| Project/Area Number |
15K13986
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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 |
Communication/Network engineering
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
Yamada Isao 東京工業大学, 工学院, 教授 (50230446)
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| Co-Investigator(Kenkyū-buntansha) |
湯川 正裕 慶應義塾大学, 理工学部(矢上), 准教授 (60462743)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 信号処理 / 部分空間追跡 / 凸最適化 |
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| Outline of Final Research Achievements |
The goal of this project has been to establish newly a robust as well as efficient adaptive subspace tracking algorithm for broader data-science applications. To keep the orthogonality among the estimated eigenvectors under severely noisy situation, we first analyzed and resolve a certain instability issue observed in an algorithm [Nguyen,Yamada 2013]. We then genelalized this algorithm to enhance the interpretability of the estimated eigenvectors by promoting their sparseness. Numerical experiments demonstrate that the proposed algorithm (i) can improve the subspace tracking performance and (ii) can propote the interpretability of the estimate of the principal generalized eigenvector. Moreover, we also investigated certain closely related parameter estimation and signal recovery problems to the sparsity aware subspace tracking problems.
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| Academic Significance and Societal Importance of the Research Achievements |
部分空間追跡は、オンライン型アルゴリズムであり、ビッグデータの分析に適用可能にした「主成分分析の一般化」と考えてよい。本プロジェクトでは、[Nguyen,Yamada 2013]で稀に観測されていた数値的不安定性の要因特定と不安定性を解消する簡易な手法を確立したばかりでなく、エル１ノルムをペナルティ項に持つ新しいオンラインアルゴリズムに拡張することにより、推定された固有ベクトルの可解釈性が高めることに成功した。更に上記課題に相補的なパラメータ推定・信号復元問題について検討し、大きな成果を得ることができた。
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