Hybrid Metric-Induced Nonnegative Matrix Factorization

NMF is a promising feature representation method for data analysis. Matrix decomposition losses can be described using different metrics, based on which different NMF algorithms can be developed. However, a small Euclidean distance metric is not guaranteed to have a small cosine similarity metric, and vice versa. To overcome the shortcomings of these metrics, we integrate these two metrics to present a novel hybrid metric-induced NMF (HMNMF) model. The update rules for the HMNMF algorithm are obtained using the gradient descent method to resolve the optimization problem. The proposed algorithm is proven to be convergent, which implies that it is reasonable and stable. The proposed HMNMF approach is compared with different metric-induced NMF algorithms for face recognition, the experimental results confirm the effectiveness and good performance of the proposed algorithm.