Exploring the Relationship between Conic Affinity of NMF Dictionaries and Speech Enhancement Metrics

Nonnegative Matrix Factorization(NMF) has been successfully used in speech enhancement. In the training phase NMF produces speech and noise dictionaries, whose elements are non-negative, while in the testing phase it estimates a non-negative activation matrix to express the enhanced speech signal as a conic combination of those dictionaries. This nonnegativity property enables us to interpret them as convex polyhedral cones that lie in the positive orthant. Conic affinity could be useful when designing NMF-based systems for unseen noise conditions, which operate by selecting an appropriate noise dictionary amongst a pool of potential candidates. To that end, we examine two conic affinity measures, one based on cosine similarity, while the other is based on euclidean distance from a point to a cone. Moreover, we construct an algorithm to show that conic affinity correlates with speech enhancement performance metrics.