Revision #890 → #1488 · back to history
addedPrincipal component analysis (PCA)0f2b30a334d7
addedPrincipal components of a point cloud7918053a7bfb
addedBest-fitting line24bc9aabe75b
addedFirst and k-th principal components23e610dec28b
addedPrincipal components are eigenvectors of the covariance matrix19d8930332de
addedPCA as orthogonal linear transformationd4c4630f2e54
addedMaximum of Rayleigh quotient equals largest eigenvalue229772689e40
addedFirst principal component score4ed79cec0b3f
addedk-th principal component via deflationf4960e8e8ddc
addedWeight vectors are eigenvectors of X^T X10cf844bd65c
addedLoadings in PCAcf528e800919
addedZero sample covariance between different principal components6bf78d3abdd1
addedPrincipal components transformation diagonalises empirical covariance matrixe1fab3f094b4
addedSingular value decomposition of X6736b5135bc4
addedRight singular vectors equal eigenvectors of X^T X402c80dc8d5e
addedEckart–Young theorem (truncated SVD is best rank-L approximation)a93cd7b0b008
addedOptimal k-dimensional fit (Eckart–Young in PCA form)811c95926d55
addedEffect of variable rescaling on covariance matrix96e247d35483
addedEffect of failing to mean-center9f98b6fa4f3e
addedPCA on correlation matrix equals PCA on covariance of standardized data3d7f9df37105
addedProperty 1 — trace maximised by leading eigenvectorsbdc0c616036d
addedProperty 2 — trace minimised by trailing eigenvectors1125f8f1d252
addedProperty 3 — spectral decomposition of Σa64de23da134
addedInformation-theoretic optimality of PCA (Linsker)d7955782198e
addedPCA minimises upper bound on information loss for non-Gaussian signal5f2eec30349b
addedKarhunen–Loève transform via covariance methodb76b246c1ceb
addedExistence of orthonormal P diagonalising cov(X)070fa31d8b9c
addedTwo correlated variables — 45° rotation under PCA77a5a6ffde43
addedOxford Internet Survey four attitude components3ae2c13a0669
addedSpike-triggered covariance analysis in neuroscienceceb50ba0998c