RECORD
Sequential Low-Rank Change Detection
Machine Learning · Submitted 3 Oct 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Hence, we may be able to detect the low-rank change using sample covariance matrices of the sketches without having to recover the original covariance matrix.
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The abstract, sentence by sentence
Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. To achieve dimensionality reduction, we present a sketching-based approach for rank change detection using the low-dimensional linear sketches of the original high-dimensional observations. The premise is that when the sketching matrix is a random Gaussian matrix, and the dimension of the sketching vector is sufficiently large, the rank of sample covariance matrix for these sketches equals the rank of the original sample covariance matrix with high probability. Hence, we may be able to detect the low-rank change using sample covariance matrices of the sketches without having to recover the original covariance matrix. We character the performance of the largest eigenvalue statistic in terms of the false-alarm-rate and the expected detection delay, and present an efficient online implementation via subspace tracking.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. | background 1.00 | 0.04 | 0.03 | asserted 1.00 |
| s1 | We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. | method 0.93 | 0.64 | 0.06 | asserted 0.95 |
| s2 | To achieve dimensionality reduction, we present a sketching-based approach for rank change detection using the low-dimensional linear sketches of the original high-dimensional observations. | method 0.74 | 0.89 | 0.09 | asserted 1.00 |
| s3 | The premise is that when the sketching matrix is a random Gaussian matrix, and the dimension of the sketching vector is sufficiently large, the rank of sample covariance matrix for these sketches equals the rank of the original sample covariance matrix with high probability. | method 0.59 | 0.25 | 0.11 | hedged possibility 0.50 |
| s4 | Hence, we may be able to detect the low-rank change using sample covariance matrices of the sketches without having to recover the original covariance matrix. | interpretation 0.77 | 0.31 | 0.30 | hedged possibility 1.00 |
| s5 | We character the performance of the largest eigenvalue statistic in terms of the false-alarm-rate and the expected detection delay, and present an efficient online implementation via subspace tracking. | contribution 0.92 | 0.94 | 0.27 | asserted 1.00 |
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Original abstract
Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. To achieve dimensionality reduction, we present a sketching-based approach for rank change detection using the low-dimensional linear sketches of the original high-dimensional observations. The premise is that when the sketching matrix is a random Gaussian matrix, and the dimension of the sketching vector is sufficiently large, the rank of sample covariance matrix for these sketches equals the rank of the original sample covariance matrix with high probability. Hence, we may be able to detect the low-rank change using sample covariance matrices of the sketches without having to recover the original covariance matrix. We character the performance of the largest eigenvalue statistic in terms of the false-alarm-rate and the expected detection delay, and present an efficient online implementation via subspace tracking.
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Start with an initialization of the subspace $U_0$, using the sequence of observations $x_1, x_2, …$, we may update the subspace using stochastic gradient descent on grassmannian manifolds, e.g., via the GROUSE algorithm [ref] .
Global Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation · Online implementation via subspace tracking · 0.96
Cites as background 1 paper
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The goal of sparse PCA is to estimate such sparse subspaces (see, e.g., [ref] ).
Optimal Estimation and Rank Detection for Sparse Spiked Covariance Matrices · Introduction · 0.95
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