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

Saito S, Hirata Y, Sasahara K, Suzuki H - PLoS ONE (2015)

Bottom Line: 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.Moreover, we present several results and insights from experiments using real data from Twitter.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan.

ABSTRACT
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.

No MeSH data available.


Related in: MedlinePlus

Iterative algorithm for Time Evolving Nonnegative Matrix Factorisation (TENMF).TENMF is an extension of Nonnegative Matrix Factorisation, to track the time-evolution of the W(tk)s. Starting from initialised W(t0) and H(t0), we update as introduced in Ref. [16] and the method section. From the second time step, we use the decomposed result of one step back as initial conditions. Here we assume that two consecutive time-sequential matrices have a similarity. Since NMF converges to local optima, the process would result in a convergence to ‘near’ local optima, and would not lose temporal development information, i.e., preserve the similarity to the result of one step back.
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pone.0139085.g001: Iterative algorithm for Time Evolving Nonnegative Matrix Factorisation (TENMF).TENMF is an extension of Nonnegative Matrix Factorisation, to track the time-evolution of the W(tk)s. Starting from initialised W(t0) and H(t0), we update as introduced in Ref. [16] and the method section. From the second time step, we use the decomposed result of one step back as initial conditions. Here we assume that two consecutive time-sequential matrices have a similarity. Since NMF converges to local optima, the process would result in a convergence to ‘near’ local optima, and would not lose temporal development information, i.e., preserve the similarity to the result of one step back.

Mentions: If we simply apply NMF for time-sequential matrices, NMF loses pieces of information on the temporal development, because NMF decomposes the matrices arbitrarily. To solve this time-sequential problem, we propose here a Nonnegative Matrix Factorisation algorithm for time-evolving data. The idea behind Time Evolving Nonnegative Matrix Factorisation (TENMF) is to use W and H at time tk to estimate W and H at time tk+1. Let us denote W and H, at time tk by W(tk) and H(tk). NMF often converges to a local optimal solution, and the solution is highly affected by the initial condition [17–19]. Hence, if we set a seed as W(tk) and H(tk), the next (W(tk+1),H(tk+1)) would converge to a ‘near’ local optimal solution, i.e. the locally optimal solution whose basin contains the current matrices. This convergence preserves the connection between (W(tk),H(tk)) and (W(tk+1),H(tk+1)). Applying the algorithm of NMF, introduced in the method section, the discussion above yields an algorithm as Fig 1.


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

Saito S, Hirata Y, Sasahara K, Suzuki H - PLoS ONE (2015)

Iterative algorithm for Time Evolving Nonnegative Matrix Factorisation (TENMF).TENMF is an extension of Nonnegative Matrix Factorisation, to track the time-evolution of the W(tk)s. Starting from initialised W(t0) and H(t0), we update as introduced in Ref. [16] and the method section. From the second time step, we use the decomposed result of one step back as initial conditions. Here we assume that two consecutive time-sequential matrices have a similarity. Since NMF converges to local optima, the process would result in a convergence to ‘near’ local optima, and would not lose temporal development information, i.e., preserve the similarity to the result of one step back.
© Copyright Policy
Related In: Results  -  Collection

License
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getmorefigures.php?uid=PMC4587956&req=5

pone.0139085.g001: Iterative algorithm for Time Evolving Nonnegative Matrix Factorisation (TENMF).TENMF is an extension of Nonnegative Matrix Factorisation, to track the time-evolution of the W(tk)s. Starting from initialised W(t0) and H(t0), we update as introduced in Ref. [16] and the method section. From the second time step, we use the decomposed result of one step back as initial conditions. Here we assume that two consecutive time-sequential matrices have a similarity. Since NMF converges to local optima, the process would result in a convergence to ‘near’ local optima, and would not lose temporal development information, i.e., preserve the similarity to the result of one step back.
Mentions: If we simply apply NMF for time-sequential matrices, NMF loses pieces of information on the temporal development, because NMF decomposes the matrices arbitrarily. To solve this time-sequential problem, we propose here a Nonnegative Matrix Factorisation algorithm for time-evolving data. The idea behind Time Evolving Nonnegative Matrix Factorisation (TENMF) is to use W and H at time tk to estimate W and H at time tk+1. Let us denote W and H, at time tk by W(tk) and H(tk). NMF often converges to a local optimal solution, and the solution is highly affected by the initial condition [17–19]. Hence, if we set a seed as W(tk) and H(tk), the next (W(tk+1),H(tk+1)) would converge to a ‘near’ local optimal solution, i.e. the locally optimal solution whose basin contains the current matrices. This convergence preserves the connection between (W(tk),H(tk)) and (W(tk+1),H(tk+1)). Applying the algorithm of NMF, introduced in the method section, the discussion above yields an algorithm as Fig 1.

Bottom Line: 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.Moreover, we present several results and insights from experiments using real data from Twitter.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, Japan.

ABSTRACT
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.

No MeSH data available.


Related in: MedlinePlus