L1-norm Regularized L1-norm Best-fit line problem

Background Conventional Principal Component Analysis (PCA) is a widely used technique to reduce data dimension. PCA finds linear combinations of the original features capturing maximal variance of data via Singular Value Decomposition (SVD). However, SVD is sensitive to outliers, and often leads to high dimensional results. To address the issues, we propose a new method to estimate best-fit one-dimensional subspace, called l1-norm Regularized l1-norm. Methods In this article, we describe a method to fit a lower-dimensional subspace by approximate a non-linear, non-convex, non-smooth optimization problem called l1 regularized l1-norm Best- Fit Line problem; minimize a combination of the l1 error and of the l1 regularization. The procedure can be simply performed using ratios and sorting. Also ,we present applications in the area of video surveillance, where our methodology allows for background subtraction with jitters, illumination changes, and clutters. Results We compared our performance with SVD on synthetic data. The numerical results showed our algorithm successfully found a better principal component from a grossly corrupted data than SVD in terms of discordance. Moreover, our algorithm provided a sparser principal component than SVD. However, we expect it to be faster on multi-node environment. Conclusions This paper proposes a new algorithm able to generate a sparse best-fit subspace robust to outliers. The projected subspaces sought on non-contaminated data, differ little from that of traditional PCA. When subspaces are projected from contaminated data, it attain arguably significant both smaller discordance and lower dimension than that of traditional PCA.https://scholarscompass.vcu.edu/gradposters/1074/thumbnail.jp

Robust Principal Component Analysis for Background Subtraction: Systematic Evaluation and Comparative Analysis

The analysis and understanding of video sequences is currently quite an active research field. Many applications such as video surveillance, optical motion capture or those of multimedia need to first be able to detect the objects moving in a scene filmed by a static camera. This requires the basic operation that consists of separating the moving objects called "foreground" from the static information called "background". Many background subtraction methods have been developed (Bouwmans et al. (2010); Bouwmans et al. (2008)). A recent survey (Bouwmans (2009)) shows that subspace learning models are well suited for background subtraction. Principal Component Analysis (PCA) has been used to model the background by significantly reducing the data's dimension. To perform PCA, different Robust Principal Components Analysis (RPCA) models have been recently developed in the literature. The background sequence is then modeled by a low rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. However, authors compare their algorithm only with the PCA (Oliver et al. (1999)) or another RPCA model. Furthermore, the evaluation is not made with the datasets and the measures currently used in the field of background subtraction. Considering all of this, we propose to evaluate RPCA models in the field of video-surveillance. Contributions of this chapter can be summarized as follows: 1) A survey regarding robust principal component analysis and 2) An evaluation and comparison on different video surveillance dataset

Cyber Security Network Anomaly Detection and Visualization

This MQP presents a novel anomaly detection system for computer network traffic, as well as a visualization system to help users explore the results of the anomaly detection. The detection algorithm uses a novel approach to Robust Principal Component Analysis, to produce a lower dimensional subspace of the original data, for which a random forest can be applied to predict anomalies. The visualization system has been designed to help cyber security analysts sort anomalies by attribute and view them in the context of normal network activity. The system consists of an overview of firewall logs, a detail view of each log, and a feature view where an analyst can see which features of the firewall log were implicated in the anomaly detection algorithm

Cyber Security Network Anomaly Detection and Visualization

This MQP presents a novel anomaly detection system for computer network traffic, as well as a visualization system to help users explore the results of the anomaly detection. The detection algorithm uses a novel approach to Robust Principal Component Analysis, to produce a lower dimensional subspace of the original data, for which a random forest can be applied to predict anomalies. The visualization system has been designed to help cyber security analysts sort anomalies by attribute and view them in the context of normal network activity. The system consists of an overview of firewall logs, a detail view of each log, and a feature view where an analyst can see which features of the firewall log were implicated in the anomaly detection algorithm