Robust principal component analysis¶

Robust principal component analysis (RPCA) seeks a decomposition of a matrix as a sum of a low-rank and sparse matrix, i.e.,

\[M = L + S,\]

where a balance is sought between the rank of \(L\) and the number of nonzeros in \(S\). Such a balance is (weakly) imposed via convex relaxations of penalties on the number of nonzero singular values of \(L\) and entries of \(S\) to their \(\ell_1\) counterparts. In particular, a solution is sought for the problem

\[\min_{L,S} \| L \|_* + \| \text{vec}(S) \|_1 \text{ such that } M = L + S,\]

where \(\| \cdot \|_*\) denotes the nuclear norm and \(\| \text{vec}(\cdot) \|_1\) denotes the entrywise one-norm.

Python API¶

RPCA(M[, ctrl=None])¶

C++ API¶

class RPCACtrl¶

bool useALM¶

bool usePivQR¶

bool progress¶

Int numPivSteps¶

Int maxIts¶

Real tau¶

Real beta¶

Real rho¶

Real tol¶

RPCACtrl()¶

void RPCA(const ElementalMatrix<F> &M, ElementalMatrix<F> &L, ElementalMatrix<F> &S, const RPCACtrl<Base<F>> &ctrl = RPCACtrl<Base<F>>())¶

C API¶

ElError ElRPCADist_s(ElConstDistMatrix_s M, ElDistMatrix_s L, ElDistMatrix_s S)¶

ElError ElRPCADist_d(ElConstDistMatrix_d M, ElDistMatrix_d L, ElDistMatrix_d S)¶

ElError ElRPCADist_c(ElConstDistMatrix_c M, ElDistMatrix_c L, ElDistMatrix_c S)¶

ElError ElRPCADist_z(ElConstDistMatrix_z M, ElDistMatrix_z L, ElDistMatrix_z S)¶