PIECEWISE CONSTANT NONNEGATIVE MATRIX FACTORIZATION

In this paper we propose a non-negative matrix factorization (NMF) model with piecewise-constant activation coefficients. This structure is enforced using a total variation penalty on the rows of the activation matrix. The resulting optimiza-tion problem is solved with a majorization-minimization pro-cedure. The proposed algorithm is well suited to analyze data explained by underlying piecewise-constant sequences of states. Its properties are first illustrated using synthetic data. We then use it to solve a video structuring problem that involves both segmentation and clustering tasks. An improve-ment over a state-of-the-art temporally smoothed NMF algo-rithm of both clustering and segmentation quality measures is observed. Index Terms—Non-negativematrix factorization, tempo-ral smoothing, total variatio