Searching and mining biomedical literature databases are common ways of generating scientific hypotheses by biomedical researchers. Clustering can assist researchers to form hypotheses by seeking valuable information from grouped documents effectively. Although a large number of clustering algorithms are available, this paper attempts to answer the question as to which algorithm is best suited ...

In essence, the network is a way of encoding information underlying social management system. Ubiquitous systems rarely exist alone and have dynamic complexity. For complex systems, it difficult to extract represent multi-angle features data only by using non-negative matrix factorization. Existing deep NMF models integrating multi-layer struggle explain results obtained after mid-layer NMF. th...

We present a converged algorithm for Tikhonov regularized nonnegative matrix factorization (NMF). We specially choose this regularization because it is known that Tikhonov regularized least square (LS) is the more preferable form in solving linear inverse problems than the conventional LS. Because an NMF problem can be decomposed into LS subproblems, it can be expected that Tikhonov regularized...

Non-negative Matrix Factorization (NMF) and Probabilistic Latent Semantic Indexing (PLSI) have been successfully applied to document clustering recently. In this paper, we show that PLSI and NMF (with the I-divergence objective function) optimize the same objective function, although PLSI and NMF are different algorithms as verified by experiments. This provides a theoretical basis for a new hy...

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex...

The objective of single-channel source separation is to accurately recover source signals from mixtures. Non-negative matrix factorization (NMF) is a popular approach for this task, yet previous NMF approaches have not optimized directly this objective, despite some efforts in this direction. Our paper introduces discriminative training of the NMF basis functions such that, given the coefficien...

A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernelbased orthogonal multiplicative update rules to solve the subspace clustering problem. In nonlin...

Performance of Non-negative Matrix Factorisation (NMF) can be diminished when the underlying factors consist of elements that overlap in the matrix to be factorised. The use of `0 sparsity may improve NMF, however such approaches are generally limited to Euclidean distance. We have previously proposed a stepwise `0 method for Hellinger distance, leading to improved sparse NMF. We extend sparse ...

Nonnegative Matrix Factorization (NMF) techniques has aroused considerable interests from the field of artificial intelligence in recent years because of its good interpretability and computational efficiency. However, in many real world applications, the data features usually evolve over time smoothly. In this case, it would be very expensive in both computation and storage to rerun the whole ...

Nonnegative matrix factorization (NMF) approximates a nonnegative matrix by the product of two low-rank nonnegative matrices. Since it gives semantically meaningful result that is easily interpretable in clustering applications, NMF has been widely used as a clustering method especially for document data, and as a topic modeling method. We describe several fundamental facts of NMF and introduce...