PCA Instruments

EM Algorithms for PCA and Sensible PCA

Smart PCA

PCA can be smarter and makes more sensible projections. In this paper, we propose smart PCA, an extension to standard PCA to regularize and incorporate external knowledge into model estimation. Based on the probabilistic interpretation of PCA, the inverse Wishart distribution can be used as the informative conjugate prior for the population covariance, and useful knowledge is carried by the pri...

Circular PCA

Experimental time courses often reveal a nonlinear behaviour. Analysing these nonlinearities is even more challenging when the observed phenomenon is cyclic or oscillatory. This means, in general, that the data describe a circular trajectory which is caused by periodic gene regulation. Nonlinear PCA (NLPCA) is used to approximate this trajectory by a curve referred to as nonlinear component. Wh...

PCA Notes

1.1 Power iteration We would like to recover the largest singular value σ 1 , and corresponding singular vectors u 1 and v 1. To simplify the discussion, assume that σ 2 < σ 1 We consider the following optimization problem min p∈R n ,q∈R m A − pq T 2 F s.t.p 2 = 1 Let f (p, q) = A − pq T 2 F. The optimizers are shown to be (p * , q *) = (u 1 , σ 1 v 1) (up to a sign change). This problem can be...

Bio-reactor monitoring with multiway-PCA and Model Based-PCA