| Project/Area Number |
24650150
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Statistical science
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| Research Institution | Nara Women's University |
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Principal Investigator |
KUME Kenji 奈良女子大学, 名誉教授 (10107344)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| 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 / 線形フィルター / 特異スペクトル解析法 / 完全再構成フィルタ / アダプティブ・フィルタ / 画像分解 / 主成分分析 / クラスター解析 / 時系列データ |
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| 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.
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