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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

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].

References

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