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A sequential majorization method for approximating weighted time series of finite rank

A sequential majorization method for approximating weighted time series of finite rank
A sequential majorization method for approximating weighted time series of finite rank
The low-rank Hankel matrix optimization has become one of the main approaches to the signal extraction from noisy time series of finite rank. The approach is particularly effective if different weights are enforced to the data points to reflect their relative importance. Two guiding principles for developing such an approach are (i) the Hankel matrix optimization should be computationally tractable, and (ii) the objective in the optimization should be a close approximation to the original weighted least-squares. In this paper, we introduce a sequential approximation that satisfies (i) and (ii) based on the technique of majorization. A new approximation is constructed as soon as a new iterate is computed from the previous approximation and it makes use of the latest gradient information of the objective, leading to more accurate an approximation to the objective.The resulting sub problem bears a similar structure to an existing scheme and hence can be efficiently solved.Convergence of the sequential majorization method (\texttt{SMM}) is guaranteed provided that the solution of the sub problem satisfies a sandwich inequality.We also compare \texttt{SMM} with two leading methods in literature on real-life problems.Significant improvement is observed in some cases.
Singular spectrum analysis, time series of finite rank, Hankel matrix, majorization method
615-630
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Shen, Jian
7d3b8471-60c8-4398-879d-7733b5083fae
Xiu, Naihua
8e84e128-101b-4b57-aa47-e6002470ae9d
Qi, Hou-Duo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Shen, Jian
7d3b8471-60c8-4398-879d-7733b5083fae
Xiu, Naihua
8e84e128-101b-4b57-aa47-e6002470ae9d

Qi, Hou-Duo, Shen, Jian and Xiu, Naihua (2018) A sequential majorization method for approximating weighted time series of finite rank. Statistics and Its Interface, 11 (4), 615-630. (doi:10.4310/SII.2018.v11.n4.a6).

Record type: Article

Abstract

The low-rank Hankel matrix optimization has become one of the main approaches to the signal extraction from noisy time series of finite rank. The approach is particularly effective if different weights are enforced to the data points to reflect their relative importance. Two guiding principles for developing such an approach are (i) the Hankel matrix optimization should be computationally tractable, and (ii) the objective in the optimization should be a close approximation to the original weighted least-squares. In this paper, we introduce a sequential approximation that satisfies (i) and (ii) based on the technique of majorization. A new approximation is constructed as soon as a new iterate is computed from the previous approximation and it makes use of the latest gradient information of the objective, leading to more accurate an approximation to the objective.The resulting sub problem bears a similar structure to an existing scheme and hence can be efficiently solved.Convergence of the sequential majorization method (\texttt{SMM}) is guaranteed provided that the solution of the sub problem satisfies a sandwich inequality.We also compare \texttt{SMM} with two leading methods in literature on real-life problems.Significant improvement is observed in some cases.

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Accepted/In Press date: 22 December 2017
e-pub ahead of print date: 19 September 2018
Keywords: Singular spectrum analysis, time series of finite rank, Hankel matrix, majorization method

Identifiers

Local EPrints ID: 416837
URI: https://eprints.soton.ac.uk/id/eprint/416837
PURE UUID: 8f50786f-499f-4667-bf3d-c63885f458b0
ORCID for Hou-Duo Qi: ORCID iD orcid.org/0000-0003-3481-4814

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Date deposited: 11 Jan 2018 17:30
Last modified: 14 Mar 2019 05:20

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