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Visualization of Multidimensional Multivariate Large Dataset Presented by: Zhijian Pan zpan@cs.umd.edu University of Maryland
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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
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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
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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
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MDMV Visualization Category Broadly categorized into five groups: –Brushing –Panel Matrix –Iconography –Hierarchical Displays –Non-Cartesian Displays
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Group 1 Brushing –Direct manipulation of MDMV visualization display:labeling, enhanced linking –E.g. brushing a scatterplot matrix
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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)
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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
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Group 4 Hierarchical Displays: –map a subset of variates into different hierarchical display –Dynamic interactive analysis –the Ted Mihalisin paper, more details followed
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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
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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
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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
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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
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Group 4 (cont’d) From 7D to 2D:
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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
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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
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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
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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)
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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)
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Group 5 (cont’d) Application example: –Economic model of a real country –8 variables: AgricultureAgriculture FishingFishing MiningMining ManufacturingManufacturing ConstructionConstruction GovernmentGovernment MiscellaneousMiscellaneous GNPGNP
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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
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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)
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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
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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
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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
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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.
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