Sparse Beta-Divergence Tensor Factorization Library

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Based off of this beta-NTF project this library is specially-built to handle tensors where the sparsity implies missing data. Most libraries are formulated around the handling of images which are dense or nearly dense. However, we’re interested in factorizing highly sparse (>99.9%) tensors and have written NTFLib for this use case.

Currently, we only support rank-3 tensors, but extending to this to higher rank tensors is fairly straightforward.

The algorithm implemented by beta_ntf features standard multiplicative updates minimizing β-divergence, which were recently shown to guarantee a decrease of the cost-function at each step. For recent references on the topic, check for example:

  • A. Cichocki, R. Zdunek, A. H. Phan, and S. Amari, Nonnegative matrix and tensor factorizations : Applications to exploratory multi-way data analysis and blind source separation, Wiley Publishing, September 2009.
  • C. Févotte and J. Idier, Algorithms for nonnegative matrix factorization with the beta-divergence, Neural Computation 23 (2011), no. 9, 2421–2456.
  • Virtanen, Tuomas, Monaural Sound Source Separation by Perceptually Weighted Non-Negative Matrix Factorization, Technical report, Tampere University of Technology, Institute of Signal Processing, 2007.