Multiple Dimensional Visualization

Dimension 1 dimensional data Given price information of 200 or more houses, please find ways to visualization this dataset

2-Dimensional Dataset I also know the distances from the houses to office. Please find ways to visualization both the distances and prices of the houses.

3-Dimensional Dataset I also know the builders of the houses. Please find ways to visualization the distances, prices, and builders of the houses.

Multi-Dimensional Dataset I collected more information about the houses, including home school ranking, distances to shopping centers etc. Please find ways to visualize the dataset!?

Table-based techniques HeatMap, tablelens Geometric techniques Methods Scatterplot matrices, parallel coordinates, landscapes, Dust&Magnet Icon-based techniques glyphs, shape-coding, color icons Hierarchical techniques Dimensional stacking, worlds-within-worlds Pixel-oriented techniques Recursive pattern, circle segments, spiral, axes techniques,

Example Data: Iris Scientists measured the sepal length, sepal width, petal length, petal width of many kinds of iris...

The Iris Data Multi-Dimensional data set

Multi-dimensional (Multivariate) Dataset

Multivariate Dataset Data Item (Object, Record, Case)

Multivariate Dataset Dimension (Variable, Attribute)

Table-Based Techniques Improving spreadsheet or table with visualization Heatmap Table Lens

Heatmap Use value to color mapping From Dr. M. Ward

Heatmap After Sort to find groups

Example: DNA Microarray DNA Microarrays are small, solid supports onto which the sequences from thousands of different genes are immobilized, or attached, at fixed locations.

Example: DNA Microarray Converted to a table From Human Microbial Identification Microarray core (MIM) at The Forsyth Institute

Example: DNA Microarray Using R to draw a Heatmap from Microarray Data (from Molecular Organisation and Assembly in Cells Warwick Univ.) Gene expression profile of adult T-cell acute lymphocytic leukemia identifies distinct subsets of patients with different response to therapy and survival (Chiaretti et al. Blood 2004)

Table Lens Rao R., Card S. K.: The Table Lens: Merging Graphical and Symbolic Representation in an, Proc. Human Factors in Computing Systems CHI 94 Conf., Boston, MA, 1994, pp. 318-322.

Table Lens Interactive Focus+Context Visualization for Tabular Information

Geometry-based Techniques Step1: geometric transformations and projections of data Step2: Visualization Scatterplot-matrices [And 72, Cle 93] Parallel coordinates [Ins 85, ID 90] Parallel Glyphs [Fanea:05] Parallel Sets [Bendix:05] Star coordinates [Kan 2000] Landscapes [Wis 95] Dust & Magnet [Yi 2005] Projection Pursuit Techniques [Hub 85] Prosection Views [FB 94, STDS 95] Hyperslice [WL 93]

The simplest 2-D Scatterplot

Scatterplot Matrix Extend scatterplot to multi-dimensions Iris

Cars Scatterplot Matrix

Cluttered Scatterplot Matrix However, for very large data set OHSUMED dataset: 215 dimensions

Projection Pursuit Techniques For High-Dimensional Dataset locate projections to low-dimensional space that reveal most details about dataset structure extract and analyze projections structures from projections Two general approaches: manual and automatic

1-Dimensional Visualization

Parallel Coordinates

Geometry of Data Items straight lines Pak Wong, 1997

Cluster Cluster and Outlier A group of data items that are similar in all dimensions Outlier A data item that is similar to Few or No other data items

Cluster

Outlier

Star Coordinates Use radial coordinates E. Kandogan, Star Coordinates: A Multidimensional Visualization Technique with Uniform Treatment of Dimensions, InfoVis 2000 http://zoonek.free.fr/blosxom//r/2006-08- 7_The_Grammar_of_Graphics.html

Landscape Hot topics of a news collection L. Nowell, E. Hetzler, and T. Tanasse. Change Blindness in Information Visualization: A Case Study. Infovis 2001

Create landscape Landscape Documents (data items) Keywords (dimensions) N-d vector for each documents Projection from N-d space to 2-d space Landscape view Wise, J., Thomas, J., et al. Visualizing the Non-Visual: Spatial Analysis and Interaction with Information from Text Documents, Infovis 95

Hierarchical Methods Visualization of the data using a hierarchical partitioning into subspaces Dimensional Stacking

Dimensional Stacking Imagine each data item (4 attributes) as a small block. We place all blocks on a table Add grids on the table. Place the blocks in the grids according to their values of attribute1

Dimensional Stacking Add grids in grids. Place the blocks in the grids according to their values of attribute2.

Dimensional Stacking Add grids in grids. Place the blocks in the grids according to their values of attribute3

Dimensional Stacking Add grids in grids. Place the blocks in the grids according to their values of attribute4

Dimensional Stacking Fix one block!

Dimensional Stacking Fix another block

Dimensional Stacking Dimensional stacking

Dimensional Stacking visualization of oil mining data with longitude and latitude mapped to the outer x-, y- axes and ore grade and depth mapped to the inner x-, y- axes M. Ward, Worcester Polytechnic Institute

Icon-Based Methods Visualizing data values as features of icons Star glyph Chernoff-Faces Stick Figures Shape Coding Color Icons TileBars

Recall Parallel Coordinates

Star Glyphs Space out variables at equal angles around a circle Each arm encodes a variable s value 1 data item with 4 attributes 4 data items in the iris dataset

Glyph Positioning By order in the dataset By values in one dimension By values in two dimensions By similarity By location? By time? Star Glyph

Profile Glyphs Each bar encodes a variable s value 1 data item with 4 attributes 4 data items in the iris dataset

Chernoff faces 1973, Herman Chernoff

Mapping Quality of Life with Chernoff Faces Joseph G. Spinelli and Yu Zhou

Mapping Quality of Life with Chernoff Faces

Pixel-Oriented Techniques Each value - one colored pixel (value ranges -> fixed colormap) Values for each attribute are presented in separate subwindows Values of the same data item are at the same positions of all subwindows Keim s tutorial notes in Infovis 00

Pixel Layout and Orders

Challenge Textures of the subwindows reflect patterns. How to order and lay the pixels out to get informative textures?

Pixel-Oriented Techniques Dr. D. Keim s tutorial notes in Infovis 00

Query-Independent Techniques Space-Filling Curve Arrangements

Query-Independent Techniques Recursive pattern arrangements Designing Pixel-Oriented Visualization Techniques, Keim, 2000

Query-Dependent Techniques Visualize only the data relevant to the context of a specific query data items (a1, a2,..., am) & query (q1, q2,... qm) distances (d1, d2,... dm) extend distances by overall distance (dm+1) Map distances to color (for each attribute) Visualize each distance value by one colored pixel

Query-Dependent Techniques Spiral technique Designing Pixel-Oriented Visualization Techniques, Keim, 2000

Query-Dependent Techniques Circular technique Designing Pixel-Oriented Visualization Techniques, Keim, 2000

Query-Dependent Techniques Circular technique 50 stocks in 20 years (dimensions) Designing Pixel-Oriented Visualization Techniques, Keim, 2000

Major References Jing Yang, Lecture notes, UNCC Colin Ware. Information visualization, 2004 Daniel Keim. Tutorial note in InfoVis 2000 John Stasko. Course slides, Fall 2005