Visualization of Multidimensional Multivariate Large Dataset Presented by: Zhijian Pan University of Maryland

Description  Covered papers: –Alfred Inselberg, Multidimensional Detective –Ted Mihalisin, Visualizing Multivariate Functions, Data, and Distributions  The problem: Visualization and analysis of large dataset with multiple parameters or factors, and the key relationships among themVisualization and analysis of large dataset with multiple parameters or factors, and the key relationships among them MDMV problemMDMV problem

Key words explanation  Multidimensional: –The dimensionality of independent variables  Multivariate: –The dimensionality of dependent variables  Example: –3-D volume space+temperature+pressure produces 3D2V data  The data set could larger than number of pixels

Four Stages of Development  1st:Graphical representation of either one or two variate data, e.g. scatterplot, scatterplot matrix  2 nd :Two dimensional graphics, but encoding multiple parameters, e.g. color, size,shape coding  3 rd :High dimensional graphics, high speed computation, single display, such as Parallel Coords  4 th :elaboration and assessment of various visualization techniques

MDMV Visualization Category  Broadly categorized into five groups: –Brushing –Panel Matrix –Iconography –Hierarchical Displays –Non-Cartesian Displays

Group 1  Brushing –Direct manipulation of MDMV visualization display:labeling, enhanced linking –E.g. brushing a scatterplot matrix

Group 2  Panel Matrix (pairwise 2-D plot, n-D box) –E.g. Hyperbox: n*n lines, n*(n-1)/2 faces –Elaboration of scatterplot matrix –Adding interactive data navigation (hyperbox cutting)

Group 3  Iconography: Glyphs: graphical entities which encode MDMV with shape, size, color, and position. –E.g. faceglyph: size and position of eyes, nose, mouth; curvature of mouth; angle of eyebrows

Group 4  Hierarchical Displays: –map a subset of variates into different hierarchical display –Dynamic interactive analysis –the Ted Mihalisin paper, more details followed

Group 4 (cont’d)  New term: speed=the hierarchical axes  E..g. Three variables:x,y,and z: {0,1,2}  X the fastest axis, Z the slowest axis

Group 4 (Cont’d)  Visualizing 3 variables: –2 interdependent variables: x, y: x= -2, -1, 0, 1, 2;x= -2, -1, 0, 1, 2; y= -2, -1, 0, 1, 2y= -2, -1, 0, 1, 2 –1 dependent variable: z = x**2 + y**2 –so, a 2D1V problem –x fastest, y slowest

Group 4 (Cont’d)  3d1v: W = (x**2) * (e**-y) + z Top panel speed order : x, y, z Bottom panel speed order: z, y, x

Group 4 (cont’d)  What if the number of the data points greatly exceeds the number of horizontal pixels assigned to the panel?  Example: 7 independent variables + each has 10 values = 10,000,000 points  Need: – hierarchical subspace zooming to reduce dimension

Group 4 (cont’d)  From 7D to 2D:

Group 4 (cont’d)  example: experiment data visualization: –Dependent: specific heat –Independent: Fastest: temperature (white) :gaussian peakFastest: temperature (white) :gaussian peak Then alloy concentration (blue): linear increaseThen alloy concentration (blue): linear increase Then magnetic field (red) :nonlinear decreaseThen magnetic field (red) :nonlinear decrease

Group 5  Parallel Coordinates –So many class presentations have already been done! –Everybody is already expert using it –What are some basic ideas behind it? –Cartesian v.s. Parallel Coords

Group 5 (cont’d)  A Cartesian line: –L: x 2 = mx 1 +b –A set of points sampled on this line On Parallel Coords: –Each point becomes a line –The set of points becomes a set of intersecting lines

Group 5 (cont’d)  The intersect point:  The location of the intersect point is important! –Between two axes: inversely proportional (x1 α 1/x2) –Outside two axes: directly proportional (x1 α x2)

Group 5 (cont’d)  Application example –Aircraft collision checking –Converting the problem into detecting a four dimension geometric intersection –Collision at (2,2,2,1)

Group 5 (cont’d)  Application example: –Economic model of a real country –8 variables: AgricultureAgriculture FishingFishing MiningMining ManufacturingManufacturing ConstructionConstruction GovernmentGovernment MiscellaneousMiscellaneous GNPGNP

Group 5 (cont’d)  A Least Squares function defines the boundary region in 8 dimension space  Any point (polygon) inside the boundary represents a feasible economic policy for the country

Group 5 (cont’d)  Discoveries: –No policy would favor Agriculture without also favoring Fishing: (x1 α x2) –Inverse relationship between Fishing and Mining: resource competition: (x1 α 1/x2)

Notes on the References  The Inselberg’s paper: –11 citations found on researchIndex –Application in knowledge discovery, user interface, aircraft design, etc.  Ted Mihalisin paper: –Only one citation found

Contribution  Inselberg’s paper: –Transform MDMV hyperspace relations into a 2-D geometric pattern problem –empirical studies demonstrated the ability extending the strength with trade-off analysis, discover sensitivities, and optimization  Mihalisin’s paper: –Hierarchical technique visualizing data points greatly exceeding number of pixels

Critique  Inselberg’s paper: –No comparison with other MDMV techniques –No examples supporting the claim that displayed objects can be recognized under projective transformations  Mihalisin’s paper: –Limited number of values for each variable visualized in one display –No discussion of potential information loss with coarse-grained grid

Favorite Sentence  “You can’t be unlucky all the time!” –Multiple techniques exist for MDMV visualization problem –Each has strength and weakness –Whichever you start with, you can’t be unlucky all the time! –Integration and collaboration of existed tools remain to be active research topics.