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Unformatted text preview: ∑ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = n i n i n n h x x nh x p 1 1 ) ( ϕ has the following property E[p n (x)] = N( μ , σ 2 +h n 2 ) 3. Consider the following set of two dimensional vectors from three categories: ω 1 ω 2 ω 3 X 1 X 2 X 1 X 2 X 1 X 2 10 0 5 10 2 8 0 10 0 5 5 2 5 2 5 5 10 4 (a) Plot the decision boundary resulting from the nearest neighbor rule just for categorizing ω 1 and ω 2. Find the sample mean m 1 and m 2 and on the same figure sketch the decision boundary corresponding to classifying x by assigning it to the category of the nearest sample mean. (b) Repeat part (a) for categorizing only ω 1 and ω 3. (c) Repeat part (a) for categorizing only ω 2 and ω 3. (d) Repeat part (a) for threecategory classifier, classifying ω 1, ω 2 and ω 3....
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 Fall '06
 Kriegman
 Matrices, Covariance, Recursion, CN, Covariance and correlation, Estimation of covariance matrices

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