Consider a two-class problem in ( mathbb R ^d ) with class labels red and green. Let ( mu red ) and ( mu green ) be the means of the two classes. Given tes

Question

Consider a two-class problem in $ \mathbb{R}^d $ with class labels red and green. Let $ \mu_{red} $ and $ \mu_{green} $ be the means of the two classes. Given test sample $ x \in \mathbb{R}^d $, a classifier calculates the squared Euclidean distance (denoted by $ \| \cdot \|^2 $) between $ x $ and the means of the two classes and assigns the class label that the sample $ x $ is closest to. That is, the classifier computes $$ f(x) = \| \mu_{red} - x \|^2 - \| \mu_{green} - x \|^2 $$
and assigns the label red to $ x $ if $ f(x) < 0 $, and green otherwise. Which of the following statements is/are correct?

Accepted Answer

C. $ f(x) = w^T x + b $, where $ w $ and $ b $ are functions of $ \mu_{red} $ and $ \mu_{green} $

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