Interactive Visual Exploration

Transcription

1 Interactive Visual Exploration of High Dimensional Datasets Jing Yang Spring Challenges of High Dimensional Datasets High dimensional datasets are common: digital libraries, bioinformatics, simulations, process monitoring, and surveys Example: image analysis dataset: tens to hundreds of dimensions newswire dataset: hundreds to thousands of dimensions Challenges of visualizing high dimensional datasets: Clutter on the screen Difficult user navigation in the data space 2 1

2 Example OHSUMED dataset: 215 dimensions 215*215 = 46,225 plots 215 axes 3 Visual Hierarchical Dimension Reduction (VHDR) J. Yang, M.O. Ward, E.A. Rundensteiner and S. Huang VisSym

3 Motivation - Dimension Reduction Idea: Project a high-dimensional dataset to a lower- dimensional subspace Visualize data items in the lower-dimensional subspace Existing Approaches: Principal Component Analysis Multidimensional Scaling Kohonen s Self Organizing Map Problems: Information loss No intuitive meaning of generated dimensions Little user interaction allowed. 5 Inspiration Hierarchical parallel coordinate: data item hierarchy 6 3

4 Key Ideas of VHDR Use dimension hierarchy to convey dimension relationships Allow users to learn the dimension hierarchy Allow users to select dimensions or dimension clusters to form subspaces of interests 7 Dimension Hierarchy Similar dimensions form cluster, clusters are grouped into larger clusters a dimension hierarchy of a 5-d dataset 8 4

5 VHDR Framework Step 1: build dimension hierarchy Step 2: navigate and manipulate dimension hierarchy Step 3: interactively select clusters from dimension hierarchy to form lowerdimensional subspaces 9 Overview 10 5

6 Build Dimension Hierarchy Automatic dimension clustering Cluster dimensions according to dissimilarities* among them *Dissimilarity - measure of how dimensions are dissimilar to each other Manual hierarchy modification Discussion: How to calculate dissimilarity between two dimensions? Ref: Ankerst, M., Berchtold, S., and Keim, D. A. Similarity clustering of dimensions for an enhanced visualization of multidimensional data. InfoVis Navigate and Manipulate Dimension Hierarchy InterRing - Radial space filling hierarchy navigation tool [yang:2002] Modification Selection Radius distortion Circular distortion Rolling up/drilling down Rotation Zooming/Panning 12 6

7 Construct Lower-Dimensional Subspaces Strategy 1: construct a subspace with closely related dimensions 13 Construct Lower-Dimensional Subspaces Strategy 2: construct a subspace that covers major variance of the dataset 14 7

8 Dimension Cluster Representation Representative Dimension - a dimension that represents a cluster of dimensions Approaches to assigning or generating a representative dimension: 1. Select a dimension from the cluster 2. Average all dimensions in the cluster 3. Use principal component analysis to generate weighted sum of dimensions within a cluster 15 Examples representative dimension representative dimension Approach - select Approach - average 16 8

9 Dissimilarity Representation Goal: visualize dissimilarity of dimensions in a dimension i cluster. Approaches: Axis Width Three Axes Diagonal Plots Outer and Inner Sticks Mean-Band Example: select 3 dimension clusters (dimensions) in Census-Income dataset 17 Dissimilarity Representation : Axis Width Method 18 9

10 Dissimilarity Representation : Three Axis Method 19 Dissimilarity Representation : Three Axis Method 20 10

11 Dissimilarity Representation : Diagonal Plots Method No dissimilarities representation Dissimilarities represented in diagonal plots 21 Generality VHDR is a general framework that can be extended to multiple display techniques We have applied VHDR to: Parallel Coordinates Star Glyphs Scatterplot Matrices Dimensional Stacking Hierarchical Parallel Coordinates Hierarchical l Star Glyphs Hierarchical Scatterplot Matrices Hierarchical Dimensional Stacking 22 11

12 Other Clustering Approach Visualization of Large-Scale Customer Satisfaction Surveys Using a Parallel Coordinate Tree, D. Brodbeck et. al. Infovis

13 Interactive Hierarchical Dimension Ordering, Spacing and Filtering For Exploration of High Dimensional Datasets Jing Yang, Wei Peng, Matthew O. Ward and Elke A. Rundensteiner InfoVis Motivation Large number of dimensions need to be managed Ordering, spacing, filtering etc

14 Overview General: includes dimension ordering, dimension spacing and dimension filtering Interactive: allows user interactions throughout the whole process Hierarchical: groups dimensions into a hierarchy h and builds most algorithms and user interactions upon this hierarchy to increase scalability 27 Dimension Ordering (1) Random order 28 14

15 Dimension Ordering (2) Ordered by similarity 29 Dimension Ordering (3) Order dimensions for different purposes: Similarity-oriented ordering: put similar dimensions close to each other Importance-oriented ordering: map more important dimensions to more significant positions or attributes. t The order of importance can be decided by Principal Component Analysis (PCA) 30 15

16 Dimension Ordering (4) Challenges for ordering high dimensional datasets: Similarity-oriented ordering is NP-Complete It is hard to decide the order of the importance of a large number of dimensions using PCA Our solution: reduce the complexity of the ordering problem using the dimension hierarchy Order each dimension cluster the order of the dimensions is decided in a depthfirst traversal of the dimension hierarchy 31 Hierarchical Ordering Illustration 32 16

17 Dimension Ordering (6) Random order Similarity-oriented order 33 Dimension Spacing (1) Idea of dimension spacing: Convey dimension relationship information by varying the spacing between adjacent axes 34 17

18 Dimension Spacing (2) Dimensions spaced according to similarity: similar dimensions are close to each other 35 Dimension Spacing Distortion (1) 36 18

19 Dimension Spacing Distortion (2) Before After 37 Dimension Filtering (1) Idea of dimension filtering: Similar dimensions can be omitted; Unimportant dimensions can be omitted

20 Dimension Filtering (2) Unfiltered Filtered 39 Conclusion The proposed approach Improves the manageability of dimensions in high dimensional data sets and reduces the complexity of the ordering, spacing and filtering tasks; Allows flexible user interactions ti for dimension ordering, spacing and filtering with dimension hierarchies

21 Value and Relation (VaR) Display Jing Yang, Anilkumar Patro, Shiping Huang, Nishant Mehta, Matthew O. Ward and Elke A. Rundensteiner InfoVis Motivation Challenges: Can high dimensional datasets be visualized without dimension reduction to avoid information loss? Can dimension relationships be visualized in the same display as data values? 42 21

22 Challenge - Visualization without Dimension Reduction Visualize SkyServer dataset (361 dimensions) using existing techniques: Parallel Coordinates: 361 axes Scatterplot Matrix: 130,321 scatterplots Pixel-Oriented techniques without overlaps: 50,000 data items: 18,050,000 pixels (23 times of number of pixels in a 1024*768 screen) Hint: Use Pixel-Oriented techniques and allow overlaps 43 Challenge - Dimension Relationship Visualization Sorting dimensions in a 1D or 2D grid [Ankerst 98] Not effective beyond hundreds of dimensions Spacing between dimensions [Yang 2003] Only relationships of adjacent dimensions are revealed Pixel-Oriented: Sort 50 dimensions in a 2D grid [Ankerst 98] 44 22

23 Challenge - Dimension Relationship Visualization (con.) Recall data item relationship visualization: MDS: SPIRE Galaxies [Wise:95] Hint: Using MDS to layout dimensions SPIRE Galaxies: Map data items to a 2D display using MDS [Wise: 95] 45 Our Proposal: Value and Relation (VaR) Display d3 Pixel-Oriented glyph d1 d2 d4 d1 d2 d3 d4 d1 d2 d3 d Multi-Dimensional Scaling 46 23

24 Value and Relation Display Features: Explicitly conveys data values without dimension reduction Explicitly conveys dimension relationships Provides a rich set of interaction tools SkyServer dataset: 361 dimensions, 50,000 data items 47 Overlap Detection and Reduction Extent Scaling Dynamic Masking Zooming and Panning Showing Names Layer Reordering Manual Relocation Automatic Shifting SkyServer Dataset 48 24

25 Distortion Goal: Focus-within-context Features: Enlarges clicked glyphs Keeps size of other glyphs SkyServer Dataset 49 Data Item Reordering Pixel-oriented techniques: Data item ordering is critical VaR display: Initial display Manual reordering Census-Income-Part Dataset: 42 dimensions, 20,000 data items 50 25

26 Comparing Goal: Compare base dimension with all others Feature: Coloring by value difference of dimensions being compared AAUP Dataset: 14 dimensions, 1,131 data items 51 Goal: Selection Select dimensions for further interaction or visualization Selection tools in VaR display: Manual selection - flexibility Automatic selection - efficiency Select related dimensions Select unrelated dimensions 52 26

27 Automatic Selection for Unrelated Dimensions Input: A base dimension Related threshold Output: Dimensions covering major data variance Algorithm: Iteratively ti select unrelated dimensions and filter related dimensions Related work: Maximum subspace [MacEachren:03] SkyServer Dataset 53 Scale to Large Datasets Out5D Dataset Store glyphs as texture objects Extent scaling and relocating: resize, relocate texture objects Reordering and recoloring: regenerate texture objects Use random sampling Users interactively set threshold Random sampling is triggered automatically Without sampling (16K data items) With sampling (5K data items) 54 27

28 Discussion Is pixel-oriented technique the only choice for generating dimension glyphs? Histogram, Scatterplot, Is 2D MDS the only approach to layout dimensions? 3D MDS, SOM, Treemap, Animation Is correlation the most informative relationship among dimensions? Multivariate relationships 55 Value and Relation Display: Interactive Visual Exploration of Large Datasets with Hundreds of Dimensions. J. Yang, D. Hubball, M. Ward, E. Rundensteiner and W. Ribarsky IEEE Transactions on Visualization and Computer Graphics 13(3) 56 28

29 XRay Dimension Glyphs Each glyph: a scatterplot X: a base dimension i that t is the same for all glyphs Y: the dimension it represents Density based display Bright: sparse Dark: dense Unoccupied area: semitransparent 57 XRay Dimension Glyphs A real dataset with 89 dimensions and 10,417 data items in Pixel and XRay Vars

30 Jigsaw Map Dimension Layout Dimension hierarchy Using H-Curve to create a Jigsaw Map M. Wattenberg. A note on space-filling visualizations and space-filling curves. InfoVis 2005, pages Jigsaw Map Dimension Layout A real dataset with 838 dimensions and 11,413 data items in Pixel-Jigsaw VaR and XRay-Jigsaw VaR 60 30

31 Rainfall Dimension Layout Metaphor: Rain Center Bottom: focus dimension D Speed of a dimension: related to its correlation to D Time: user controllable 61 Rainfall Dimension Layout 62 31

32 Data Item Selection and Masking Visual query style data item selection Data item based masking (a) No mask (b) Opaque mask (c) Semi-transparent mask 63 Labeling (a) All labels are shown (b) Labels of selected dimensions are shown (c) Angled labels in Jigsaw map layout 64 32

33 Possible Applications of VaR Display Interactively exploring high dimensional data Revealing data item relationships Revealing dimension relationships Guiding automatic data analysis Assessing results Manually tuning parameters Human-driven dimension reduction Constructing subspaces using selection tools Visualizing subspaces in VaR or other displays 65 Semantic Image Browser: Bridging Information Visualization with Automated Intelligent Image Analysis Jing Yang 1, Jianping Fan 1, Daniel Hubball 1, Yuli Gao 1, Hangzai Luo 1, William Ribarsky 1, and Matthew Ward 2 1 University of North Carolina at Charlotte 2 Worcester Polytechnic Institute Acknowledgements: This work is supported by NVAC 66 33

34 Motivation Interactive image exploration: Applications: personal image management, satellite image analysis,... Background: Automated semantic image analysis Gap between semantic image analysis and image exploration Goals: Facilitate image exploration using analysis results Evaluate, monitor and improve analysis processes 67 Semantic Image Browser Overview Annotation engine Automated t semantic image classification process Multiple coordinated views Image view MDS, Rainfall, Sequential Content view VaR Interactions Search by sample image Search by semantic content Interactive annotation examination and modification Zooming, panning, distortion 68 34

35 Annotation Engine Content-Based Image Annotation [fan:2004] Low level visual features Semantic contents Semantic concepts Semantic contents: high h dimensional i dataset t data items: images dimensions: contents values: 1 (image contains the content) or 0 (otherwise) 69 Image View MDS layout Corel collection (1100 images, 20 contents) 70 35

36 Navigation Tools 71 Image View Rainfall Layout 72 36

37 Content View VaR display [yang:2004] Content blocks Pixel-oriented techniques [Keim 94] Color assignment Unselected images: Red - 1 Gray 0 Selected images: Blue 1 Light gray - 0 MDS layout of content blocks Interactions Corel image collection (1100 images, 20 contents) 73 Search by Sample Image 74 37

38 Search by Semantic Content 75 Annotation Evaluation and Modification Case 1: Redflower Case 2: Sailcloth 76 38

39 User Study Subjects 10 UNCC students Dataset: Corel dataset (20 contents, 1100 images) Systems compared No annotation: Unsorted Thumbnails in Explorer Semantic contents: Semantic image browser Semantic concepts: Thumbnails sorted by concepts in Explorer Tasks Task1: Find three given images Task2: Find images with certain contents Task3: Estimate percentage of images containing certain contents 77 User Study Results Task1: Find three given images Result: Sorted Explorer was better than Semantic browser Semantic browser was better than Unsorted Explorer Major reason: Annotations in the semantic concept level were more error tolerant Task2: Find images with certain contents Result was similar to task1 Task3: Estimate percentage of images containing certain contents Result: Semantic browser was faster and more accurate than sorted Explorer and unsorted Explorer Post experiment questionnaire (1 to 10 scale) Semantic browser was preferred Semantic browser was useful 78 39

40 Multivariate Visual Explanation for High Dimensional Datasets S. Barlowe, T. Zhang, Y. Liu, J. Yang and D. Jacobs VAST Worldview Gap Worldview Gap - gap between what is being shown and what actually needs to be shown to draw a straightforward representational conclusion for decision making - Amar and stasko, InfoVis 2004 best paper Filling Worldview Gap: Our approach - Embedding automatic analysis into information visualization 80 40

41 Multivariate Visual Explanation With Scatt Barlowe, Tianyi Zhang, Yujie Liu, and Donald Jacobs 81 Motivation Understanding multivariate relationships is critical in a vast number of applications Example: Economic forecasting <- unemployment, interest rates, consumer confidence, and inflation Existing multivariate visualization techniques are quite limited in helping multivariate analysis 82 41

42 What is the relationship? y0 = x0x1 + x2 Parallel Coordinates Scatterplot Matrix 83 Worldview Gap Worldview Gap - gap between what is being shown and what actually needs to be shown to draw a straightforward representational conclusion for decision making - Amar and stasko, InfoVis 2004 best paper 84 42

43 Multivariate Visual Explanation Goals: Multivariate relationship understanding Dimension Reduction Model Construction Approach: Integrate partial derivative calculation into multivariate visualization Partial derivative calculation and inspection Step by step visual exploration with interactive model construction and dimension reduction 85 Partial Derivative Derivative: measurement of how a function changes when values of its inputs change Example: derivative at a point in time of the position of a car: instantaneous speed Partial derivative of a function of several variables: derivative with respect to one of those variables with the others held constant 86 43

44 Partial Derivative Inspection Partial derivative calculation introduces errors 87 Partial Derivative Inspection Visually present errors to users Error inspection of a segmented dataset: y = 8x0 +x1 if x0 0.6 and x1 0.3 y = x0 7x1 otherwise 88 44

45 Visual Exploration of Partial Derivatives Show all partial derivatives together with the original dimensions? Scalability Challenge: 4-d dataset with dependent variable y and independent variables x0, x1, and x2 1 st order derivatives: y/ x0, y/ x1, y/ x2 2 nd order derivatives: y y/ x0 x0, y y/ x0 x1, y y/ x0 x2, y y/ x1 x1, y y/ x1 x2, y y/ x2 x2 Screen will be cluttered! 89 Visual Exploration of Partial Derivatives Examine all types of relationships from one display? Users would be overwhelmed! 90 45

46 Step By Step Visual Exploration Different types of correlations are examined in different steps Correlations easier to be detected will be examined first Variable with detected relationships will be excluded from further analysis 91 Step1: 1 st Order Partial Derivative Histograms Display: the histograms of 1st order partial derivatives Information to be detected: Significant independent variables Ignorable independent variables Independent variables linearly impact dependent variable Independent variable Positively or negatively impact? 92 46

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48 95 Step2: 1 st Order Partial Derivatives vs. Original Dimensions Scatterplots Information: Entangled? Dataset: y0 = x0x1 + x2, 1000 data items 96 48

49 Coordinated Visual Exploration 97 Model Construction 98 49