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Interactive Visual Exploration of High Dimensional Datasets

Jing Yang

Fall 2008

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Challenges of High Dimensional Datasets

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

Example: Ticdata2000 dataset: 86 dimensionsOHSUMED dataset: 215 dimensions SkyServer dataset: 361 dimensions

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

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Example

215*215 = 46,225 plots

OHSUMED dataset: 215 dimensions

215 axes

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Visual Hierarchical Dimension Reduction (VHDR)

J. Yang, M.O. Ward, E.A. Rundensteinerand S. Huang

VisSym’03

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Motivation - Dimension ReductionIdea:

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

Existing Approaches:Principal Component Analysis Multidimensional ScalingKohonen’s Self Organizing Map

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

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Inspiration

Hierarchical parallel coordinate: data item hierarchy

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Key Ideas of VHDR

Use dimension hierarchy to convey dimension relationshipsAllow 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

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

Manual hierarchy modificationDiscussion:

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

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Navigate and Manipulate Dimension Hierarchy

InterRing - Radial space filling hierarchy navigation tool [yang:2002]ModificationSelectionRadius distortionCircular distortionRolling up/Drilling downRotationZooming/Panning

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Construct Lower-Dimensional Subspaces

Strategy 1: construct a subspace with closely related dimensions

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Construct Lower-Dimensional Subspaces

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 cluster3. Use principal component analysis to generate

weighted sum of dimensions within a cluster

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Examples

Approach - averageApproach - select

representative dimensionrepresentative dimension

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Dissimilarity Representation

Approaches:Axis WidthThree AxesDiagonal PlotsOuter and Inner SticksMean-Band

Goal: visualize dissimilarity of dimensions in a dimension cluster.

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

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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

No dissimilarities representation

Dissimilarities represented in diagonal plots

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GeneralityVHDR is a general framework that can be

extended to multiple display techniques

We have applied VHDR to:

Parallel CoordinatesStar GlyphsScatterplot MatricesDimensional Stacking

Hierarchical Parallel CoordinatesHierarchical 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. Infovis2003

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

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

InfoVis’03

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

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Dimension Ordering (1)

Random order

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Dimension Ordering (2)

Ordered by similarity

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Dimension Ordering (3)Order dimensions according to different

purposes:Similarity-oriented ordering: put similar dimensions close to each otherImportance-oriented ordering: map more important dimensions to more significant 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 hierarchyOrder each dimension clusterthe order of the dimensions is decided in a depth-first traversal of the dimension hierarchy

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Hierarchical OrderingIllustration

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Dimension Ordering (6)

Random order Similarity-oriented order

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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)

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

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p g(1)

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Dimension Spacing Distortion (2)

Before After

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Dimension Filtering (1)

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

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Dimension Filtering (2)

Unfiltered Filtered

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Conclusion

The proposed approachImproves the manageability of dimensions in high dimensional data sets and reduces the complexity of the ordering, spacing and filtering tasks;Allows flexible user interactions for dimension ordering, spacing and filtering with dimension hierarchies.

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Value and Relation (VaR) Display

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

InfoVis’04

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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?

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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)

Hint:Use Pixel-Oriented techniques and allow overlaps

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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]

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Challenge - Dimension Relationship Visualization (con.)

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

Recall data item relationship visualization:MDS: SPIRE Galaxies [Wise:95]

Hint: Using MDS to layout dimensions

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Our Proposal: Value and Relation (VaR) Display

d1 d2 d3 d4

d1d2d3

00.70.60.7

0.700.30.2

0.60.300.1

0.70.20.10

d4

d4d1d2

d3

Multi-Dimensional Scaling

Pixel-Oriented glyph

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SkyServer dataset: 361 dimensions, 50,000 data items

Value and Relation Display

Features: Explicitly conveys data values without dimension reductionExplicitly conveys dimension relationshipsProvides a rich set of interaction tools

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Overlap Detection and Reduction

Extent ScalingDynamic MaskingZooming and PanningShowing NamesLayer ReorderingManual Relocation

Automatic Shifting

SkyServer Dataset

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Distortion

Goal: Focus-within-context

Features: Enlarges clicked glyphs Keeps size of other glyphs

SkyServer Dataset

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Data Item Reordering

Pixel-oriented techniques:Data item ordering is critical

VaR display: Initial displayManual 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 being compared

AAUP Dataset: 14 dimensions, 1,131 data items

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Selection

Goal:Select dimensions for further interaction or visualization

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

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: Iteratively select unrelated dimensions and filter related dimensions

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

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Scale to Large Datasets

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

Use random sampling Users interactively set thresholdRandom sampling is triggered automatically

Without sampling (16K data items)

With sampling (5K data items)

Out5D Dataset

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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 relationshipamong dimensions? Multivariate relationships

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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)

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XRay Dimension Glyphs

Each glyph: a scatterplotmatrix

X: a base dimension that is the same for all glyphsY: the dimension it represents

Density based displayBright: sparseDark: dense

Unoccupied area: semi-transparent

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

XRay Dimension Glyphs

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

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

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

Jigsaw Map Dimension Layout

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Rainfall Dimension LayoutMetaphor: RainCenter Bottom: focus dimension DSpeed of a dimension: related to its correlation to DTime: user controllable

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Rainfall Dimension Layout

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Data Item Selection and Masking

Visual query style data item selectionData item based masking

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

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Labeling

(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

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

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Semantic Image Browser: Bridging Information Visualization with Automated Intelligent 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

Acknowledgements: This work is supported by NVAC

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Motivation

Interactive image exploration:Applications: personal image management, satellite image analysis, ...

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

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

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Semantic Image Browser Overview

Annotation engineAutomated semantic image classification process

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

Interactions 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]

Low level visual featuresSemantic contentsSemantic concepts

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

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Image View – MDS layout

Corel collection (1100 images, 20 contents)

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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 blocks

Pixel-oriented techniques [Keim 94]Color assignment

Unselected images:Red - 1 Gray – 0

Selected images:Blue – 1Light gray - 0

MDS layout of content blocksInteractions

Corel image collection (1100 images, 20 contents)

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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 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

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

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User Study ResultsTask1: Find three given images

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 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 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 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

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Multivariate 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

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What is the relationship?

Scatterplot MatrixParallel Coordinates

y0 = x0x1 + x2

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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

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Multivariate Visual ExplanationGoals:

Multivariate relationship understandingDimension Reduction Model Construction

Approach: Integrate partial derivative calculation into multivariate visualization

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

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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 those variables with the others held constant

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Partial Derivative Inspection

Partial derivative calculation introduces errors

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Partial Derivative InspectionVisually 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

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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/∂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!

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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 in 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 derivativesInformation to be detected:

Significant independent variablesIgnorable independent variablesIndependent variables linearly impact dependent variable Independent variable Positively or negatively impact?

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Step2: 1st Order Partial Derivativesvs. Original Dimensions Scatterplots

Information:Entangled?

Dataset: y0 = x0x1 + x2, 1000 data items

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Coordinated Visual Exploration

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Model Construction