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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.


Simulation of TENMF for merging and division in a matrix.TENMF learns the merging and division of clusters. (a), (c) Snapshots of time-sequential matrices V(tk)s describing (a) merging and (c) division of clusters. (a) There are three clusters at time t = 1, which are represented by three blocks aligned diagonally in the matrix. As time evolves, two of the three clusters gradually merge with each other, and finally constitute a single cluster at time t = 100. (c) The reversed sequence of the matrices in (a). (b), (d) Snapshots of W(tk)s decomposed by TENMF from the time-sequential matrices shown in (a) and (c), respectively. (d) Our algorithm tracks the division of the original matrices, since the 2nd column, which is filled with relatively low values, assume the role of tracking the growth of the elements in the cluster, whereas the corresponding part of the original cluster, a part of 1st column, disappears gradually. In addition, our algorithm can track the merging of the original.
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pone.0139085.g003: Simulation of TENMF for merging and division in a matrix.TENMF learns the merging and division of clusters. (a), (c) Snapshots of time-sequential matrices V(tk)s describing (a) merging and (c) division of clusters. (a) There are three clusters at time t = 1, which are represented by three blocks aligned diagonally in the matrix. As time evolves, two of the three clusters gradually merge with each other, and finally constitute a single cluster at time t = 100. (c) The reversed sequence of the matrices in (a). (b), (d) Snapshots of W(tk)s decomposed by TENMF from the time-sequential matrices shown in (a) and (c), respectively. (d) Our algorithm tracks the division of the original matrices, since the 2nd column, which is filled with relatively low values, assume the role of tracking the growth of the elements in the cluster, whereas the corresponding part of the original cluster, a part of 1st column, disappears gradually. In addition, our algorithm can track the merging of the original.

Mentions: Fig 3 shows the result of the experiment in the second setting. In order to simulate merging, we firstly generate three blocks, and we gradually increase random values in two other blocks so that there seem to exist two blocks at the final state. For simulating division, we perform the same procedure backwards.


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)

Simulation of TENMF for merging and division in a matrix.TENMF learns the merging and division of clusters. (a), (c) Snapshots of time-sequential matrices V(tk)s describing (a) merging and (c) division of clusters. (a) There are three clusters at time t = 1, which are represented by three blocks aligned diagonally in the matrix. As time evolves, two of the three clusters gradually merge with each other, and finally constitute a single cluster at time t = 100. (c) The reversed sequence of the matrices in (a). (b), (d) Snapshots of W(tk)s decomposed by TENMF from the time-sequential matrices shown in (a) and (c), respectively. (d) Our algorithm tracks the division of the original matrices, since the 2nd column, which is filled with relatively low values, assume the role of tracking the growth of the elements in the cluster, whereas the corresponding part of the original cluster, a part of 1st column, disappears gradually. In addition, our algorithm can track the merging of the original.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4587956&req=5

pone.0139085.g003: Simulation of TENMF for merging and division in a matrix.TENMF learns the merging and division of clusters. (a), (c) Snapshots of time-sequential matrices V(tk)s describing (a) merging and (c) division of clusters. (a) There are three clusters at time t = 1, which are represented by three blocks aligned diagonally in the matrix. As time evolves, two of the three clusters gradually merge with each other, and finally constitute a single cluster at time t = 100. (c) The reversed sequence of the matrices in (a). (b), (d) Snapshots of W(tk)s decomposed by TENMF from the time-sequential matrices shown in (a) and (c), respectively. (d) Our algorithm tracks the division of the original matrices, since the 2nd column, which is filled with relatively low values, assume the role of tracking the growth of the elements in the cluster, whereas the corresponding part of the original cluster, a part of 1st column, disappears gradually. In addition, our algorithm can track the merging of the original.
Mentions: Fig 3 shows the result of the experiment in the second setting. In order to simulate merging, we firstly generate three blocks, and we gradually increase random values in two other blocks so that there seem to exist two blocks at the final state. For simulating division, we perform the same procedure backwards.

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.