Nonnegative matrix factorizations are often encountered in data mining applications where they used to explain datasets by a small number of parts. For many these it is desirable that there exists unique nonnegative factorization up trivial modifications given scalings and permutations. This means model parameters uniquely identifiable from the data. Rigidity theory bar joint frameworks field s...

In 1907, Oskar Perron showed that a positive square matrix has a unique largest positive eigenvalue with a positive eigenvector. This result was extended to irreducible nonnegative matrices by Geog Frobenius in 1912, and to irreducible nonnegative tensors and weakly irreducible nonnegative tensors recently. This result is a fundamental result in matrix theory and has found wide applications in ...

Micro-blogging services, such as Twitter, offer opportunities to analyse user behaviour. Discovering and distinguishing behavioural patterns in micro-blogging services is valuable. However, it is difficult and challenging to distinguish users, and to track the temporal development of collective attention within distinct user groups in Twitter. In this paper, we formulate this problem as trackin...

Abstract. Any given nonnegative matrix A ∈ R can be expressed as the product A = UV for some nonnegative matrices U ∈ R and V ∈ R with k ≤ min{m, n}. The smallest k that makes this factorization possible is called the nonnegative rank of A. Computing the exact nonnegative rank and the corresponding factorization are known to be NP-hard. Even if the nonnegative rank is known a priori, no simple ...

We relate some minimax functions of matrices to some spectral functions of matrices. If A is a nonnegative n X n matrix, v(A) is the gametheoretic value of A, and p(A) is the spectral radius of A, then v(A) < p(A). Necessary and sufficient conditions for v(A) = p(A) are given. It follows that if A is nonnegative and irreducible and n > 1, then v(A) < p(A). Also, if, for a real matrix A and a po...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author He Zhang Name of the doctoral dissertation Advances in Nonnegative Matrix Decomposition with Application to Cluster Analysis Publisher School of Science Unit Department of Information and Computer Science Series Aalto University publication series DOCTORAL DISSERTATIONS 127/2014 Field of research Machine Learning Manuscript su...

The original Hopfield neural networks model is adapted so that the weights of the resulting network are time varying. In this paper, the Discrete Hopfield neural networks with weight function matrix DHNNWFM the weight changes with time, are considered, and the stability of DHNNWFM is analyzed. Combined with the Lyapunov function, we obtain some important results that if weight function matrix W...