# Matrix Cofactorization for Joint Representation Learning and Supervised Classification -- Application to Hyperspectral Image Analysis

## TL;DR

This paper introduces a matrix cofactorization approach that jointly models representation learning and supervised classification, specifically applied to hyperspectral image analysis, unifying unmixing and classification tasks.

## Contribution

It proposes a novel hierarchical matrix cofactorization framework coupling representation learning with supervised classification, with a convergence-guaranteed optimization algorithm.

## Key findings

- Effective on synthetic data
- Successful application to hyperspectral images
- Unifies unmixing and classification techniques

## Abstract

Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this paper, a method coupling these two approaches is designed using a matrix cofactorization formulation. Each task is modeled as a factorization matrix problem and a term relating both coding matrices is then introduced to drive an appropriate coupling. The link can be interpreted as a clustering operation over a low-dimensional representation vectors. The attribution vectors of the clustering are then used as features vectors for the classification task, i.e., the coding vectors of the corresponding factorization problem. A proximal gradient descent algorithm, ensuring convergence to a critical point of the objective function, is then derived to solve the resulting non-convex non-smooth optimization problem. An evaluation of the proposed method is finally conducted both on synthetic and real data in the specific context of hyperspectral image interpretation, unifying two standard analysis techniques, namely unmixing and classification.