222 2 22 2 22 2 22 2 2 2 22 2 2 22 2 22 2 2 2 22 2 2

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Unformatted text preview: 22 2 2 2 2 2222 2 2 2 2 2 2 2 222 222 2222 222 2 22 2 22 2 22 2 2 2 22 2 2 22 2 22 2 2 2 22 2 2 2222 22 2222222 22222 2 22 2 22 2 222 222 22 2 2 2 2 2 222 2222 2 2 22 222 2 2 22 22 2 2 2 2 22 2222 2222 22222 2 22 2 2 2 2 22 2 22 2 22 2 2 2 2 222 222 2 2 22 2 2 2 2 22 2 2 2 22 2 2 22 2 2 22 2 2 22 2 22 2 2 2 22 22 2 222 2 22 2 2 2222 222 22 2 2 2 2 2 2 2 22 22 22 1 2 22 2 222 2222 2 22 2 2 2 2 2 2 22 2 2 2 2 2 2 2 1 1 2 1 2 2 2 2 2 2 22 2 2 2 2 1 1 11 2 2 22222 2 22 2 11 1 2 22 2 1 1 11 22 2 2 22 2 11 1 1 1 1 1 11 1 1 1 111 1 1 111 11 1 1 1 2 22 1 11 1 1 11 1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 1 1 11111 11 111 1111111 1 1 1 1 1 11 11 1 11 1 1 1 1 11 1 11 1 11 1 11111111 1 111 1 11 11 1 11 1 1 1 1 1 1111 111 11 1 1 1 1 1 1 11 1 1 1 1 1 1 1 11 11111 1 1 1 1 1 1 111 1 1 1 1 11 1111 1 111 1 11 1 1 1 1 1111 1 1 1 1 1 1 11111111 1 11 1 1 1 1 1 1 11 11 11 1 1 1 1 1 1 1 111 1 11 1 1 1111111 1 1111 11111 11 1 1 1 1 1 11 1 11 1 11 11 1 11111 1 1 1 1 1 11 1 1 1 11 1111 11 111111 111 1 1 1 1 1 1 1 11 11 1 11 11 1 1 1 11 1 1 1 1 11 11 11111 1 1 1 1 1 11111 11 1 1 1 1 11 11 1 1 11 1 1 11 1 1 111 11111111 11 11 1 1 1 11 1 11 1 1 1 1 1 1 111 111 111 1 1 1 1 1 1 1 111 11 1 1 111 1 11 11 1 1 11 1 1 1 1 1 1 1 111 1 1 1 1 3 3 X2 X2 3 3 1 1 X1 X1 The data come from three classes in R2 and are easily separated by linear decision boundaries. The right plot shows the boundaries found by linear discriminant analysis. The left plot shows the boundaries found by linear regression of the indicator response variables. The middle class is completely masked (never dominates)? 5 ESL Chapter 4 — Linear Methods for Classification Trevor Hastie and Rob Tibshirani Degree = 1; Error = 0.25 Degree = 2; Error = 0.03 1 1 11 11 11 1 1 1.0 11 1 1 11 11 11 11 11 1 1 11 1 11 11 1 0.5 11 1 11 11 2 22 2 2 22 2 2 2 22 2 2 2222 2 2 22 22 22 2 2222222 22 0.0 3 3 33 33 33 3 33 3 33 3 33 3 33 33 3 33 33 3 3 33 3 33 33 3 33 3 33 3 33 3 33 33 3 33 33 33 3 33 33 33 3 33 3 3 3 33 11 333 11 3 3 13 22 2 2 222222 2 2 2 2 22222222 2222 2 11 2 11 22 232 2323 2 22 22322222 2 2 2222 2222222 222 2 22 22 222222 321 3 3 11 33 111 3 11 3 3 3 11 33 3 11 1 3 1 11 11 1 1 11 1 11 11 11 11 11 11 11 11 11 1 11 1 1 1 3 1 1 1 1 1 1 1 1 3 3 1...
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