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This algorithm is used for dimension reduction. Input: a set of vectors {Xn є }, and dimension d,d

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This Iterative algorithm is used for grouping of vectors. Input: a set of vectors {Xn є D}, number of groups-P. Output: a set of vectors {Xn є D}, which are labeled by (1…P).

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This Iterative algorithm offers a statistical model for a set of vectors. Input: a set of vectors {Xn є D}, number of groups-P, expectations of each group, empiric probability, empiric variances. Output: a set of vectors {Xn є D}, which are labeled by (1…P).

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834.7348 250.3190- 31.1367- 27.5612- 61.6570 78.9281- PCA +(x,y) 834.7348 250.3190- 31.1367- 27.5612- 61.6570 78.9281- 233 454

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22111111 22211111 21211111 22211321 22211121 32211211 33311111 33311111 22111111 22111111 22111111 22211111 22211111 32211111 33311111 33311111 inputoutput

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Definition: given two segmentations, A and B, the RI test will be: When the function I{X} is an indicator function.

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76.19% 86.67%

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80.74% 87.55%

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70.42% 64.13%

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Portfolio Statistics Portfolio Expected Return: E(r p ) = w T r Portfolio Variance: 2 p = w T w Sum of portfolio weights: = w T 1 –where w is.

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