Factorising large image datasets John Ashburner Principal Component Analysis Need to reduce dimensions for data mining Reduced feature set that explains as much of the data as possible PCA can be optimised via an EM algorithm Preserve privacy across sites Deal with missing data Simple PCA not a good model of brain images Privacy-preserving decomposition Hospital 1 Hospital 2 F2F2 F2F2 P F1F1 F1F1 Data (F) N W2W2 W2W2 K W1W1 W1W1 Features (W) N P H H Spatial basis functions (H) K Simple PCA approach Original images (from 581) Reconstructions from 64 components Generalised PCA Logistic PCA suitable for factorising binary data Principal Geodesic Analysis For learning shape models Shape and appearance model Mininise the following objective function w.r.t. W (features), (average), A (eigen- appearances) and H (eigen-warps): Shape Appearance Regularisation Shape and appearance eigen- modes First of 50 eigenmodesFirst of 64 eigenmodes Data (only 2D) Faces (64 out of 490) Grey matter maps (64 of 581) Full model fit Shape and appearance Shape and appearance (logistic) Shape model only Warped average faceWarped average GM Full model fit Shape and appearance Shape and appearance (logistic) Appearance model only Appearance fit (no warping) Model samples (1) Samples from face modelSamples from brain model Model samples (2) Samples from face modelSamples from brain model