# Cross-product Penalized Component Analysis (XCAN)

## TL;DR

XCAN is a flexible sparse matrix factorization method that balances variance maximization and structural preservation, enabling versatile data exploration across disciplines.

## Contribution

Introduces XCAN, a novel cross-product penalized component analysis method that extends previous PCA frameworks for improved data exploration.

## Key findings

- Effective in diverse data exploration tasks
- Balances variance and structure in factorization
- Applicable across multiple disciplines

## Abstract

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.