Sequential Principal Curves Analysis Toolbox (SPCA)

SPCA is a manifold learning technique that identifies the curvilinear coordinates of a data set. It defines an invertible transform that can be tuned for NonLinear ICA (infomax) or optimal Vector Quantization (error minimization), and can be used in Dimensionality Reduction, Domain Adaptation, and Classification problems. The explicit form of the identified features (and associated nonlinear ‘filters’) makes it useful to model sensors in theoretical neuroscience.

Illustrative Results I: Learning Nonlinear Features Identification of curved features and the effect of the metric in SPCA in a curved 2D manifold. Note the different marginal PDFs in the direction perpendicular to the principal curve: Laplacian and Uniform PDFs of increasing variance.

Infomax and Error Minimization through SPCA. 500 randomly selected samples of the sets were transformed using SPCA with different metrics. Results are analyzed in terms of independence (Mutual Information) and reconstruction error (RMSE).

Illustrative Results II: Image Coding According to Different Optimization Criteria.