Principal angles preserving property of Gaussian random projection for subspaces

Jiao, Yuchen; Li, Gen; Gu, Yuantao

doi:10.1109/globalsip.2017.8308656

Cited by 3 publications

(3 citation statements)

References 24 publications

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“…Recent works [44,45] have studied the distance preserving properties of compressed data points, using random projections. More recently, Jiao et al [46] theoretically concluded that the distance between the two subspaces is almost constant after random projection. However, the traditional coded apertures cannot preserve the spectral signature similarities between any pair of vectors on the compressed domain, for the random projection cannot retain orthogonality, and the vectors that define the orthogonal basis of the subspace cannot be normalized.…”

Section: Multiframe Cassi Coding Pattern Optimization For Csi Subspacmentioning

confidence: 99%

Classification of Remote Sensing Images Through Reweighted Sparse Subspace Representation Using Compressed Data

Zhu¹,

Zhao²,

Wu³

2021

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In many real-world scenarios, subspace clustering essentially aims to cluster unlabeled high-dimensional data into a union of finite-dimensional linear subspaces. The problem is that the data are always high-dimensional, with the increase of the computation, storge, and communication of various intelligent data-driven systems. This paper attempts to develop a method to cluster spectral images directly using the measurements of compressive coded aperture snapshot spectral imager (CASSI), eliminating the need to reconstruct the entire data cube. Assuming that compressed measurements are drawn from multiple subspaces, a novel algorithm was developed by solving a 1-norm minimization problem, which is known as reweighted sparse subspace clustering (RSSC). The proposed algorithm clusters the compressed measurements into different subspaces, which greatly improves the clustering accuracy over the SSC algorithm by adding a reweighted step. The compressed CASSI measurements obtained using the coherence-based coded aperture can improve the performance of the proposed spectral image clustering method. The accuracy of our spectral image clustering approach was verified through simulations on two real datasets.

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Section: Multiframe Cassi Coding Pattern Optimization For Csi Subspacmentioning

confidence: 99%

Classification of Remote Sensing Images Through Reweighted Sparse Subspace Representation Using Compressed Data

Zhu¹,

Zhao²,

Wu³

2021

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Section: Related Workmentioning

confidence: 99%

“…To study subspace RIP in a systematic way, our previous works Jiao et al (2017 study the canonical angles preserving property of Gaussian random projection. However, the requirement on the reduced dimension n in the result of Jiao et al (2017) is polynomial in the failing probability δ, which is not as rigourous as the exponential relationship in this work. In addition, all these results are restricted to Gaussian case, while the result in this paper works for a wider class of random matrices, including partial Fourier matrices which are more useful in practice.…”

Section: Related Workmentioning

confidence: 99%

Compressed Subspace Learning Based on Canonical Angle Preserving Property

Jiao¹,

Li²,

2019

Preprint

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Union of Subspaces (UoS) is a popular model to describe the underlying lowdimensional 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.

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Subspace Principal Angle Preserving Property of Gaussian Random Projection

Jiao

Shen

et al. 2018

2018 IEEE Data Science Workshop (DSW)

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Principal angles preserving property of Gaussian random projection for subspaces

Cited by 3 publications

References 24 publications

Classification of Remote Sensing Images Through Reweighted Sparse Subspace Representation Using Compressed Data

Classification of Remote Sensing Images Through Reweighted Sparse Subspace Representation Using Compressed Data

Compressed Subspace Learning Based on Canonical Angle Preserving Property

Subspace Principal Angle Preserving Property of Gaussian Random Projection

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