Eigenfilter interpretation of singular spectrum analysis and its application

2014 Fiscal Year Final Research Report

• Project/Area Number: 24650150
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: Nara Women's University
• Principal Investigator: KUME Kenji 奈良女子大学, 名誉教授 (10107344)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 特異スペクトル解析 / 線形フィルタ / 時系列解析 / 画像処理

Outline of Final Research Achievements

Singular spectrum analysis (SSA) is an algorithm to analyse the time series or　the digital image data. Conventional treatment of SSA is based on the singular　value decomposition of the trajectory matrix. In this study, I have shown that the SSA can be interpreted as the adaptive generation of the complete set of linear filters and their two-step point-symmetric operation to the original data. From this interpretation, ① SSA is reformulated with the filtering interpretation, ②it becomes to be quite easy to extend the SSA algorithm to higher dimensional data with arbitrary dimension, ③the relationship between the SSA decomposition and the spectral structure of the original data becomes to be clearer, ④the clustering analysis of the decomposed time series becomes to be easy, ⑤ SSA algorithm is extended by introducing the weight factor, and it opens the possibility for the better forecasting algorithm with SSA.

Free Research Field

データ科学