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Interactive Visual Exploration of High Dimensional Datasetsof High Dimensional Datasets

Jing Yang

S i 2010

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Spring 2010

Challenges of High Dimensional Datasets

High dimensional datasets are common: digital g glibraries, bioinformatics, simulations, process monitoring, and surveys

Example: image analysis dataset: tens to hundreds of dimensionsnewswire dataset: hundreds to thousands of dimensions

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Challenges of visualizing high dimensional datasets:Clutter on the screenDifficult user navigation in the data space

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Example

OHSUMED dataset: 215 dimensions

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215*215 = 46,225 plots 215 axes

Visual Hierarchical Dimension Reduction (VHDR)Reduction (VHDR)

J. Yang, M.O. Ward, E.A. Rundensteiner and S. Huang

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VisSym’03

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Motivation - Dimension ReductionIdea:

Project a high-dimensional dataset to a lower-Project a high dimensional dataset to a lowerdimensional subspaceVisualize data items in the lower-dimensional subspace

Existing Approaches:Principal Component Analysis Multidimensional Scaling

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gKohonen’s Self Organizing Map

Problems: Information lossNo intuitive meaning of generated dimensionsLittle user interaction allowed.

Inspiration

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Hierarchical parallel coordinate: data item hierarchy

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Key Ideas of VHDR

Use dimension hierarchy to convey dimension y yrelationshipsAllow users to learn the dimension hierarchy Allow users to select dimensions or dimension clusters to form subspaces of interests

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Dimension Hierarchy

Similar dimensions form cluster, clusters are grouped into larger clusters

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a dimension hierarchy of a 5-d dataset

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VHDR Framework

Step 1: build dimension hierarchy Step 2: navigate and manipulate dimension hierarchyStep 3: interactively select clusters from dimension hierarchy to form lower-dimensional subspaces

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Overview

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Build Dimension Hierarchy

Automatic dimension clusteringgCluster dimensions according to dissimilarities*among them*Dissimilarity - measure of how dimensions are dissimilar to each other

Manual hierarchy modificationDiscussion:

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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’98

Navigate and Manipulate Dimension Hierarchy

InterRing - Radial space g pfilling hierarchy navigation tool [yang:2002]ModificationSelection

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Radius distortionCircular distortionRolling up/Drilling downRotationZooming/Panning

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Construct Lower-Dimensional Subspaces

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Strategy 1: construct a subspace with closely related dimensions

Construct Lower-Dimensional Subspaces

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Strategy 2: construct a subspace that covers major variance of the dataset

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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

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3. Use principal component analysis to generate weighted sum of dimensions within a cluster

Examples

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representative dimensionrepresentative dimension

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Dissimilarity Representation

Goal: visualize dissimilarity of dimensions in a di i l t

Approaches:Axis WidthThree AxesDiagonal Plots

dimension cluster.

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Outer and Inner SticksMean-Band

Example: select 3 dimension clusters (dimensions) in Census-Income dataset

Dissimilarity Representation : Axis Width Method

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Dissimilarity Representation : Three Axis Method

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Dissimilarity Representation : Three Axis Method

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Dissimilarity Representation : Diagonal Plots Method

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No dissimilarities representation

Dissimilarities represented in diagonal plots

GeneralityVHDR is a general framework that can be

extended to multiple display techniquesextended to multiple display techniques

We have applied VHDR to:

Parallel CoordinatesStar Glyphs

Hierarchical Parallel CoordinatesHi hi l St Gl h

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Scatterplot MatricesDimensional Stacking

Hierarchical Star GlyphsHierarchical Scatterplot

MatricesHierarchical Dimensional

Stacking

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Other Clustering Approach

Visualization of Large-Scale Customer Satisfaction Surveys Using a Parallel Coordinate Tree, D. Brodbeck et. al. Infovis 2003

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Interactive Hierarchical Dimension Ordering, Spacing and Filtering For Exploration of High Dimensional DatasetsDimensional Datasets

Jing Yang, Wei Peng, Matthew O. Wardand Elke A. Rundensteiner

InfoVis’03

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InfoVis 03

Motivation

Large number of dimensions need to be managed

Ordering, spacing, filtering etc.

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Overview

General: includes dimension ordering, dimension spacing and dimension filteringInteractive: allows user interactions throughout the whole processHierarchical: groups dimensions into a hi h d b ild t l ith d

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hierarchy and builds most algorithms and user interactions upon this hierarchy to increase scalability

Dimension Ordering (1)

28Random order

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Dimension Ordering (2)

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Dimension Ordering (3)

Order dimensions for different purposes:Similarity-oriented ordering: put similar dimensions close to each otherImportance-oriented ordering: map more important dimensions to more significant

iti tt ib t Th d f

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positions or attributes. The order of importance can be decided by Principal Component Analysis (PCA)

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Dimension Ordering (4)Challenges for ordering high dimensional datasets:

Similarity-oriented ordering is NP-CompleteIt 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

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p g yOrder each dimension clusterthe order of the dimensions is decided in a depth-first traversal of the dimension hierarchy

Hierarchical OrderingIllustration

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Dimension Ordering (6)

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Random order Similarity-oriented order

Dimension Spacing (1)

Idea of dimension spacing:Convey dimension relationship information by varying the spacing between adjacent axes

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Dimension Spacing (2)

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Dimensions spaced according to similarity: similar dimensions are close to each other

Dimension Spacing Distortion (1)

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Dimension Spacing Distortion (2)

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Before After

Dimension Filtering (1)

Idea of dimension filtering:Similar dimensions can be omitted;Unimportant dimensions can be omitted.

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Dimension Filtering (2)

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Unfiltered Filtered

Conclusion

The proposed approachImproves the manageability of dimensions in high dimensional data sets and reduces the complexity of the ordering, spacing and filtering tasks;All fl ibl i t ti f

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Allows flexible user interactions for dimension ordering, spacing and filtering with dimension hierarchies.

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Value and Relation (VaR) Display p y

Jing Yang, Anilkumar Patro, Shiping Huang, NishantMehta, Matthew O. Ward and Elke A. Rundensteiner

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InfoVis’04

Motivation

Challenges:gCan high dimensional datasets be visualized without dimension reduction to avoid information loss ?Can dimension relationships be visualized in the same display as data values?

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p y

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Challenge - Visualization without Dimension Reduction

Visualize SkyServer dataset (361 dimensions) using existing techniques: Parallel Coordinates: 361 axesScatterplot Matrix: 130,321 scatterplotsPixel-Oriented techniques without overlaps: 50,000 data items: 18,050,000 pixels (23 times of number of pixels in a 1024*768 screen)

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pixels in a 1024 768 screen)

Hint:Use Pixel-Oriented techniques and allow overlaps

Challenge - Dimension Relationship Visualization

Sorting dimensions in a 1DSorting dimensions in a 1D or 2D grid [Ankerst 98]

Not effective beyond hundreds of dimensions

Spacing between dimensions [Yang 2003]

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dimensions [Yang 2003]Only relationships of adjacent dimensions are revealed Pixel-Oriented: Sort 50 dimensions

in a 2D grid [Ankerst 98]

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Challenge - Dimension Relationship Visualization (con.)

R ll d t it l ti hiRecall data item relationship visualization:MDS: SPIRE Galaxies [Wise:95]

Hint:

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SPIRE Galaxies: Map data items to a 2D display using MDS [Wise: 95]

Hint: Using MDS to layout dimensions

Our Proposal: Value and Relation (VaR) Display

d3

d4d1d2

d3

Pixel-Oriented glyph

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d1 d2 d3 d4

d1d2d3

0 0.1 0.2 0.7

0.1 0 0.3 0.6

0.2 0.3 0 0.7

0.7 0.6 0.7 0d4

Multi-Dimensional Scaling

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Value and Relation Display

Features:Features: Explicitly conveys data values without dimension reductionExplicitly conveys dimension relationships

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SkyServer dataset: 361 dimensions, 50,000 data items

Provides a rich set of interaction tools

Overlap Detection and Reduction

Extent ScalingExtent ScalingDynamic MaskingZooming and PanningShowing NamesLayer ReorderingManual Relocation

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Manual Relocation

Automatic Shifting

SkyServer Dataset

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Distortion

G lGoal: Focus-within-context

Features: Enlarges clicked glyphs Keeps size of other l h

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glyphs

SkyServer Dataset

Data Item Reordering

Pixel-oriented htechniques:

Data item ordering is critical

VaR display: Initial displayM l d i

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Manual reordering

Census-Income-Part Dataset: 42 dimensions, 20,000 data items

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Comparing

Goal: Compare base dimension with all others

Feature: Coloring by value difference of dimensions

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difference of dimensions being compared

AAUP Dataset: 14 dimensions, 1,131 data items

Selection

Goal:Goal:Select dimensions for further interaction or visualization

Selection tools in VaR display:Manual selection - flexibilityAutomatic selection - efficiency

Select related dimensions

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Select related dimensionsSelect unrelated dimensions

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Automatic Selection for Unrelated Dimensions

Input: A base dimension“Related” threshold

Output: Dimensions covering major data variance

Algorithm: It ti l l t

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Iteratively select unrelated dimensions and filter related dimensions

Related work:Maximum subspace [MacEachren:03] SkyServer Dataset

Scale to Large Datasets

Store glyphs as texture objects

Out5D Dataset

Store glyphs as texture objectsExtent scaling and relocating: resize, relocate texture objects ☺Reordering and recoloring: regenerate texture objects

Use random sampling

Without sampling (16K data items)

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Use random sampling Users interactively set thresholdRandom sampling is triggered automatically

With sampling (5K data items)

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Discussion

Is pixel-oriented technique the only choice forIs 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

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3D MDS, SOM, Treemap, Animation…

Is correlation the most informative relationshipamong dimensions? Multivariate relationships

Value and Relation Display: Interactive Visual Exploration of Large Datasets with Hundreds of Dimensions.Dimensions.

J. Yang, D. Hubball, M. Ward, E. Rundensteiner and W. Ribarsky

IEEE Transactions on Visualization and Computer Graphics 13(3)

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Computer Graphics 13(3)

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XRay Dimension Glyphs

Each glyph: a scatterplot X b di i th t iX: a base dimension that is the same for all glyphs

Y: the dimension it represents

Density based displayBright: sparseDark: dense

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Dark: dense

Unoccupied area: semi-transparent

XRay Dimension Glyphs

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A real dataset with 89 dimensions and 10,417 data items in Pixel and XRay Vars.

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Jigsaw Map Dimension LayoutDimension hierarchyUsing H-Curve to create a Jigsaw Map

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M. Wattenberg. A note on space-filling visualizations and space-filling curves. InfoVis 2005, pages 181–186

Jigsaw Map Dimension Layout

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A real dataset with 838 dimensions and 11,413 data items in Pixel-Jigsaw VaR and XRay-Jigsaw VaR

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Rainfall Dimension Layout

Metaphor: RainCenter Bottom: focus dimension DSpeed of a dimension: related to its correlation to D

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Time: user controllable

Rainfall Dimension Layout

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Data Item Selection and Masking

Visual query style data item selectionData item based masking

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(a) No mask (b) Opaque mask (c) Semi-transparent mask

Labeling

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(a) All labels are shown

(b) Labels of selected dimensions are shown

(c) Angled labels in Jigsaw map layout

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Possible Applications of VaR Display

Interactively exploring high dimensional dataRevealing data item relationshipsRevealing dimension relationships

Guiding automatic data analysisAssessing resultsManually tuning parameters

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Human-driven dimension reductionConstructing subspaces using selection toolsVisualizing subspaces in VaR or other displays

Semantic Image Browser: Bridging Information Visualization with Automated Intelligent Image AnalysisIntelligent Image Analysis

Jing Yang1, Jianping Fan1, Daniel Hubball1, Yuli Gao1, Hangzai Luo1, William Ribarsky1, and Matthew Ward2

1 University of North Carolina at Charlotte2Worcester Polytechnic Institute

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Acknowledgements: This work is supported by NVAC

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MotivationInteractive image exploration:

A li ti l i t t llitApplications: personal image management, satellite image analysis, ...

Background: Automated semantic image analysisGap between semantic image analysis and image exploration

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Goals:Facilitate image exploration using analysis resultsEvaluate, monitor and improve analysis processes

Semantic Image Browser Overview

Annotation engineA t t d ti i l ifi tiAutomated semantic image classification process

Multiple coordinated viewsImage view – MDS, Rainfall, SequentialContent view – VaR

Interactions Search by sample image

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Search by sample imageSearch by semantic contentInteractive annotation examination and modificationZooming, panning, distortion

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Annotation Engine

Content-Based Image Annotation [fan:2004][fan:2004]

Low level visual featuresSemantic contentsSemantic concepts

Semantic contents: hi h di i l d t t

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high dimensional datasetdata items: imagesdimensions: contentsvalues: 1 (image contains the content) or 0 (otherwise)

Image View – MDS layout

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Navigation Tools

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Image View – Rainfall Layout

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Content View

VaR display [yang:2004]Content blocksContent blocks

Pixel-oriented techniques [Keim 94]Color assignment

Unselected images:Red - 1 Gray – 0

Selected images:Blue – 1

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Light gray - 0

MDS layout of content blocksInteractions

Corel image collection (1100 images, 20 contents)

Search by Sample Image

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Search by Semantic Content

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Annotation Evaluation and Modification

Case 1: RedflowerCase 2: Sailcloth

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User StudySubjects

10 UNCC students10 UNCC students Dataset: Corel dataset (20 contents, 1100 images)Systems compared

No annotation: Unsorted Thumbnails in ExplorerSemantic contents: Semantic image browserSemantic concepts: Thumbnails sorted by concepts in Explorer

Tasks

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TasksTask1: Find three given imagesTask2: Find images with certain contentsTask3: Estimate percentage of images containing certain contents

User Study ResultsTask1: Find three given images

Result:Result: Sorted Explorer was better than Semantic browserSemantic browser was better than Unsorted Explorer

Major reason: Annotations in the semantic concept level were more “error tolerant”

Task2: Find images with certain contentsResult was similar to task1

Task3: Estimate percentage of images containing certain

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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

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Multivariate Visual Explanation for High Dimensional Datasetsfor High Dimensional Datasets

S. Barlowe, T. Zhang, Y. Liu, J. Yang and D. Jacobs

VAST 2008

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Worldview GapWorldview Gap - gap between what is being shown and what actually needs tobeing shown and what actually needs to be shown to draw a straightforward representational conclusion for decision making

- Amar and stasko, InfoVis 2004 best paper

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Filling Worldview Gap:Our approach - Embedding automatic analysis

into information visualization

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Multivariate Visual ExplanationMultivariate Visual Explanation

With Scatt Barlowe, Tianyi Zhang, Yujie Liu, and Donald Jacobs

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Motivation

Understanding multivariate relationships is critical in a vast number of applicationsExample:

Economic forecasting <- unemployment, interest rates, consumer confidence, and inflation

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Existing multivariate visualization techniques are quite limited in helping multivariate analysis

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What is the relationship?

y0 = x0x1 + x2

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Worldview Gap

Worldview Gap - gap between what isWorldview Gap gap between what is being shown and what actually needs to be shown to draw a straightforward representational conclusion for decision making

A d k I f Vi 2004 b

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- Amar and stasko, InfoVis 2004 best paper

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Multivariate Visual ExplanationGoals:

Multivariate relationship understandingDimension Reduction Model Construction

Approach: Integrate partial derivative calculation into multivariate visualization

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Partial derivative calculation and inspectionStep by step visual exploration with interactive model construction and dimension reduction

Partial Derivative

Derivative: measurement of how a functionchanges 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

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variables: derivative with respect to one of those variables with the others held constant

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Partial Derivative Inspection

Partial derivative calculation introduces errorsPartial derivative calculation introduces errors

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Partial Derivative InspectionVisually present errors to users

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Error inspection of a segmented dataset:y = 8x0 +x1 if x0 ≥ 0.6 and x1 ≤ 0.3 y = x0−7x1 otherwise

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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

1st order derivatives: ∂y/∂x0 ∂y/∂x1 ∂y/∂x2

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1st order derivatives: ∂y/∂x0, ∂y/∂x1, ∂y/∂x22nd 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!

Visual Exploration of Partial Derivatives

Examine all types of relationships from one display? Users would be overwhelmed!

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Step By Step Visual Exploration

Different types of correlations are examined i diff t tin different stepsCorrelations easier to be detected will be examined firstVariable with detected relationships will be excluded from further analysis

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Step1: 1st Order Partial Derivative Histograms

Display: the histograms of 1st order partial d i tiderivativesInformation to be detected:

Significant independent variablesIgnorable independent variablesIndependent variables linearly impact

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p y pdependent variable Independent variable Positively or negatively impact?

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Step2: 1st Order Partial Derivativesvs. Original Dimensions Scatterplots

Information:Entangled?g

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Coordinated Visual Exploration

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Model Construction

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