter the state of a computational application. In the case of a visualization scene, its basic components (the pre-attentive stimuli) must be altered.

The second condition arises from the need of having interaction techniques that are well defined, which directs us towards generality. An interaction technique, then, must be applicable to any visualization technique, even if not efficiently.

We identify the following interaction paradigms:
• Parametric: the visualization is redefined, visually (e.g., scrollbar) or textually (e.g., type-in), by modifying position, shape or color parameters.
• View transformation: this interaction adds physical touch to the visualization scene, whose shape (size) and position can be changed through scale, rotation, translation and/or zoom, not necessarily all of them, as in the FastmapDB tool [2];
• Filtering: a user is allowed to visually select a subset of items that, through pre-attentive factors such as color (brushing) and shape (selection contour), will be promptly differentiated for user perception.
• Details-on-demand: detailed information about the data that generated a particular visual entity can be retrieved at any moment and presented in the scene.
• Distortion: allows visualizations to be projected so that different perspectives (positions) can be observed and defined simultaneously.

In proposing this taxonomy we focused on generalizing the rationale of how visualization scenes are engendered and how they are presented to our cognitive system.

Such a general characterization results in a taxonomy that does not rely on specific details on how techniques operate. Rather, it considers their fundamental constituent parts: how they perform spatialization and how they employ pre-attentive stimuli to convey meaning.

Existing taxonomies categorize techniques based on diverse and detailed information on how techniques perform a visual mapping. This diversity and detailing (refer to Section 2) include, e.g., axes arrangement (“stacked techniques”), specific representational patterns (“iconic and pixel-oriented techniques”), predisposition of representativeness (“network and tree techniques”), dimensionality (“2D/3D techniques”) and interaction (“static/dynamic techniques”). Although such approaches can suitably describe the set of available techniques, they lack analytical power because the core constituents of the techniques are diffused within the taxonomical structure.

Our approach results in an extensible taxonomy that can accommodate new techniques as, in fact, any technique will rely on common foundational basis.

Lohse, G. L., Biolsi, K., Walker, N., & Rueter, H. H. (1994). A classification of visual representations. Communications of the ACM, 37(12), 36-49.

Lohse, G. L., Biolsi, K., Walker, N., & Rueter, H. H. (1994). A classification of visual representations. Communications of the ACM, 37(12), 36-49.

information visualization

本研究的目的在於對視覺資訊進行分類，組織這個領域內的系統性研究，提供發展理論所需的概念。對於圖像的分類可分為功能性與結構性兩種，功能性分類著重於圖形的用途與目的，結構性分類則是注重圖形的形式。由於視覺表現是表達知識的資料結構，以知覺推論(perceptual inferences)，取代複雜難困難的認知比較與計算，能夠有助於問題解決與發現，因此本研究將探討結構性分類。過去的分類大多是根據研究者本身的直覺，本研究則是首先讓16位受試者對60種視覺表現進行歸類。程序如下：
1. 每一位受試者對所有的視覺表現，根據本身認為視覺表現間的相似性進行歸類。
2. 以上述的歸類結果，計算每一對受試者之間的Jaccard係數，然後利用完全連接叢集分析(Complete linkage cluster analysis)，找出與其他受試者分類結果最不相同的受試者(outliers)。
3. 刪除分類結果的不相同受試者後，以其他所有受試者的分類結果，建立視覺表現的相似性矩陣，並且進行視覺表現的完全連接叢集分析，進行歸類。歸類結果共計為11個基本類別：圖形(graphs)、表格(tables)、圖像表格(graphical tables)、時間圖表(time charts)、網絡(networks)、結構示意圖(structure diagrams)、程序示意圖(process diagrams)、地圖(maps)、統計地圖(cartograms)、圖標(icons)與照片影像(pictures)。
4. 蒐集受試者對所有視覺表現的評分資料。評分標準包括
-- 空間性(spatial)-非空間性(nonspatial),
-- 非時間性(nontemporal)-時間性(temporal),
-- 難以理解(hard to understand)-容易理解(easy to understand),
-- 具體(concrete)-抽象(abstract),
-- 連續(continuous)-離散(discrete),
-- 吸引人(attractive)-不吸引人(unattractive),
-- 強調整體(emphasizes whole)-強調部分(emphasizes parts),
-- 非數值(nonnumeric)-數值(numeric),
-- 靜態結構(static structure)-動態結構(dynamic process),
-- 包含許多資訊(conveys a lot of information)-包含很少資訊(conveys little information)。
5. 進行主成分分析(principal component analysis, CPA)，嘗試減少評分標準的項目。結果發現這10個評分標準相對獨立並且具有相接近的重要性，因此全數保留。
6. 利用分類與回歸樹(classification and regression trees, CART)建立一個二元分類樹(binary classification tree)藉以決定10個評分標準的評分資料能否預測叢集分析所得到的歸類結果。
7. 最後，以判別分析(discriminant analysis)再次檢驗評分結果和歸類結果的關係。

圖形以幾何物件的位置與大小來表現數量資訊。表格是文字，數字，符號或它們的組合的排列(arrangement)，以緊湊格式呈現出一組事實或關係，可進一步分為數量形表格(numerical table)與圖形表格。比較圖形和表格的呈現方式，圖形強調整體的呈現，而表格著重在部分。時間圖表用以呈現時間性資料。網絡顯示組成份子之間的關係，符號表示組成份子的存在或不存在，以線條、箭頭、接近、相似或包含等方式表示組成份子之間的關係。結構示意圖是物理對象的靜態描述，表達對象的真實座標面向；程序示意圖描述物理對象間動態、連續和時間性的相互關係和程序。比較結構示意圖和地圖與統計地圖，人們可以透過結構示意圖了解性質關係，但從地圖與統計地圖可以得到數量和性質關係。地圖是實際地理的象徵表現，使用符號或文字描繪特定特徵的地理位置，統計地圖則是將數量資料加入地圖上。相較於地圖，使用者較難理解統計地圖。圖標賦予單一的解釋或意義，照片是物件或場景的真實影像。

McCormick, DeFami, and Brown [16] define visualization as “the study of mechanisms in computers and in humans which allow them in concert to perceive, use, and communicate visual information.”

Our research focuses on classifying visual information. Classification lies at the heart of every scientific field. Classifications structure domains of systematic inquiry and provide concepts for developing theories to identify anomalies and to predict future research needs.

Extant taxonomies of graphs and images can be characterized as either functional or structural. 

Functional taxonomies focus on the intended use and purpose of the graphic material. For example, consider the functional classification developed by Macdonald-Ross [14]. ... Other examples of functional classifications can be found in Tufte [22].

A functional classification does not reflect the physical structure of images, nor is it intended to correspond to an underlying representation in memory [1].

In contrast, structural categories are well learned and are derived from exemplar learning. They focus on the form of the image rather than its content. Rankin [18] and Bertin [2] developed such structural categories of graphs.

Rankin used the number of dimensions and graph forms to determine his classification of graph types. Major categories in this scheme include rectilinear cartesian coordinate graphs, polar coordinate graphs, bar graphs, line graphs, matrix diagrams, trilinear charts, response surfaces, topographic charts, and conversion scales.

We adopt the view that visual representations are data structures for expressing knowledge [11, 19].

As such, visual representations can facilitate problem-solving and discovery by providing an efficient structure for expressing the data. Cognitive efficiency results when perceptual inferences replace arduous cognitive comparisons and computations. Since the primary advantage of visual information is that the representation conveys the data structure directly, we chose to develop a structural classification.

Few previous taxonomies and classification schemes for visual representations are based on experimental data; most rely instead simply on the author’s intuitions

Our research focuses on how people classify visual representations into meaningful, hierarchically structured categories.

Our classification (Lohse et al. [12]) was based on subjects’ ratings of the visual similarity between visual representations, and we identified six basic categories of visual representations: graphs, tables, maps, diagrams, networks, and icons.

In addition, we tentatively identified two dimensions that distinguish these clusters. One dimension suggested that a graphic could express either continuous or discrete information, while the second dimension suggested that some visual representations are more efficient than others for conveying information.

The 60 graphical items shown in Figure 1 were used in this study. ... Sixteen subjects were recruited from the students and staff of the University of Michigan.

First, subjects examined all 60 items and named each one to insure that they were familiar with the entire range of items before beginning the rating task. ... Next, subjects rated each of the 60 items on 10 nine-point Likert scales. The 10 rating scales were derived from a frequency analysis of keywords used by subjects to describe each cluster of items during the sorting task of our two previous studies [12, 13].
-- spatial-nonspatial,
-- nontemporal-temporal,
-- hard to understand-easy to understand,
-- concrete-abstract,
-- continuous-discrete,
-- attractive-unattractive,
-- emphasizes whole-emphasizes parts,
-- nonnumeric-numeric,
-- static structure-dynamic process,
-- conveys a lot of information-conveys little information

The final procedure was a bottom-up sorting task, the 60 items were placed randomly on a large table, and the subjects were asked to sort them into groups of similar items. Subjects were given no explicit criteria for judging similarity and could create any number of groups and any number of items per group. Once the subjects had completed their initial groupings, they described each group and explained why all the items in the group were similar. After the experimenter recorded these descriptions, the subjects grouped their initial groupings into higher-order clusters of similar groups. Again, the experimenter recorded the subjects’ explanations of why all the items within a cluster were similar. This process was repeated until all 60 items were placed in a single group.

We first clustered the subjects to determine whether any were obvious outliers among the subjects who sorted the graphics. As a measure of similarity between pairs of subject sorts, we used the Jaccard coefficient [9], which is computed as follows: Jaccard(i, j) = A/(N-B), where A is the number of pairs of graphics in which the members of the pair appear in the same groups for the sortings of both subjects i and j; B is the number of pairs of graphics for which the members of the pair appear in different groups in both subjects' sorts; and N is the total number of graphic pairs or n(n-1)/2 ,where n is the number of graphics.

Complete linkage cluster analysis [10] was then applied to the matrix of Jaccard coefficients. The resulting tree diagram suggested that subject 11 sorted the graphic items in a manner different from the other subjects, and therefore, the data for this subject was removed from all subsequent analyses.

In order to identify groups or clusters of items in the subjects' sortings, a matrix of similarities was constructed by counting the number of times each pair of graphics was grouped together in the subjects’ lowest level sorts. ... The similarity matrix was then used as the basis for complete linkage hierarchical clustering. The resulting tree had nine primary classes or clusters of graphics, two of which had subclasses. These 11 classes are described.

We next sought to determine if the rating scales (that were based on our previous work [12, 13]) were predictive of class membership or clusters derived from the sorting data. To do this, we followed a three-step procedure. First, we used principle components analysis to determine if the 10 scales could be reduced to a smaller set of underlying dimensions. Then we used two different methods for classification: classification trees [3] and discriminant analysis [7]. These techniques were used on the average ratings of the 10 scales for each of the 57 graphical items (i.e., with the three singleton items removed).

A principle components analysis of the data revealed that only one scale, amount of information conveyed, explained less than 9% of the total variance (see Table l). No single scale explained more than 16% of the total variance. The analysis suggests the 10 scales are relatively independent (i.e., nonredundant) and of approximately equal importance (in terms of variance explanation), so we therefore make use of all 10 in the analyses.

The Classification and Regression Trees (CART) methodology [3] was next used to construct a binary classification tree (Figure 3) in order to determine if the ratings on the 10 scales were predictive of membership in the clusters yielded by the hierarchical clustering analysis.

As an additional check on the relationship between the rating scales and the classes derived from the sorting task, we used discriminant analysis. As with the CART methodology, the purpose of the discriminant analysis was to determine the relationship between the rating scales and the sort-derived classes.

Overall, our analyses all provide confirmatory evidence of the taxonomic structure of the graphic items presented in Figure 3. In addition, the results of both the CART analysis and the discriminant analysis suggest that the 10 rating scales can be used as predictors of class membership in the classification.

Eleven categories of visual representations emerged from the classification: graphs, tables, graphical tables, time charts, networks, structure diagrams, process diagrams, maps, cartograms, icons, and pictures. Here we describe these major groups and the type of knowledge conveyed by each class of representation.

Graphs encode quantitative information using position and magnitude of geometric objects. One-, two-, or three-dimensional numerical data is plotted on a Cartesian Coordinate or polar coordinate system. Common graph types include scatterplot, categorical, line, stacked bar, bar, pie, box, fan, response surface, histogram, star, polar coordinate, and Chernoff face graphs.

Graphs emphasize the whole display as compared with tabular data that emphasize parts of the display. ... Tables have less abstract symbolic notation than graphs. 

Tables are an arrangement of words, numbers, signs, or combinations of them to exhibit a set of facts or relationships in a compact format.

Two groups of tables appeared in the classification: graphical and numerical. The primary distinction depended on how numeric information is coded in the table. Graphical tables, like the auto repair records (number 7), used shading to encode frequency of repair data, whereas the statistical table of the critical values of the t statistic (number 21) shows only numeric data. Numerical tables emphasize parts of the whole representation (e.g., individual data values).

Time charts display temporal data. They differ from tables in their emphasis on temporal data.

Network charts show the relationships among components. Symbols indicate the presence or absence of components. Correspondences among the components are shown by lines, arrows, proximity, similarity, or containment. 

There are two types of diagrams, both of which express spatial data.

Structure diagrams are a static description of a physical object. The spatial data expresses the true coordinate dimensions of the object.

Process diagrams describe the interrelationships and processes associated with physical objects. The spatial data expresses dynamic, continuous, or temporal relationships among the objects in process diagrams.

The main difference among similarity measures for maps, cartograms, and structure diagrams is that maps and cartograms express more numeric information than structure diagrams. Thus, people might reason about qualitative relationships from structure diagrams, but reason about qualitative and quantitative relationships from maps and cartograms.

Maps are symbolic representations of physical geography. Maps depict geographic locations of particular features using symbols or lettering.

Maps differ from cartograms in that cartograms super-impose quantitative data over a base map. Therefore, it is not surprising that subjects felt cartograms were more difficult to understand than true maps.

Cartograms are spatial maps that show quantitative data.

Icons impart a single interpretation or meaning for a picture.

Photo-realistic pictures are realistic images of an object or scene. ... Interval properties and distance properties of real world space between objects are preserved in images.

However, subjects in our study characterized photo-realistic images as conveying the least amount of information of all categories in our classification. ... Thus, pictures may contain a great amount of information, but attention must be directed to the visual details of the picture to enable decoding of this information from the picture.

Although photo-realistìc images conveyed less information than all categories in our classification, questions regarding how expert/novice differences influence interpretation also need to be addressed. ... These findings suggest that rather than limit a visualization to an exact copy of a real world object, we can enhance photo-realistic images by enhancing the characteristics of some pixels in the image (smart pixels) to direct and focus our attention to specific information that is relevant to the current task.

Subjects judged cartograms as being hard to understand relative to either maps or graphs. ... As companies develop geographic information systems for superimposing quantitative and spatial information it is important that designers recognize limitations of cartograms for expressing certain types of information and examine alternative visualization tools for expressing such data.

However, it seems more likely that the three-dimensional representations convey more information only to people with an appropriate graph schema for processing information from a novel display format. ... The absence of an accurate diagram schema for displays with unanticipated formats delayed information processing and caused more information processing errors.

Thus, expert-novice differences may not only be a function of graphic arts training but also be a function of having appropriate graph schemata for a particular functional area of expertise.

Wiley [23] found that subjects with graphic arts training remember ordinary pictures better than subjects without graphic arts training, but that memory for unique pictures was consistently high for all subjects regardless of their level of graphic arts training. We might expect to differences between the memory organizations of graph schemata for experts and novices, as novices often lack the necessary schemata to understand the symbolic notation of the graph. However, DcSanctis and jarvenpaa [6] have shown that practice and training can improve the ability to decode information from graphs.

Our classification suggests that network charts present nonspatial information that is difficult to understand. It is important to determine how to present spatial information to facilitate understanding.

Temporal data are more difficult to show in static graphics than cyclic data. Given this limitation of static graphics, it may be important for visualization tools to use dynamic displays or animation for analyzing temporal data. 

Our objectives for developing a classification of visual representations were fivefold:

-- structure systematic inquiry;
-- convey concepts for developing theories;
-- identify anomalies; 

-- predict future research needs;
-- communicate knowledge.

Our classification is subject to four caveats. First, the sample of visual representations influences how well we can generalize our findings. Had we developed our classification from a larger set of items (600 instead of 60), it is not known whether the 10 Likert scales would still characterize all of the items in the classification. Furthermore, we have not identified deep, hierarchical structure within a cluster. For example, what are the major subdivisions within graphs?

Second, the sample of people whose judgments are used to develop the classification must be representative of the entire range of potential users. We have conducted three different experiments using 40 different subjects with a wide range of education, cultural, and graphic arts backgrounds. However, this is still only a small sample from the large population of graph users.

Third, different classification techniques for collecting and analyzing data can and do produce different taxonomies. However, we have used three different techniques over three studies, and each technique has revealed a similar pattern of results.

Finally, our efforts have focused primarily on perceived similarity. We have not investigated whether or not these categories apply to the interpretation of graphics or to the recall of graphical information. For a classification to be useful in both graphical design and research formulation, the classification must represent structure that is used by people in interpreting graphs. This evaluation of our reported classification is our current research goal.

Shneiderman, B. (1996, September). The eyes have it: A task by data type taxonomy for information visualizations. In Visual Languages, 1996. Proceedings., IEEE Symposium on (pp. 336-343). IEEE.

Shneiderman, B. (1996, September). The eyes have it: A task by data type taxonomy for information visualizations. In Visual Languages, 1996. Proceedings., IEEE Symposium on (pp. 336-343). IEEE.

information visualization

科學視覺化是使得一般的三維現象可以觀看與理解，資訊視覺化則是讓統計資料、股市交易、電腦目錄與文件集合等展現樣式、叢集、缺口與分離的部分。能夠提供方向(orientation)與脈絡(context)，選取區域，提供動態回應來發現變化等功能的視覺化呈現，將更具吸引力。根據視覺資訊搜尋真言(Visual Information-Seeking Mantra)「先全面概觀(overview first)，放大並過濾(zoom and filter)，然後選擇細節觀看(then details on demand)」，本研究提出一個資料類型與任務並重的分類架構。

此一分類架構上包含七種資料類型以及七種任務。七種資料類型描述了任務領域的資料物件以及解決問題實的組織情形，包括一維資料、二維資料、三維資料、時間資料、多維資料、樹狀資料與網路資料。
1. 一維資料：一維資料為文件、程式原始碼及按字母排列的名錄等以某種序列方式(sequential manner)組織的線性資料(linear data)。可以提供給使用者的方法包括發現項目的數量、尋找具有某種特徵的項目與觀察某一項目的所有特徵。介面設計的重點則包括整體概觀的呈現、捲動以及選取的方法。
2. 二維資料：二維資料包含地圖、樓層配置或新聞版面等平面資料，二維資料集合內的每一個項目涵蓋整體區域的一部分。可以提供使用者的方法包括發現接鄰的項目、項目相互間的包含情形、項目間的路徑以及計數、過濾和選擇細節觀看等基本任務。
3. 三維資料： 三維資料為分子、人體、建築物等具有體積的真實物件(real-world objects)。可以提供使用者的方法包括發現接鄰、上下、內外等關係以及其他基本任務，並且需要讓使用者在觀看物件時能夠了解它們的位置與方向。
4. 時間資料：在呈現醫療紀錄、專案管理和歷史性資料時會經常使用時間表，與一維資料不同在於時間資料的項目有起始與終止的時間，並且可以彼此重疊。常見的使用方式包括發現一個時間點或一段時期之前開始、之後結束或經過的所有項目。
5. 多維資料：由於資料項目具有n個特徵，大部分的關連式或統計資料庫都被視為多維資料，以n維空間上的點來表現資料項目，以便進行處理。處理的方法有發現樣式(patterns)、叢集(clusters)、變數間的相關(correlations)、差距(gaps)以及分離的部分(outliers)。
6. 樹狀資料：階層式或樹狀結構的特徵為除了根以外，項目集合內的每一個項目都有一個連結連到一個親代項目(parent item)。提供的使用方式，除了針對項目和連結的基本任務以外，還有階層數量、每一項目的子項目數量，結構相似的項目等和結構特性有關的任務。

7. 網路資料： 資料項目連結到不特定的項目時可採用網路資料。除了針對項目和連結的基本任務以外，提供給使用者的方式還有兩個資料項目間的最短路徑或成本最小的路徑或是整個網路上遊歷。

七種任務則包括：概觀集合全體情形(Overview)、放大感興趣的項目(Zoom)、過濾不感興趣的項目(Filter)、選取並取得詳細的資訊(Details-on-demand)、觀看項目間的關連(Relate)、保持過去的動作(History)和抽取部分集合(Extract)。

A useful starting point for designing advanced graphical user interfaces is the Visual Information-Seeking Mantra: overview first, zoom and filter, then details on demand.

This paper offers a task by data type taxonomy with seven data types (one-, two-, three-dimensional data, temporal and multi-dimensional data, and tree and network data) and seven tasks (overview, Zoom, filter, details-on-demand, relate, history, and extracts).

Visual displays become even more attractive to provide orientation or context, to enable selection of regions, and to provide dynamic feedback for identifying changes (for example, a weather map). 

Scientific visualization has the power to make ,atomic, cosmic, and common three-dimensional phenomena (such as heat conduction in engines, airflow aver wings, or ozone holes) visible and

comprehensible.

Abstract information visualization has the power to reveal patterns, clusters, gaps, or outliers in

statistical data, stock-market trades, computer directories, or document collections.

To sort out the prototypes and guide researchers to new opportunities, I propose a type by task taxonomy (TTT) of information viisualizations.

I assume that users are viewing collections of items, where items have multiple attributes. In all seven data types (1-, 2-, 3-dimensional data, temporal and multi-dimensional data, and tree and network data) the items have attributes and a basic search task is to select all items that satisfy values of a set of attributes.

The data types are on the left side of the TTT characterize the task-domain information objects and are organized by the problems users are trying to solve.

The tasks across the top of the TTT are task-domain information actions that users wish to perform.

The seven tasks are:
Overview: Gain an overview of the entire collection.
Zoom : Zoom in on items of interest
Filter: filter out uninteresting items.
Details-on-demand: Select an item or group and get details when needed.
Relate: View relationships among items.
History: Keep a history of actions to support undo, replay, and progressive refinement.
Extract: Allow extraction of sub-collections and of the query parameters.

1-dimensional: linear data types include textual documents, program source code, and alphabetical lists of names which are all organized in a sequential manner. Each item in the collection is a line of text containing a string of characters. Additional line attributes might be the date of last update or author name. Interface design issues include what fonts, color, size to use and what overview, scrolling, or selection methods can be used. User problems might be to find the number of items, see items having certain attributes (show only lines of a document that are section titles, lines of a program that were changed from the previous version, or people in a list who are older than 21 years), or see an item with all its attributes.

2-dimensional: planar or map data include geographic maps, floorplans, or newspaper layouts. Each
item in the collection covers some part of the total area and may be rectangular or not. Each item has task-domain attributes such as name, owner, value, etc. and interface-domain features such as size, color, opacity, etc. While many systems adopt a multiple layer approach to dealing with map data, each layer is 2-dimensional. User problems are to find adjacent items, containment of one item by another, paths between items, and the basic tasks of counting, filtering, and details-on-demand.

3-dimensional: real-world objects such as molecules, the human body, and buildings have items with volume and some potentially complex relationship with other items. Computer-assisted design systems for architects, solid modelers, and mechanical engineers are built to handle complex 3-dimensional relationships. Users' tasks deal with adjacency plus above/below and inside/outside relationships, as well as the basic tasks. In 3-dimensional applications users must cope with understanding their position and orientation when viewing the objects, plus the serious problems of occlusion. Solutions to some of these problems are proposed in many prototypes with techniques such as overviews, landmarks, perspective, stereo display, transparency, and color coding.

Temporal: time lines are widely used and vital enough for medical records, project management, or historical presentations to create a data type that is separate from 1-dimensional data. The distinction in temporal data is that items have a start and finish time and that items may overlap. Frequent tasks include finding all events before, after, or during some time period or moment, plus the basic tasks.

Multi-dimensional: most relational and statistical databases are conveniently manipulated as multidimensional data in which items with n attributes become points in a n-dimensional space. The interface representation can be 2-dimensional scattergrams with each additional dimension controlled by a slider (Ahlberg and Shneiderman, 1994). Buttons can used for attribute values when the cardinality is small, say less than ten. Tasks include finding patterns, clusters, correlations among pairs of variables, gaps, and outliers. Multi-dimensional data can be represented by a 3-dimensional scattergram but disorientation (especially if the users point of view is inside the cluster of points) and occlusion (especially if close points are represented as being larger) can be problems. The technique of parallel coordinates is a clever innovation which makes some tasks easier, but takes practice for users to comprehend (Inselberg, 1985).

Tree: hierarchies or tree structures are collections of items with each item having a link to one parent item (except the root). Items and the links between parent and child can have multiple attributes. The basic tasks can be applied to items and links, and tasks related to structural properties become interesting, for example, how many levels in the tree? or how many children does an item have? While it is possible to have similar items at leaves and internal nodes, it is also common to find different items at each level in a tree.

Network: sometimes relationships among items cannot be conveniently captured with a tree structure and it is useful to have items linked to an arbitrary number of other items. While many special cases of networks exist (acyclic, lattices, rooted vs. un-rooted, directed vs. undirected) it seems convenient to consider them all as one data type. In addition to the basic tasks applied to items and links, network users often want to know about shortest or least costly paths connecting two items or traversing the entire network.

Overview: Gain an overview of the entire collection. Overview strategies include zoomed out views of each data type to see the entire collection plus an adjoining detail view. ... Another popular approach is the fisheye strategy (Furnas, 1986) which has been applied most commonly for network browsing (Sarlcar and Brown, 1994; Bartram et al., 1995). The fisheye distortion magnifies one or more areas of the display, but zoom factors in prototypes are limited to about 5. ... Adequate overview strategies are a useful criteria to look for. Along with an overview plus detail (also called context plus focus) view there is a need for navigation tools to pan or scroll through the
collection.

Zoom: Zoom in on items of interest. Users typically have an interest in some portion of a collection, and they need tools to enable them to control the zoom focus and the zoom factor. ... Zooming could be on one dimension at a time by moving the zoom-bar controls or by adjusting the size of the field-of -view box.

Filter: filter out uninteresting items. Dynamic queries applied to the items in the collection is one of the key ideas in information visualization (Ahlberg et al., 1992; Williamson and Shneiderman, 1992). By allowing users to control the contents of the display, users can quickly focus on their interests by eliminating unwanted items.

Details-on-demand: Select an item or group and get details when needed. Once a collection has been trimmed to a few dozen items it should be easy to browse the details about the group or individual items.

Relate: View relationships among items.

History : Keep a history of actions to support undo, replay, and progressive refinement. It is rare that a single user action produces the desired outcome. Information exploration is inherently a process with many steps, so keeping the history of actions and allowing users to retrace their steps is important.

Extract: Allow extraction of sub-collections and of the query parameters. Once users have obtained the item or set of items they desire, it would be useful to be able to extract that set and save it to a file in a format that would facilitate other uses such as sending by email, printing,
graphing, or insertion into a statistical or presentation package. An alternative to saving the set, they might want to save, send, or print the settings for the control widgets.

These ideas are attractive because they present information rapidly and allow for rapid user-controlled exploration. If they are to be fully effective, some of these approaches require novel data structures, high-resolution color displays, fast data retrieval, specialized data structures, parallel computation, and some user training.

Card, S. K., & Mackinlay, J. (1997, October). The structure of the information visualization design space. In Information Visualization, 1997. Proceedings., IEEE Symposium on (pp. 92-99). IEEE.

Card, S. K., & Mackinlay, J. (1997, October). The structure of the information visualization design space. In Information Visualization, 1997. Proceedings., IEEE Symposium on (pp. 92-99). IEEE.

information visualization

根據Bertin[5]，圖學(graphics)包括至少兩種的用法，一是當某人已經了解某些資訊時，做為傳播這些資訊方法；另一則是當某人為了解這些資訊時，對圖形物件的操作與覺察。這兩種的用法不應混淆。
先前有關資訊視覺化設計空間的研究，包括Keller[1]列舉出科學視覺化(scientific visualization)的技術，Chuah and Roth[2]對資訊視覺化的任務提出分類架構，Shneiderman[3] 提出一個的資料型態-任務的矩陣做為分類架構。本研究整合上述的研究，並參考 Bertin[5, 6] 和 Mackinlay’s [7]對圖形的符號學(semiotics)，提出資訊視覺化設計空間的架構，如下圖所示。

在上面的架構裡，資料部分包含原始的資料D，經由某一個轉換函數F過濾或重新編碼得到的新資料D'。視覺化包含標記(mark, M)、控制處理(controlled processing, CP)、視網膜特性(retinal property, R)和空間上的位置(XYZ)和時間(T)等部分。互動技術部分則有觀看技術(view techniques, V)和介面小工具技術(widget techniques, W)。資料的類型可以是名義型(Nominal)、順序型(Ordered)以及數量型(Quantitative)，其中的數量型資料也包括空間資料以及地理上的座標。視覺化基本上由一組的標記以及它們的視網膜特性和空間與時間的位置組成，標記可以為點(points)、線(lines)、面(areas)、表面(surfaces)或體(volumes)，視網膜特性則包括了顏色(color)、大小(size)、連結(connection)和閉合(enclosure)。

Our analysis builds on recent attempts to understand parts of the design space.

Keller[1] lists techniques used in scientific visualization.

Chuah and Roth[2] taxonomizes the tasks of information visualization.

Shneiderman[3] proposes a “data type by task” matrix.

Our analysis is closest in spirit to Tweedie’s [4], who also starts from Bertin.

Our analysis starts from an expanded version of Bertin’s [5, 6] and Mackinlay’s [7] analysis of the semiotics of graphics.

Graphics, according to Bertin[5], have at least two distinct uses, which should not be confused: first, as the means of communicating some information (in which case a person already understands the information) and second, for graphical processing (in which case a person uses the manipulation and perception of graphical objects to understand the information).

The major distinction we make for data is whether their values are

Nominal (are only = or ≠ to other values),

Ordered (obeys a < relation), or are

Quantitative (can do arithmetic on them).

We denote these as N, O, and Q respectively.

In a more detailed analysis, we would also note the cardinality of a variable, since one of the points of information visualization is to allow visual processing in regions of high cardinality.

We distinguish subtypes of Q for intrinsically spatial variables Qxy and spatial variables that are actually geophysical coordinates Qlon.

We also distinguish between data D that is in the original dataset from data D’ that has been selected from this set and possibly transformed by some filter or recoding function F.

Human visual processing involves two levels: automatic and controlled processing[8].

Automatic processing works on visual properties such as position and color. It is highly parallel, but limited in power.

Controlled processing works on abstract encodings such as text. It has powerful operations, but is limited in capacity.

An elementary visual presentation consists of a set of marks (such as Points, Lines, Areas, Surfaces, or Volumes), their retinal properties (such as Color and Size), and their position in space and time (such as the XY plane in classical graphics and XYZT or 3D space plus time in information visualization). We also include, following [7], the properties of Connection (denoted “—”) and Enclosure (denoted “[]”).

Thus, visualizations are composed from the following visual vocabulary:

Marks: (Point, Line, Area, Surface, Volume)

Controlled Processing Graphical Features

Automatically Processed Graphical Properties

Retinal encodings: (Color, Size, Shape, Gray-level, Orientation, Texture, Connection, Enclosure)

Position: (X, Y, Z, T)

We focus here on two interactive techniques: View techniques (such as focus+context), which distort the space-time of the visualization, and Widget techniques, which add user interface objects (such as buttons) to the visualization.

Symbol	Meaning
D	Data Type ::= N (Nominal), O (Ordinal), Q (Quantitative). QX (Intrinsically spatial), Qlon (Geographical) NxN (Set mapped to itself - graphs)
F	Function for recoding data ::= f (unspecified) > (filter) s (sorting) mds (multidimensional scaling) ↑ (interactive input to a function)
D’	Recoded Data Type (see D)
CP	Control Processing tx (text)
M	Mark types ::= P (Point) L (Line) S (Surface) A (Area) V (Volume)
R	Retinal properties ::= C (Color) S (Size) — (Connection) [] (Enclosure)
XYZT	Position in space time ::= N, O, Q, * (non-semantic use of space-time)
V	View transformation ::=hb(hyperbolic mapping)
W	Widget ::= sl(slider) rb(radio buttons)

Scientific visualization generally starts from data whose variables are intrinsically spatial.

Variable

D

F

D'

CP

M

R

X

Y

Z

T

V

W

Samples

N

P

Ozone

Q

f

O

C

Lon.

Qlon

Q

Lat.

Qlat

Q

Height

Q

Q

Date

Q

Q

The rows of the table describe the variables with the case variable (“Samples”) at the top and the value variables below.

The nominal (N) set of Samples is mapped to point marks (P in column M), which have their retinal property of color (C in column R) mapped to the Ozone variable.

The ozone mapping includes a function (f) that converts the quantitative (Q) ozone measurements to an ordinal (O) set that can be easily mapped to a set of colors.

The quantitative (Q) variables of Longitude, Latitude, and Height are mapped to the positions X, Y, and Z, which determine the position of the point marks. The Date variable is mapped to time (T), which creates an animated visualization.

Table 1 makes it clear that Figure 1 is a 3D animated visualization involving colored points.

Variable

D

F

D'

CP

M

R

X

Y

Z

T

V

W

Office

L

Lon.

Qlon

Q

Lat.

Qlat

Q

Profit

Q

Sz

Q

f

N

C

The Offices variable is mapped to line marks (L).

The Profit variable is mapped to the size of these lines (Sz in the R column). Profits are also mapped to the Z-axis and via a function (f) to a nominal set indicating the sign of the profits. This nominal set is mapped to the color of the lines (C in the R column). Table 2 clearly reveals that multiple graphical techniques are used to describe the Profit variable in order to enhance the perception of this important data variable.

Multi-dimensional plots take variables that are not intrinsically spatial and map them onto X and Y, e.g.,
Q --> X,
Q --> Y.
When point marks are positioned on these axes, the result is the conventional scatterplot that is often used in statistical graphics.

Landscapes lay information out on a surface, typically the XY plane. Landscapes may be of several sorts: real geographical coordinates, real spatial variables, or completely abstract mappings
{Qlon or QX, or Q} --> X
{Qlat or QY or Q} --> Y.
If the mapping extends to
Q--> Z, we call it an information space.

Node and link diagrams allow the encoding of linkage information between entities. They can be thought of as a mapping from a Nominal set to itself {NxN}. These are then mapped into XY.

Trees can also be visualized as nested enclosures. Shneiderman and colleagues [16] have done a space-filling form of enclosure tree called Tree-Maps. At one level in a tree, the children of a node divide up the X dimension of the visualization, at the next level they divide up the Y dimension of the node in which they are enclosed. The division proceeds alternating between X and Y until the leaves of the tree are reached. This method uses all of the space.

In this paper we have sketched part of a scheme for mapping the morphology of the design space of visualizations.

Two levels of analysis not addressed in this short paper are the larger organizational structure of information spaces and the organization of user tasks.

With respect to the larger organizational structure, we have previously suggested in the text area an analysis into information space, workspace, sensemaking tools, and documents and surveyed systems in each of these areas [20].

For user’s tasks, we have previously suggested notions of “knowledge crystallization”, comprising in part “information foraging” [21] and “sensemaking”[22].

Besides helping to organize the literature, our present analysis suggests regions of new visualizations because it concentrates on the mappings between data and presentation.

The table notation, in particular, organizes these mappings in a way that reveals when a data set is mapped to a graphical property in isolation, with overloading, or via distortion.

The key issue for effective visualization is that users must be able to invert this mapping and perceive the data in the visualization.

Chi, E. H. (2000). A taxonomy of visualization techniques using the data state reference model. In Information Visualization, 2000. InfoVis 2000. IEEE Symposium on (pp. 69-75). IEEE.

Chi, E. H. (2000). A taxonomy of visualization techniques using the data state reference model. In Information Visualization, 2000. InfoVis 2000. IEEE Symposium on (pp. 69-75). IEEE.

information visualization

先前進行資訊視覺化分類技術分類架構的研究[Shneiderman96, Chi97, North98, CMS99]時，研究者大多從相容於技術的資料領域(data domains)著手，以資料為中心的觀點進行分析。例如：[CMS99]擴充Card and Mackinlay 的資料導向分類架構[Card97]，將視覺化領域區分為科學視覺化(Scientific Visualization)、地理資訊系統(GIS)、多維圖(Multi-dimensional Plots)、多為表格(Multi-dimensional Tables)、資訊地景與空間(Information Landscapes and Spaces)、節點與連結(Node and Link)、樹狀圖(Trees)和文本轉換(Text Transforms)等子類別。由於在應用上實作的人員可以快速地確認分析所需的各種技術，這樣的方式大多被認為是有用的。然而這些方法並無法讓實作人員了解如何應用與實做這些技術。

本研究使用資料狀態模型(data state model)，提出資訊視覺化分類技術分類架構的新方法，此一新方法從資訊視覺化技術的資料類型(data type)與處理的運作步驟(processing operating steps)，對資訊視覺化的設計空間(design space)進行目前最詳細與最全面的分析，不僅讓研究人員可以了解設計的空間，也可以幫助實作人員了解如何資訊視覺化技術應用得更廣泛。此一分類架構包含四個資料層次、三種在不同層次間的資料結構進行轉換的資料轉換(data transforms)以及四種不改變資料結構在層次內的運作(with stage operations)。四個資料層次與三種資料轉換的說明分別如表 1和表2。

表 1 資料層次

層次 (Stage)	描述
數值 (Value)	原始資料 (The raw data)
分析性抽象化 (Analytical Abstraction)	關於資料的資料或者資訊，也就是後設資料(meta-data.)
視覺抽象化 (Visualization Abstraction)	可以使用視覺化技術使其可視於螢幕的資訊
視圖 (View)	最後呈現給使用者觀看與理解的視覺化映射結果(visualization mapping)

表 2 資料轉換

處理步驟 (Processing Step)	描述
資料轉換 (Data Transformation)	從數值中產生分析性抽象化的形式(通常透過抽取)。
視覺化轉換 (Visualization Transformation)	取得分析性抽象化並將其。Takes an analytical abstraction and further reduces it into some form of visualization abstraction, which is visualizable content.
視覺映射轉換 (Visual Mapping Transformation)	Takes information that is in a visualizable format and presents a graphical view.

這種分類架構將資料模組間的相依性(dependencies)獨立出來，清楚地指出資料和運算間的互動，有助於了解各種視覺化技術的相似性與差異，並且建構新的視覺化與互動方式，具有可以再利用(reuse)既有運算的優點。

In previous work, researchers have attempted to construct taxonomies of information visualization techniques by examining the data domains that are compatible with these techniques.

This is useful because implementers can quickly identify various techniques that can be applied to their domain of interest.

However, these taxonomies do not help the implementers understand how to apply and implement these techniques.

In this paper, we will extend and then propose a new way to taxonomize information visualization techniques by using the Data State Model [Chi98].

The paper shows that the Data State Model not only helps researchers understand the space of design, but also helps implementers understand how information visualization techniques can be applied more broadly.

There have been several efforts to produce various information visualization taxonomies [Shneiderman96, Chi97, North98, CMS99].

In this paper, we will present a detailed analysis of a large number of visualization techniques using the Data State Model. The contribution is that our analysis of the information visualization design space is the most detailed and thorough to date. It is more detailed in the sense that we have broken each technique down by not only its data type, but also by its processing operating steps.

Most previous work focused on constructing taxonomies of information visualization techniques

uses a data-centric point of view.

In an article describing the design space of information visualization techniques, Card and Mackinlay started constructing a data-oriented taxonomy [Card97], which is subsequently expanded in [CMS99]. This taxonomy divides the field of visualization into several subcategories: Scientific Visualization, GIS, Multi-dimensional Plots, Multi-dimensional Tables, Information Landscapes and Spaces, Node and Link, Trees, and Text Transforms.

OLIVE is a taxonomy assembled by students in Shneiderman’s information visualization class [Olive99], and divides information visualization techniques using eight visual data types: temporal, 1D, 2D, 3D, multi-D, Tree, Network, and Workspace.

Figure 1 shows an overview of the Data State Model [Chi98], which breaks down each technique into four Data Stages, three types of Data Transformation and four types of Within Stage operators.

The visualization data pipeline is broken into four distinct Data Stages: Value, Analytical Abstraction, Visualization Abstraction, and View (See Table 1).

Stage	Description
Value	The raw data.
Analytical Abstraction	Data about data, or information, a.k.a. meta-data.
Visualization Abstraction	Information that is visualizable on the screen using a visualization technique.
View	The end-product of the visualization mapping, where the user sees and interprets the picture presented to her.

Transforming data from one stage to another requires one of the three types of Data Transformation operators: Data Transformation, Visualization Transformation, and Visual Mapping Transformation (Table 2).

Processing Step	Description
Data Transformation	Generates some form of analytical abstraction from the value (usually by extraction).
Visualization Transformation	Takes an analytical abstraction and further reduces it into some form of visualization abstraction, which is visualizable content.
Visual Mapping Transformation	Takes information that is in a visualizable format and presents a graphical view.

Within each Data Stage, there are also operators that do not change the underlying data structures. These are the Within Stage Operators, of which there are four types, corresponding to the four Data Stages: Within Value, Within Analytical Abstraction, Within Visualization Abstraction, and Within View.

(1) some operators create new kinds of data sets, whereas some operators create filtered subsets, which is the difference between Transformation and Within Stage operators, 

(2) that the same Visualization Abstractions can be mapped using a variety of Visual Mapping Transformation operators.

By isolating dependencies, we can more easily reuse different parts of the pipeline to construct new information visualizations.

With a clearer understanding of the interactions between the data and the operators, implementers will be more equipped to construct new interactions or new visualizations.

For each of the visualization techniques, the results of the analysis help us classify and choose how to implement the different operators in a large visualization system. For example, many hierarchical techniques share similar operating steps that can be standardized in a system. Implementers may take advantage of these similarities.

For implementers, the taxonomy also directly specifies the sequential ordering of operators that are possible in a given visualization technique. In this way, it specifies the system module dependencies that are induced between the operators. Knowing these dependencies enables implementers to better organize their system for modularity.

This is because the Data State Model helps categorization and taxonomization, which expose the dependencies between visualization modules and the similarities and differences among visualization techniques.

Keim, D. A. (2001). Visual exploration of large data sets. Communications of the ACM, 44(8), 38-44.

Keim, D. A. (2001). Visual exploration of large data sets. Communications of the ACM, 44(8), 38-44.

information visualization

視覺資料探索(visual data exploration)將人類的知覺能力運用在大量資料探索過程裡，減少過程中所需要的認知能力，實際上也就是將資料以某種視覺形式呈現，讓資料分析師可以獲得其中蘊涵的洞悉(insight)，做出結論，並且與其互動。視覺資料探索運用的時機包括對資料的認識有限以及對於探索的目的模糊等。此外，除可可以讓使用者直接處理資料，相較於自動化的資料探勘技術，視覺資料探索具有可以容易地處理高度不同類的(imhomogeneous)及有雜訊的資料、直覺、不需要了解複雜的數學或統計學演算法與參數等優點。

視覺資料探索的過程大抵上遵循所謂的資訊搜尋箴言(information seeking mantra) [11] 的三步驟，概觀全體 (overview)、放大與過濾(zoom and filter)、選取與觀看細節 (details-on-demand)。相關的技術可以從三個標準進行歸類。
1. 被視覺化的資料類型(the data type to be visualized)：一維(如時間資料)、二維(如地圖)、多維(如關連式資料表)、文件與超文件、階層與圖式資料、演算法與軟體。
2. 如何在螢幕上安排資料以及如何處理資料的多維度(multiple dimensions)等視覺化技術(the visualization technique)。
3. 使視覺化產生動態改變及將多個獨立視覺化聯繫與合併的互動(interaction)技術與在深入的同時保留資料全體概觀的扭曲變形(distortion)技術。

視覺資料探索可以根據它們對特定資料特性的適合性進行評估與比較。任務特性則包括叢集(clustering)、分類(classification)、關連(associations)、多變量熱點(multivariate hot spots)等，視覺化的特性包括視覺重疊(visual overlap)和學習曲線(learning curve)，希望能夠提供有限的視覺重疊、快速學習和良好的回收。

Visual data exploration seeks to integrate humans in the data exploration process, applying their perceptual abilities to the large data sets now available. The basic idea is to present the data in some visual form, allowing data analysts to gain insight into it and draw conclusions, as well as interact with it.

The visual representation of the data reduces the cognitive work needed to perform certain tasks.

Visual data exploration is especially useful when little is known about the data and the exploration goals are vague.

In addition to granting the user direct involvement, visual data exploration involves several main advantages over the automatic data mining techniques in statistics and machine learning:

• Deals more easily with highly inhomogeneous and noisy data;

• Is intuitive; and

• Requires no understanding of complex mathematical or statistical algorithms or parameters.

A visual representation provides a much higher degree of confidence in the findings of the exploration than a numerical or textual representation of the findings.

Visual data exploration, also known as the “information seeking mantra” [11], usually follows

a three-step process: overview, zoom and filter, and details-on-demand.

These techniques are classified using three criteria: the data to be visualized, the technique itself, and the interaction and distortion method (see Figure 1).

The classification begins with the data type to be visualized [11], including whether it is:

• One-dimensional (such as temporal data, as in Figure 2);

• Two-dimensional data (such as geographical maps, as in Figure 3);

• Multidimensional data (such as relational tables, as in Figure 4);

• Text and hypertext (such as news articles and Web documents);

• Hierarchies and graphs (such as telephone calls and Web sites, as in Figure 5); and

• Algorithms and software (such as debugging operations).

The visualization technique fits into one or more of the following categories, as identified in Figure 1:

• Standard 2D/3D displays using standard 2D or 3D visualization techniques (such as x-y plots and

landscapes) for visualizing the data.

• Geometrically transformed displays using geometric transformations and projections to produce useful visualizations.

• Icon-based displays that visualize each data item as an icon (such as stick figures) and the dimension values as features of the icons.

• Dense pixel displays that visualize each dimension value as a color pixel and group the pixels belonging to each dimension into an adjacent area [6].

• Stacked displays that visualize the data partitioned hierarchically.

The techniques associated with each of these categories differ in how they arrange the data on the

screen (such as 2D display or semantic arrangement) and how they deal with multiple dimensions

in case of multidimensional data (such as multiple windows, icon features, and hierarchy).

Interaction techniques, which allow users to interact directly with a visualization, include filtering, zooming, and linking, thus allowing the data analyst to make dynamic changes of a visualization according to the exploration objectives; they also make it possible to relate and combine multiple independent visualizations.

Interactive distortion techniques support the data exploration process by preserving an overview of the data during drill-down operations. Basically, they show portions of the data with a high level of detail and other portions with a lower level of detail.

Visualization techniques and visual data exploration systems can be evaluated and compared with respect to their suitability for certain data characteristics (such as data types, number of dimensions,

number of data items, and category). Task characteristics include clustering, classification, associations, and multivariate hot spots; visualization characteristics include visual overlap and learning curve.

Desirable visualization characteristics for any technique include limited visual overlap, fast learning, and good recall.

Undesirable visualization characteristics include occlusions and line crossings that might appear to the user/viewer as an artifact limiting the usefulness of the visualization technique.

Fekete, J. D., Van Wijk, J. J., Stasko, J. T., & North, C. (2008). The value of information visualization. In Information Visualization: Human-Centered Issues and Perspectives (pp. 1-18). Springer Berlin Heidelberg.

Fekete, J. D., Van Wijk, J. J., Stasko, J. T., & North, C. (2008). The value of information visualization. In Information Visualization: Human-Centered Issues and Perspectives (pp. 1-18). Springer Berlin Heidelberg.

Information Visualization

Card, Mackinlay, and Shneiderman [2]將視覺化(visualization)定義為「為了增強認知，利用電腦支援、互動的資料視覺表現」。他們並指出歸納視覺能增強認知的方式在於
-- 增加可運用的記憶與處理資源
-- 減少資訊的蒐尋
-- 增強樣式的辨認
-- 產生知覺推理(perceptual inference)運作
-- 使用知覺注意機制進行監控
-- 將資訊以可處理的媒介進行編碼

根據Ware [26]，前注意處理理論(preattentive processing theory)和格式塔理論(Gestalt theory)是兩種主要的可以解釋視覺如何有效地知覺特徵和形狀的心理學理論。前注意處理理論(preattentive processing theory)解釋能夠有效處理的視覺特徵，資訊視覺化便是根據前注意處理理論選擇資料呈現的視覺編碼，藉以使感興趣的視覺查詢(visual queries)在前注意處理完成。格式塔理論則是提供描述視覺系統使了解圖像的重要原理，包括接近性(proximity)、相似性(similarity)、連續性(continuity)、對稱性(symmetry)、封閉性(closure)以及相對大小(relative size)等。

本研究認為資訊視覺化的最佳應用為極大資訊空間的探索，當人們尚未知道問題何在或是想提出更好、更有意義的問題時，提供檢視資料來進行了解，產生新的發現或者洞悉資料。Lin [8] 認為這種的瀏覽對資料有良好的相關結構，但同時使用者不熟悉資料集合的內容也僅有限地系統的組織方式，他們對相關資訊需求的描述有困難，對資訊的辨認比描述容易，並偏好以較少的認知負荷進行探索等情形下有幫助。因此，資訊視覺化發揮功用的過程如下：使用者提出一個他們感興趣的問題，將資料以正確的表示方式呈現，讓使用者了解這個表示方式，回答問題並且引發許多預期外的發現與問題。

資訊視覺化的價值雖然可以用使用這項技術的計畫成功來判斷，但由於視覺化往往不是這些成功的唯一方法。本研究則提出以知識增加的價值與需要的成本之間的差來計算資訊視覺化的效益。以數學的方式表示如下：
F = nm(W( ΔK) − Cs − kCe) − Ci − nCu.
其中n代表使用這種視覺化方法的使用者人數，m則是他們的平均使用次數，k則是每次探索需要的步驟數目。而每位使用者每次經由視覺化能獲得的知識價值以W( ΔK))表示，每次需要的前置成本為Cs，反覆進行探索時每一步驟花費的成本則需要Ce，並且這個視覺化技術的研究開發成本和每位使用者選擇與獲得這項技術分別為Ci和Cu。根據上面的公式，視覺化技術要獲得最大的效益需要使用的使用者愈多，然後經常使用來獲取高價值的知識，並且在時間與硬體、軟體與精力上的花費盡量少。

They (Card, Mackinlay, and Shneiderman) describe visualization as “the use of computer-supported, interactive visual representations of data to amplify cognition.” [2]

InfoVis systems are best applied for exploratory tasks, ones that involve browsing a large information space. Frequently, the person using the InfoVis system may not have a specific goal or question in mind. Instead, the person simply may be examining the data to learn more about it, to make new discoveries, or to gain insight about it. The exploratory process itself may influence the questions and tasks that arise.

InfoVis systems, on the other hand, appear to be most useful when a person simply does not know what questions to ask about the data or when the person wants to ask better, more meaningful questions. InfoVis systems help people to rapidly narrow in from a large space and find parts of the data to study more carefully.

Lin [8] describes a number of conditions in which browsing is useful:

– When there is a good underlying structure so that items close to one another can be inferred to be similar

– When users are unfamiliar with a collection’s contents

– When users have limited understanding of how a system is organized and prefer a less cognitively loaded method of exploration

– When users have difficulty verbalizing the underlying information need

– When information is easier to recognize than describe

Information Visualization is about developing insights from collected data, not about understanding a specific domain.

Information Visualization is still an inductive method in the sense that it is meant at generating new insights and ideas that are the seeds of theories, but it does it by using human perception as a very fast filter: if vision perceives some pattern, there might be a pattern in the data that reveals a structure.

Following that definition, the authors (Card, Mackinlay, and Shneiderman [2]) listed a number of key ways that the visuals can amplify cognition:
– Increasing memory and processing resources available
– Reducing search for information
– Enhancing the recognition of patterns
– Enabling perceptual inference operations
– Using perceptual attention mechanisms for monitoring
– Encoding info in a manipulable medium

According to Ware [26], there are two main psychological theories that explain how vision can be used effectively to perceive features and shapes. At the low level, Preattentive processing theory [19] explains what visual features can be effectively processed. At a higher cognitive level, the Gestalt theory [6] describes some principles used by our brain to understand an image.

Preattentive processing theory explains that some visual features can be perceived very rapidly and accurately by our low-level visual system. ... Information visualization relies on this theory to choose the visual encoding used to display data to allow the most interesting visual queries to be done preattentively.

Gestalt theory explains important principles followed by the visual system when it tries to understand an image. According to Ware [26], it is based on the following principles:

Proximity Things that are close together are perceptually grouped together;

Similarity Similar elements tend to be grouped together;

Continuity Visual elements that are smoothly connected or continuous tend to be grouped;

Symmetry Two symmetrically arranged visual elements are more likely to be perceived as a whole;

Closure A closed contour tends to be seen as an object;

Relative Size Smaller components of a pattern tend to be perceived as objects whereas large ones as a background.

Still, the process of explaining how InfoVis works remains the same: ask a question that interests people, show the right representation, let the audience understand the representation, answer the question and realize how many more unexpected findings and questions arise.

One effective line of argumentation about the value of InfoVis is through reporting the success of projects that used InfoVis techniques. These stories exist but have not been advertised in general scientific publications until recently [16,12,9]. One problem with trying to report on the success of a project is that visualization is rarely the only method used to reach the success.

Visualization can be considered as a technology, a collection of methods, techniques, and tools developed and applied to satisfy a need. Hence, standard technological measures apply: Visualization has to be effective and efficient.

The profit of visualization is defined as the difference between the value of the increase in knowledge and the costs made to obtain this insight.

A schematic model is considered: One visualization method V is used by n users to visualize a data set m times each, where each session takes k explorative steps.
The value of an increase in knowledge (or insight) has to be judged by the user. Users can be satisfied intrinsically by new knowledge, as an enrichment of their understanding of the world. A more pragmatic and operational point of view is to consider if the new knowledge influences decisions, leads to actions, and, hopefully, improves the quality of these. The overall gain now is nm(W( ΔK)), where W( ΔK)) represents the value of the increase in knowledge.

Concerning the costs for the use of (a specific) visualization V , these can be split into various factors. Initial research and development costs Ci have to be made; a user has to make initial costs Cu, because he has to spend time to select and acquire V , and understand how to use it; per session initial costs Cs have to be made, such as conversion of the data; and finally during a session a user makes costs Ce, because he has to spend time to watch and understand the visualization, and interactively explore the data set. The overall profit now is

F = nm(W( ΔK) − Cs − kCe) − Ci − nCu.

In other words, this leads to the obvious insight that a great visualization method is used by many people, who use it routinely to obtain highly valuable knowledge, while having to spend little time and money on hardware, software, and effort.

The costs Ce that have to be made to understand visualizations depend on the prior experience of the users as well as the complexity of the imagery shown.

The costs Cs per session and Cu per user can be reduced by tight integration with applications.

The initial costs Ci for new InfoVis methods and techniques roughly fall into two categories: Research and Development.
Research costs can be high, because it is often hard to improve on the state of the art, and because many experiments (ranging from the development of prototypes to user experiments) are needed. On the other hand, when problems are addressed with many potential usages, these costs are still quite limited.
Development costs can also be high. It takes time and effort to produce software that is stable and useful under all conditions, and that is tightly integrated with its context, but here also one has to take advantage of the large potential market. Development and availability of suitable middleware, for instance as libraries or plug-ins that can easily customized for the problem at hand is an obvious route here.