Sequential Low-Rank Change Detection

10/03/2016
by   Yao Xie, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/15/2017

Sequential detection of low-rank changes using extreme eigenvalues

We study the problem of detecting an abrupt change to the signal covaria...
research
07/23/2014

Subspace Learning From Bits

Networked sensing, where the goal is to perform complex inference using ...
research
01/26/2015

Sequential Sensing with Model Mismatch

We characterize the performance of sequential information guided sensing...
research
04/18/2023

Sharp-SSL: Selective high-dimensional axis-aligned random projections for semi-supervised learning

We propose a new method for high-dimensional semi-supervised learning pr...
research
11/09/2018

Sequential Subspace Changepoint Detection

We consider the sequential changepoint detection problem of detecting ch...
research
05/25/2023

High-dimensional Response Growth Curve Modeling for Longitudinal Neuroimaging Analysis

There is increasing interest in modeling high-dimensional longitudinal o...
research
06/15/2020

FANOK: Knockoffs in Linear Time

We describe a series of algorithms that efficiently implement Gaussian m...

Please sign up or login with your details

Forgot password? Click here to reset