Automatic Analysis of Composite Physical Signals Using Non-Negative Factorization and Information Criterion

Watanabe, Kenji; Hidaka, Akinori; Otsu, Nobuyuki; Kurita, Takio

doi:10.1371/journal.pone.0032352

Cited by 7 publications

(5 citation statements)

References 25 publications

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“…In general, clustering problems such as the K-means algorithm, EM algorithm, and Self-Organising Map have an issue that the number of clusters should be set manually in advance, as in the case of NMF. For NMF, the rank decision problem has been studied [ 21 – 24 ]. Our framework, however, requires prior knowledge about the data in advance in order to set the rank.…”

Section: Discussionmentioning

confidence: 99%

“…Thus, NMF has been studied from many perspectives [ 15 , 60 ]. The foundation of NMF has been researched, such as the algorithm [ 16 , 61 – 63 ], the rank decision problem, including sparseness constraints [ 21 – 24 ], and the initialising problem [ 17 – 19 ]. NMF has been applied to clustering problems [ 64 , 65 ], such as document [ 66 , 67 ], music analysis [ 68 , 69 ], and the community detection problem [ 70 , 71 ].…”

Section: Discussionmentioning

confidence: 99%

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Tracking Time Evolution of Collective Attention Clusters in Twitter: Time Evolving Nonnegative Matrix Factorisation

et al. 2015

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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 tracking matrices decomposed by Nonnegative Matrix Factorisation for time-sequential matrix data, and propose a novel extension of Nonnegative Matrix Factorisation, which we refer to as Time Evolving Nonnegative Matrix Factorisation (TENMF). In our method, we describe users and words posted in some time interval by a matrix, and use several matrices as time-sequential data. Subsequently, we apply Time Evolving Nonnegative Matrix Factorisation to these time-sequential matrices. TENMF can decompose time-sequential matrices, and can track the connection among decomposed matrices, whereas previous NMF decomposes a matrix into two lower dimension matrices arbitrarily, which might lose the time-sequential connection. Our proposed method has an adequately good performance on artificial data. Moreover, we present several results and insights from experiments using real data from Twitter.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Tracking Time Evolution of Collective Attention Clusters in Twitter: Time Evolving Nonnegative Matrix Factorisation

et al. 2015

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“…We can't ensure the repeatability of the results from input data with the true ranks unknown. Previous studies have shown that the rank parameters can be estimated according to the biological experiments or professional knowledge, or based on the statistics of the input data [19]. In our study, we combined the theory of spike firing rate and Takens' embedding theorem to calculate the key parameters.…”

Section: Discussionmentioning

confidence: 99%

Network connectivity revealed through non-negative matrix factorization in rat medial prefrontal cortex during working memory task

Wei¹,

Tian²

2013

2013 6th International IEEE/EMBS Conference on Neural Engineering (NER)

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Working memory (WM) is necessary for higher cognitive functions. To understand the mechanism of WM from the view of network connectivity becomes a hot topic in the field of neuroscience. The purpose of this work is to develop a sparse causal analysis (SCA) based on non-negative matrix factorization (NMF), and to investigate dynamic connections among the multi-channel spikes during WM. 16-channels spikes were obtained from 4 SD rats (10 tasks for each rat) at prefrontal cortex with implanted microelectrode arrays during WM tasks in Y-maze and transformed to continuous series. Spike series in the original recoding space were projected into the sparse space via NMF with the dimensional reduction. The G-causality (GC) values in the sparse space were calculated to analyze the connections among the spikes directly. Furthermore, the causal density (Cd) and global efficiency (E) were selected to describe the network connections quantitatively. The results show that: in the sparse space, the GC increased from 0.028±0.007 at the beginning of the task to the maximum value 0.100±0.022, Cd likewise from 0.235±0.057 to 0.483±0.056 and E from 0.350±0.065 to 0.616±0.058. The values of GC, Cd and E in the sparse space were significant higher than those in the original space, especially the maximum values (p<0.01). These findings could lead to help understanding the mechanism of connections during WM: the connections in the spike networks changed dynamically, and the strongest connection in the brain happened before the behavior. The addition, the sparse causal network method could improve the identification about network connectivity of spikes during WM and might provide an effective analysis for the connectivity of neural signals in cognitive functions.

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“…We next apply the proposed method to the task on factorization of biological signals of protein dynamics in living cells (EGFP) and chemical particle dynamics in an aqueous solution (Rh6G) [17]. Those signals were measured by using fluorescence correlation spectroscopy (FCS) [18].…”

Section: Factorizationmentioning

confidence: 99%

L<inf>p</inf>-regularized optimization by using orthant-wise approach for inducing sparsity

Kobayashi

2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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Sparsity induced in the optimized weights effectively works for factorization with robustness to noises and for classification with feature selection. For enhancing the sparsity, L 1 regularization is introduced into the objective cost function to be minimized. In general, however, L p (p < 1) regularization leads to more sparse solutions than L 1 , though L p regularized problem is difficult to be effectively optimized. In this paper, we propose a method to efficiently optimize the L p regularized problem. The method reduces the L p problem into L 1 regularized one via transforming target variables by the mapping based on L p , and optimizes it by using orthant-wise approach. In the proposed method, the L p problem is directly optimized for computational efficiency without reformulating it into iteratively reweighting scheme. The proposed method is generally applicable to various problems with L p regularization, such as factorization and classification. In the experiments on the classification using logistic regression and factorization based on least squares, the proposed method produces favorable sparse results.

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Automatic Analysis of Composite Physical Signals Using Non-Negative Factorization and Information Criterion

Cited by 7 publications

References 25 publications

Tracking Time Evolution of Collective Attention Clusters in Twitter: Time Evolving Nonnegative Matrix Factorisation

Tracking Time Evolution of Collective Attention Clusters in Twitter: Time Evolving Nonnegative Matrix Factorisation

Network connectivity revealed through non-negative matrix factorization in rat medial prefrontal cortex during working memory task

L<inf>p</inf>-regularized optimization by using orthant-wise approach for inducing sparsity

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