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A Plot for Visualizing Multivariate Data Rida E. A. Moustafa George Mason University ADM Group,AAL

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Talk Outline The Theory of MV-Plot. Detecting Linear Structures with MV-plot. Detecting Non-Linear Structures with MV-plot. Comparisons with other methods and application on real data.

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MV-Plot Theory Given an observation x=(x 1,x 2,…,x d ) We define m and v as follows: Computing m and v for every observation produces vector of m and v. What is the relationship between m and v?

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MV-Relationship in 2-d Normalizing the data in range (0,1) avoid the abs-value in computing m. Close to the PC in 2-d

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MV- detects linear structure(s) If the data is linear in the original space It will be linear in the MV-space!!

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MV- detects linear structure(s)

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Detecting Linear structure(s) Example I

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Detecting Linear structure(s) Example II

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Detecting Linear structure(s) Example III

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Detecting nonlinear data with MV-plot MV- plot can detect nonlinear structure in the data set without any changes in the equations.

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Detecting nonlinear structure

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Detecting Sphere(s) Case I: The sphere radius R The sphere center is the origin

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Detecting Sphere(s) Case II: The sphere radius R The sphere center is not the origin

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Detecting Sphere(s)

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Fisher’s IRIS data (150x4) 3-classes of( 50 point each) Process control data (600x60) 6-classes of (100 points each) Pollen data (3,848x5) (Wegman’s data) 2-classes (linear and nonlinear) Application on Real data

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Multidimensional Scaling Fisher Discriminate Analysis Principal Component Related Dimensional Reduction Methods

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IRIS (R. A. Fisher) Dataset 1 50-cases in 4-dim

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Time Series Dataset 600-cases in 60-dim

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Pollen dataset 3,848-points in 5-dim Other methods: Require more storage and speed. Even if it work, we expect bad results on this particular data. (Wegman2002)

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Pollen dataset Linear and Nonlinear mixed structures.

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The linear structure in the Pollen data set =98 Linear, 3750 nonlinear

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Summary MV-algorithm can discover the linear and nonlinear pattern at the same time. MV-algorithm can discover symmetric data. MV-algorithm deals with large multivariate data.

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