Abstract Principal Component Analysis (PCA) is one of the most widely used data analysis methods in machine learning and AI. This manuscript focuses on mathematical foundation classical PCA its application to a small-sample-size scenario large dataset high-dimensional space scenario. In particular, we discuss simple method that can be approximate latter case. also help kernel or (KPCA) for larg...

A proper circular-arc (PCA) model is a pairM = (C,A) where C is a circle and A is a family of inclusion-free arcs on C in which no two arcs of A cover C. A PCA model U is a (c, `, d, ds)-CA model when C has circumference c, all the arcs in A have length `, all the extremes of the arcs in A are at a distance at least d, and all the beginning points of the arcs in A are at a distance at least d+ ...

Algorithm 1 Suggesting Compatible Colors 1: procedure COMPATIBLECOLORS(palette t, index k, #cands Ncand, #samples Nsample, threshold (τ, κ)) 2: . Sampling candidate’s HSVs 3: f ← COMPUTEHUEPROBABILITY(t, k) . Eq. 3 or Eq. 4 4: hi← SAMPLINGFROMHUEPROB( f , Nsample) 5: si ∼N (μs,σs) . §4.2 6: vi ∼N (μv,σv) . §4.2 7: . Compute rating 8: for i = 1→ m do 9: ci← (hi, si,vi) 10: Ccand i ← COMPATIBLECA...

Mahalanobis distance of covariate means between treatment and control groups is often adopted as a balance criterion when implementing rerandomization strategy. However, this may not work well for high-dimensional cases because it balances all orthogonalized covariates equally. We propose using principal component analysis (PCA) to identify proper subspaces in which should be calculated. Not on...