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Register a new userRelative Pairwise Relationship Constrained Non-negative Matrix Factorisation
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Shuai Jiang
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and ignore the relationship among pairwise rows or columns. In many cases, such pairwise relationship enables better factorisation, for example, image clustering and recommender systems. In this paper, we propose an algorithm named, Relative Pairwise Relationship constrained Non-negative Matrix Factorisation (RPR-NMF), which places constraints over relative pairwise distances amongst features by imposing penalties in a triplet form. Two distance measures, squared Euclidean distance and Symmetric divergence, are used, and exponential and hinge loss penalties are adopted for the two measures respectively. It is well known that the so-called multiplicative update rules result in a much faster convergence than gradient descend for matrix factorisation. However, applying such update rules to RPR-NMF and also proving its convergence is not straightforward. Thus, we use reasonable approximations to relax the complexity brought by the penalties, which are practically verified. Experiments on both synthetic datasets and real datasets demonstrate that our algorithms have advantages on gaining close approximation, satisfying a high proportion of expected constraints, and achieving superior performance compared with other algorithms.
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We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and non-probabilistic approaches, and do not require additional samples to estimate the posterior. We show that in particular for matrix tri-factorisation convergence is difficult, but our variational Bayesian approach offers a fast solution, allowing the tri-factorisation approach to be used more effectively.
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Obtaining high-quality heart and lung sounds enables clinicians to accurately assess a newborns cardio-respiratory health and provide timely care. However, noisy chest sound recordings are common, hindering timely and accurate assessment. A new Non-negative Matrix Co-Factorisation-based approach is proposed to separate noisy chest sound recordings into heart, lung, and noise components to address this problem. This method is achieved through training with 20 high-quality heart and lung sounds, in parallel with separating the sounds of the noisy recording. The method was tested on 68 10-second noisy recordings containing both heart and lung sounds and compared to the current state of the art Non-negative Matrix Factorisation methods. Results show significant improvements in heart and lung sound quality scores respectively, and improved accuracy of 3.6bpm and 1.2bpm in heart and breathing rate estimation respectively, when compared to existing methods.
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