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• W2957492749 abstract "Union of Subspaces (UoS) is a popular model to describe the underlying low-dimensional structure of data. The fine details of UoS structure can be described in terms of canonical angles (also known as principal angles) between subspaces, which is a well-known characterization for relative subspace positions. In this paper, we prove that random projection with the so-called Johnson-Lindenstrauss (JL) property approximately preserves canonical angles between subspaces with overwhelming probability. This result indicates that random projection approximately preserves the UoS structure. Inspired by this result, we propose a framework of Compressed Subspace Learning (CSL), which enables to extract useful information from the UoS structure of data in a greatly reduced dimension. We demonstrate the effectiveness of CSL in various subspace-related tasks such as subspace visualization, active subspace detection, and subspace clustering." @default.
• W2957492749 created "2019-07-23" @default.
• W2957492749 creator A5011030324 @default.
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• W2957492749 date "2019-07-14" @default.
• W2957492749 modified "2023-09-23" @default.
• W2957492749 title "Compressed Subspace Learning Based on Canonical Angle Preserving Property" @default.
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• W2957492749 doi "https://doi.org/10.48550/arxiv.1907.06166" @default.
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