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Equation related to Linear Discriminant Analysis (LDA)?
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[QUOTE="StoneTemplePython, post: 6068841, member: 613025"] e_ Have you looked at pages 7 and 9 in Detail? It seems fairly clear to me that ##W## is made up. Equivalently, you choose it, and you should choose optimally (page 9). - - - - My belief, btw, is that page 8 shows ##J(W) = \frac{\det\big(W^T S_b W\big)}{\det\big(W^T S_W W\big)}## where ##S_W## and ##S_B## are symmetric positive (semi?) definite matrices. However since I've conjectured that ##W^TW = I## but ##WW^T=P## my belief is you select ##W## to be a rank ##r## matrix and hence ##J(W) = \frac{\det\big(W^T S_b W\big)}{\det\big(W^T S_W W\big)} = \frac{e_r\big(W^T S_b W\big)}{e_r\big(W^T S_b W\big)}= \frac{e_r\big(P S_b \big)}{e_r\big(P S_b \big)}= \frac{e_r\big(P S_b P\big)}{e_r\big(P S_b P\big)}## where ##e_r## is the rth elementary symmetric function of the eigenvalues of the matrix inside. But these notes clearly are part of a much bigger sequence and are not standalone. There should be a notational lookup somewhere. [/QUOTE]
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Equation related to Linear Discriminant Analysis (LDA)?
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