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diff --git a/report/paper.md b/report/paper.md index 809af3a..ef1e9c4 100755 --- a/report/paper.md +++ b/report/paper.md @@ -219,7 +219,7 @@ affect recognition the most are: glasses, hair, sex and brightness of the pictur # Question 2, Generative and Discriminative Subspace Learning -To combine both method it is possible to perform LDA in a generative subspace created by PCA. In order to +One way to combine generative and discriminative learning is made possible by performing LDA on a generative subspace created by PCA. In order to maximize class separation and minimize the distance between elements of the same class it is necessary to maximize the function J(W) (generalized Rayleigh quotient): $J(W) = \frac{W\textsuperscript{T}S\textsubscript{B}W}{W\textsuperscript{T}S\textsubscript{W}W}$. @@ -239,7 +239,7 @@ of the projected samples: $W\textsuperscript{T}\textsubscript{pca} = arg\underse = arg\underset{W}max\frac{|W\textsuperscript{T}W\textsuperscript{T} \textsubscript{pca}S\textsubscript{B}W\textsubscript{pca}W|}{|W\textsuperscript{T}W\textsuperscript{T}\textsubscript{pca}S\textsubscript{W}W\textsubscript{pca}W|}$. -However, performing PCA followed by LDA carries a loss of discriminative information. This problem can +Performing PCA followed by LDA carries a loss of discriminative information. This problem can be avoided through a linear combination of the two [@pca-lda]. In the following section we will use a 1-dimensional subspace *e*. The cost functions associated with PCA and LDA (with $\epsilon$ being a very small number) are H\textsubscript{pca}(*e*)= |