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Using Multimedia Animation with Real-time Graphic

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Using Multimedia Animation with Real-timeGraphic Overlays for Visualizing a Million Casesof Multivariate DataDianne Cook, Statistics, Iowa State University, Ames, IA,Leslie Miller, Computer Science, Iowa State university, Ames, IA,Manuel Suarez, Statistics, Iowa State University, Ames, IA,Peter Sutherland, Affymetrix, CA,Jing Zhang, Computer Science, Iowa State University, Ames, IA.AbstractThis paper discusses using preprocessing of multivariate data into projectionsconverted to images and movies to provide graphical displays for large quantitiesof data. The views are augmented with interaction so that the user can paintareas and have small subsets of the full data set overlaid as real-time graph-ics. Looking up the full data set is achieved by an indexing of the projectionsthat is created in the data pre-processing. An application of the methods onmultivariate spatio-temporal data, seasonal metric data from the United StatesGeological Survey, is discussed.1 IntroductionLarge spatio-temporal data sets are being compiled to study global climate andenvironmental conditions across the globe. A lot of data is being collected withthe support of the United States government, and consequently, it is being madeavailable to the general public: See, for example, http://www.pmel.noaa.gov/tao/,http://www.usgs.gov/pubprod/ or http://www.ucar.edu/fac data/data-resources.html.One of the hurdles to using existing graphics tools on this data is the size. Forreal-time visualization, large data presents some challenges:1. the views need to be created rapidly enough to be displayed in fractionsof a second, especially for dynamic graphics;2. a user needs to be able to interact with the views and have the responseoccur in fractions of a second;3. the screen real estate is limited and with large data many cases could mapto the same pixel;14. some common case reduction methods for multivariate real-valued datawhile sufficient for mean and variance analysis are inadequate for visual-ization where the task is to find anomalies, rare events, uncommon rela-tionships.Thus the objective is to produce visual tools which provide displays swiftly,allow the user to interact with the view, and to maximize the amount of datarepresented in the limits of screen resolution. For this pap er the goal is todemonstrate this is achievable for a million cases of multivariate data.As far back as 1990 Dr John McDonald, at the University of Washing-ton, demonstrated a software system for interactively visualizing with a millionpoints. He could rotate 3 variables by generating images of the projected data:the rotation started slowly and discontinuously, one view, next view, next view,stepwise as the images for the 3D projection were created, and then screamalong at break neck pace once the full set of images for 360owere created. Hecould brush in a scatterplot linked to other scatterplots: as the brush moved noupdates were made, but once the mouse button was released the points wouldbe highlighted. The scatterplots were displayed as pixel resolution, grey scaleimages, and color was overlaid in layers for each brush action. He used hissoftware to examine data generated from remote sensing instruments, that is,images representing a spectral band. This type of data typically comes on theorder of a million points: 1024 × 1024 = 1048576. He never published this work.The research reported in this paper re-visits McDonald’s work, adding meth-ods and software for visualizing large, multivariate space-time dependent data.It is organized as follows. The rest of this section introduces notation for thedata, describes visual methods commonly used for small data sets, and providesmore information on related work. Section 2 describes our approach to scalingmethods to a million cases. Section 3 overviews the software that we have de-veloped to test our approach, and section 4 applies the methodology on seasonalmetric data from the United States Geological Survey (USGS).1.1 Type of dataThe data is real-valued multivariate data having at least a million cases (in-stances, examples) but probably less than 15 variables (features, attributes). Insome examples there may be associated class information, such as an estimateof land use, and there may be associated time and spatial information.In mathematical notation we expect to have data of the formX =x11x12. . . x1px21x22. . . x2p............xn1xn2. . . xnpn×p=tuple1tuple2...tuplenwhere n is the number of cases, and p is the number of variables. The as sociatedclass vector may be denoted as C =c1c2. . . cn 0, the time context as2T =t1t2. . . tn 0and spatial context as S =s11s12s21s22......sn1sn2. There maybe missing values in the data.A data projection, as used to generate a scatterplot, for example, can bedenoted asY = XA =x11x12. . . x1px21x22. . . x2p............xn1xn2. . . xnpn×pa11a12a21a22......ap1ap2p×2=y11y12y21y22......yn1yn2n×2where A is an orthonormal matrix, that is the columns are vectors of length 1and each is orthogonal to all other columns.1.2 Visual methods for small datasetsThere is a lot of choice in graphical methods for displaying aspects of high-dimensions: tours (Asimov 1985, Cook, Buja, Cabrera & Hurley 1995, Wegman1991), scatterplot matrices (Carr 1985, Becker & Cleveland 1987), parallel co-ordinate plots (Inselberg 1985, Wegman 1990), and conditional plots (Becker,Cleveland & Shyu 1996). Scatterplots of two real-valued variables underly manyof the above methods, and they can be denoted as projections, projecting thedata from p-D to 2-D.In addition, direct manipulation between multiple plots provides ways oflinking information, providing more insight into high-dimensional structure.The most common linking method is linked brushing, where highlighting fea-tures in one rendering similarly highlights the corresponding features in theother renderings. Linking several marginal views allows the viewer to exploreconditional dependencies amongst variables, for example, if X is less than 10,then what is Y. Figure 1 demonstrates linking between several views..These methods are well-documented in Wilkinson (1999), Cleveland & McGill(1988), Buja & Tukey (1991). Numerous software environments provide thesetypes of tools: for example, GGobi (http://www.ggobi.org),


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