Soft orthogonal non-negative matrix factorization with sparse representation: Static and dynamic

NMF owns the ability to well interpret practical problems owing to its non-negative elements and surprisingly could dig out data's latent factors as human cognition. However, structures recognized from classic NMF are usually not fully localized and always accompanied with noises. In light of this, we introduce an improved framework called SONMFSR (Soft Orthogonal NMF with Sparse Representation), which makes full use of soft orthogonality and sparsity constraints to tackle such problems in this paper. Related experiments show that SONMFSR can excavate diverse and local structures with compact representations. Motivated by these characteristics, as well as the unprecedented need and further study for dynamic topic model (DTM) for timely event analysis, we then extend static SONMFSR to a novel DTM named SONMFSRd by introducing the constraints of emerging, evolving and fading topics. Extensive experiments on two public corpora also demonstrate the superiority of SONMFSRd to some state-of-the-art DTMs in both topic detection and tracking. In particular, SONMFSRd exhibits great potential in real-world applications, where popular topics in Two Sessions 2015 are captured and traced dynamically for possible insights. Moreover, we also provide theoretical support for the proposed schemes.