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Non-negative Matrix Factorization of a set of Economic Time Series with Graph Based Smoothing of Basis Vectors and Sparseness of the Coefficients | IEEE Conference Publication | IEEE Xplore

Non-negative Matrix Factorization of a set of Economic Time Series with Graph Based Smoothing of Basis Vectors and Sparseness of the Coefficients


Abstract:

In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful basis vector for the set of data, and indi...Show More

Abstract:

In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful basis vector for the set of data, and indicate which data use which basis vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the basis matrix, and the basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the basis matrix may not be smooth. We think that the basis vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, basis vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for basis vectors. However, the proposed method introduces the sparsity for coefficient vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient vectors and the smoothness for the basis vectors, can extract the smooth basis vectors and the original economical data are approximated as the weighted sum of the few bases vectors. This allows us to discover...
Date of Conference: 11-14 October 2020
Date Added to IEEE Xplore: 14 December 2020
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Conference Location: Toronto, ON, Canada
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I. Introduction

Extracting economic characteristics of economic data is a useful way to understand social conditions. For example, there is a study that examines the factors of stock and bond returns and finds general fluctuations in the stock and bond markets [1]. Economic data are time-series data, and there are several methods for filtering such time-series data, including Hodrick-Prescott (HP) filtering [2] and the exponential smoothing filter [3]. Furthermore, Yamada showed that the two smoothing methods can be regarded as a type of graph spectral filter [4].

Select All
1.
E. F. Fama and K. R. French, "Common risk factors in the returns on stocks and bonds", Journal of Financial Economics, pp. 3-56, 1993.
2.
R. J. Hodrick and E. C. Prescott, "Postwar us business cycles: an empirical investigation", Journal of Money credit and Banking, pp. 1-16, 1997.
3.
R. G. King and S. Rebelo, "Appendix to ”low frequency filtering and real business cycles", Journal of Economic dynamics and Controls, vol. 17, pp. 207-231, 1993.
4.
H. Yamada, "A smoothing method that looks like the hodrick–prescott filter", Econometric Theory, pp. 1-21, 2020.
5.
D. D. Lee and H. S. Seung, "Learning the parts of objects by non-negative matrix factorization", Nature, vol. 401, no. 6755, pp. 788-791, 1999.
6.
T. Kawamoto, K. Hotta, T. Mishima, J. Fujiki, M. Tanaka and T. Kurita, "Estimation of single tones from chord sounds using non-negative matrix factorization", Neural Network World, vol. 10, no. 3, pp. 429-436, 2000.
7.
K. Watanabe and T. Kurita, "Automatic factorization of biological signals measured by fluorescence correlation spectroscopy using non-negative matrix factorization", International Conference on Neural Information Processing, pp. 798-806, 2007.
8.
K. Watanabe, A. Hidaka and T. Kurita, "Automatic factorization of biological signals by using boltzmann non-negative matrix factorization", 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), pp. 1122-1128, 2008.
9.
K. Watanabe, A. Hidaka, N. Otsu and T. Kurita, "Automatic analysis of composite physical signals using non-negative factorization and information criterion", PloS one, vol. 7, no. 3, 2012.
10.
D. Cai, X. He, J. Han and T. S. Huang, "Graph regularized nonnegative matrix factorization for data representation", IEEE transactions on pattern analysis and machine intelligence, vol. 33, no. 8, pp. 1548-1560, 2010.
11.
D. Cai, X. He, X. Wu and J. Han, "Non-negative matrix factorization on manifold", 2008 Eighth IEEE International Conference on Data Mining, pp. 63-72, 2008.
12.
F. R. K. Chung, Spectral Graph Theory., American Mathematical Society, 1997.
13.
J. Eggert and E. Korner, "Sparse coding and nmf", 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No. 04CH37541), vol. 4, pp. 2529-2533, 2004.
14.
J. Le Roux, F. J. Weninger and J. R. Hershey, "Sparse nmf–half-baked or well done?", Mitsubishi Electric Research Labs (MERL) Cambridge MA USA Tech. Rep. no. TR2015-023, vol. 11, pp. 13-15, 2015.
15.
X. Lu, H. Wu, Y. Yuan, P. Yan and X. Li, "Manifold regularized sparse nmf for hyperspectral unmixing", IEEE Transactions on Geoscience and Remote Sensing, vol. 51, no. 5, pp. 2815-2826, 2012.
16.
R. de Fréin, K. Drakakis, S. Rickard and A. Cichocki, "Analysis of financial data using non-negative matrix factorization" in International Mathematical Forum, Journals of Hikari Ltd, vol. 3, pp. 1853-1870, 2008.
17.
P. Paatero and U. Tapper, "Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values", Environmetrics, vol. 5, no. 2, pp. 111-126, 1994.
18.
W. H. Lawton and E. A. Sylvestre, "Self modeling curve resolution", Technometrics, vol. 13, no. 3, pp. 617-633, 1971.
19.
D. D. Lee and H. S. Seung, "Algorithms for non-negative matrix factorization", Advances in Neural Information Processing Systems 13, pp. 556-562, 2001, [online] Available: http://papers.nips.cc/paper/1861-algorithms-for-non-negative-matrix-factorization.pdf.
20.
S. Sarkka, Bayesian filtering and smoothing., Cambridge University Press, vol. 3, 2013.
21.
Z. Zhang, Y. Xu, J. Yang, X. Li and D. Zhang, "A survey of sparse representation: algorithms and applications", IEEE access, vol. 3, pp. 490-530, 2015.
22.
D. J. Field, "What is the goal of sensory coding?", Neural computation, vol. 6, no. 4, pp. 559-601, 1994.

References

References is not available for this document.