A Compressed PCA Subspace Method for Anomaly Detection in High-Dimensional Data

Abstract

Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use for anomaly detection in high-dimensional settings, in conjunction with principal component analysis (PCA) and corresponding subspace detection methods. We assume a so-called spiked covariance model for the underlying data generation process and a Gaussian random projection. We adopt a hypothesis testing perspective of the anomaly detection problem, with the test statistic defined to be the magnitude of the residuals of a PCA analysis. Under the null hypothesis of no anomaly, we characterize the relative accuracy with which the mean and variance of the test statistic from compressed data approximate those of the corresponding test statistic from uncompressed data.Furthermore, under a suitable alternative hypothesis, we provide expressions that allow for a comparison of statistical power for detection. Finally, whereas these results correspond to the ideal setting in which the data covariance is known, we show that it is possible to obtain the same order of accuracy when the covariance of the compressed measurements is estimated using a sample covariance, as long as the number of measurements is of the same order of magnitude as the reduced dimensionality.

Principal Component Reconstruction Error for Hyperspectral Anomaly Detection

“…Theoretically, this method is robust to departures from normality as the number of discarded components increases [20], [32]. Exemplars exceeding a given threshold of reconstructive error using probabilities from the cumulative normal distribution function could then be considered anomalies or outliers in this method.…”

“…[17]- [19], compressive sensing [20], signal reconstruction [21], and replicator neural networks [22]; however, none of these applications were for remote sensing AD. Fowler and Du [23] considered the reconstruction error for signal recovery in HSI; however, they employed a separate AD step to segment background and anomalies into separate bins.…”

Incremental Principal Component Analysis Based Outlier Detection Methods for Spatiotemporal Data Streams

“…PCA is one of the most popular techniques for detecting outliers in various applications such as industrial processes (Li et al, 2000), environmental sensors (Harkatet al, 2006;Harrou et al,2013), distributed sensor networks (Chatzigiannakis and Papavassiliou, 2007), and high dimensional data (Ding and Kolaczyk, 2013). Most PCA-based models for outlier detection operate in batch mode (Chatzigiannakis and Papavassiliou, 2007;Harrou et al, 2013;Harkat et al, 2006), where the model is first trained using training data and is then used to test the remaining data for outliers.…”

Throat polyp detection based on compressed big data of voice with support vector machine algorithm

“…In [5,6], Budhaditya used the compressed sensor network data for anomaly detection based on spectrum theory method and obtained satisfactory detection results in the light of residual analysis of compressed data. In [7,8], random projection in conjunction with principal component analysis (PCA) was implemented for anomaly detection in compressed domain, and an application of this proposed methodology to detect IP-level volume anomalies in computer network traffic suggested a high relevance to practical problems. In [9], an anomaly detection criterion based on wavelet packet transform and statistic process control theory in compressed domain was used for through wall human detection.…”