Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics

Compressed sensing is an alternative to Shannon/Nyquist sampling for acquiring sparse or compressible signals. Sparse coding represents a signal as a sparse linear combination of atoms, which are elementary signals derived from a predefined dictionary. Compressed sensing, sparse approximation, and dictionary learning are topics similar to sparse coding. Matrix completion is the process of recovering a data matrix from a subset of its entries, extending the principles of compressed sensing and sparse approximation. Nonnegative matrix factorization is a low-rank matrix factorization technique for nonnegative data. All these low-rank matrix factorization techniques are unsupervised learning methods that can be applied to various data analysis tasks, such as dimension reduction, feature extraction, blind source separation, data compression, and knowledge discovery. This paper surveys emerging matrix factorization techniques drawing significant attention within machine learning, signal processing, and statistics. The discussed topics include compressed sensing, dictionary learning, sparse representation, matrix completion and recovery, nonnegative matrix factorization, and CUR matrix decomposition within the machine learning framework.