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...

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...

since they may expose to inorganic pollutants, drinking waters should be investigated andmonitored in industrialized regions. in this study, drinking water samples taken from eight different locationsin heavily industrialized region of turkey, namely marmara region, were analyzed to determine heavy metaland harmful trace element (fe, co, cd, hg, pb, zn, sb, cu, ba, mo, cr, mn and v) concentrati...

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...