Consider input X being 1-D, and Y belongs to two classes, which have equal priors and the class- conditional densities of X are shifted versions of each other, as shown in the plot below. Each within-class density of X is a mixture of two normal distributions: Class 1 (red): 0.6N(-2, %4) + 0.4N(0, 1). Class 2 (blue): 0.6N(0, %) + 0.4N(2, 1). (a) Describe the classifier obtained by LDA when the number of samples/observations goes to infinity. Justify your answer. (b) Assume instead that the prior of class 1 is twice of that the prior of class 2. Describe the classifier obtained by LDA, when the number of samples/observations goes to infinity. Justify your answer.
Consider input X being 1-D, and Y belongs to two classes, which have equal priors and the class- conditional densities of X are shifted versions of each other, as shown in the plot below. Each within-class density of X is a mixture of two normal distributions: Class 1 (red): 0.6N(-2, %4) + 0.4N(0, 1). Class 2 (blue): 0.6N(0, %) + 0.4N(2, 1). (a) Describe the classifier obtained by LDA when the number of samples/observations goes to infinity. Justify your answer. (b) Assume instead that the prior of class 1 is twice of that the prior of class 2. Describe the classifier obtained by LDA, when the number of samples/observations goes to infinity. Justify your answer.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Consider input X being 1-D, and Y belongs to two classes, which have equal priors and the class-
conditional densities of X are shifted versions of each other, as shown in the plot below.
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Each within-class density of X is a mixture of two normal distributions:
Class 1 (red): 0.6N(-2, ¼ ) + 0.4N(0, 1).
Class 2 (blue): 0.6N(0, 4 ) + 0.4N(2, 1).
(a) Describe the classifier obtained by LDA when the number of samples/observations goes
to infinity. Justify your answer.
(b) Assume instead that the prior of class 1 is twice of that the prior of class 2. Describe the
classifier obtained by LDA, when the number of samples/observations goes to infinity.
Justify your answer.
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