  Matrix factorization methods are extensively employed to understand complex
data. In this paper, we introduce the cross-product penalized component
analysis (XCAN), a sparse matrix factorization based on the optimization of a
loss function that allows a trade-off between variance maximization and
structural preservation. The approach is based on previous developments,
notably (i) the Sparse Principal Component Analysis (SPCA) framework based on
the LASSO, (ii) extensions of SPCA to constrain both modes of the
factorization, like co-clustering or the Penalized Matrix Decomposition (PMD),
and (iii) the Group-wise Principal Component Analysis (GPCA) method. The result
is a flexible modeling approach that can be used for data exploration in a
large variety of problems. We demonstrate its use with applications from
different disciplines.
