estimated relevancy. Outlier-resistant variants of PCA have also been proposed, based on L1-norm formulations (L1-PCA). Robust principal component analysis (RPCA) via decomposition in low-rank and sparse matrices is a modification of PCA that works well with respect to grossly corrupted observations. Similar techniques Independent component analysis Independent component analysis (ICA) is directed to similar problems as principal component analysis, but finds additively separable components rather than successive approximations. Network component analysis Given a matrix , it tries to decompose it into two matrices such that . A key difference from techniques such as PCA and ICA is that some of the entries of are constrained to be 0. Here is termed the regulatory layer. While in general such a decomposition can have multiple solutions, they prove that if the following conditions are satisfied : has full column rank Each column of must have at least zeroes where is the number of columns of (or alternatively the number of rows of ). The justification for this criterion is that if a node is removed from the regulatory layer along with all the output nodes connected to it, the result must still be characterized by a connectivity matrix with full column rank. must have full row rank. then the decomposition is unique up to multiplication by a scalar. Discriminant analysis of principal components Discriminant analysis of principal components (DAPC) is a multivariate method used to identify and describe clusters of genetically related individuals. Genetic variation is partitioned into two components: variation between groups and within groups, and it maximizes the former. Linear discriminants are linear combinations of alleles which best separate the clusters. Alleles that most contribute to this discrimination are therefore those that are the most markedly different across groups. The contributions of alleles to the groupings identified by DAPC can allow identifying regions of the genome driving the genetic divergence among groups In DAPC, data is first transformed using a principal components analysis (PCA) and subsequently clusters are identified using discriminant analysis (DA). A DAPC can be realized on R using the package Adegenet. (more info: adegenet on the web) Directional component analysis Directional component analysis (DCA) is a method used in the atmospheric sciences for analysing multivariate datasets. Like PCA, it allows for dimension reduction, improved visualization and improved interpretability of large data-sets. Also like PCA, it is based on a covariance matrix derived from the input dataset. The