How is the proportion of total variance explained by the k-th principal component calculated from eigenvalues lambda_1 >= lambda_2 >= ... >= lambda_d?
The variance ratio explained by component k is lambda_k / $\sum_{$$j=1}^{d} lambda_j$.
A Scree Plot in PCA is a graph plotting:
A Scree plot displays eigenvalues associated with components in descending order to identify the elbow point.
Linear Discriminant Analysis (LDA) is a supervised dimensionality reduction technique that maximizes:
$LDA maximizes Fisher's criterion J(w) = (w^{T} S_B w) / (w^{T} S_W w).$
For a classification task with C classes, what is the MAXIMUM number of non-zero linear discriminants LDA can extract?
$Between-class scatter matrix S_B has rank at most C - 1, so LDA can extract at most min(d, C - 1) linear discriminants.$
What is the key structural difference between PCA and LDA?
PCA maximizes total variance without labels (unsupervised); LDA maximizes class separability using class labels (supervised).