Sequential low-rank change detection
| Autor: | Yao Xie, Lee M. Seversky |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Rank (linear algebra)
Computer science Covariance matrix Dimensionality reduction MathematicsofComputing_NUMERICALANALYSIS 020206 networking & telecommunications 02 engineering and technology 01 natural sciences 010104 statistics & probability Matrix (mathematics) Dimension (vector space) Sliding window protocol 0202 electrical engineering electronic engineering information engineering 0101 mathematics Algorithm Change detection Eigenvalues and eigenvectors |
| Zdroj: | Allerton |
| DOI: | 10.1109/allerton.2016.7852220 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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