Tight Semi-Nonnegative Matrix Factorization
This work addresses matrix factorization for applications in biology, image processing, and information retrieval, but appears incremental as it builds on nonnegative matrix factorization.
The authors tackled the problem of matrix factorization by introducing a multi-objective optimization approach that approximates a data matrix with conical combinations of templates, ensuring uniqueness without requiring nonnegativity or convex combinations of the original data.
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization. A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix. The templates are chosen so that as far as possible only the initial data set can be represented this way. However, the templates are not required to be nonnegative nor convex combinations of the original data.