Detecting network traffic volume anomalies in real time is a key problem as it enables measures to be taken to prevent network congestion which severely affects the end users. Several techniques based on principal component analysis (PCA) have been outlined in the past which detect volume anomalies as outliers in the residual subspace. However, these methods are not scalable to networks with a large number of links. We address this scalability issue with a new approach inspired from the recently developed compressed sensing (CS) theory. This theory induces a universal information sampling sheme right at the network sensory level to reduce the data overhead. Specifically, we address exploit the compressibility characteristics of the network data and describe a framework for anomaly detection in the compressed domain. Our main theoretical contribution is a detailed theoretical analysis of the new approach which obtains the probabilistic bounds on the principal eigenvalues of the compressed data. Subsequently, we prove that volume anomaly detection using compressed data can achieve equivalent performance as it does using the original uncompressed and reduces the computational cost significantly. The experimental results on both the Abiliene and synthetic datasets support our theoretical findings and demonstrate the advantages of the new approach over the existing methods.

Learning a robust projection with a small number of training samples is still a challenging problem in face recognition, especially when the unseen faces have extreme variation in pose, illumination, and facial expression. To address this problem, we propose a framework formulated under statistical learning theory that facilitates robust learning of a discriminative projection. Dimensionality reduction using the projection matrix is combined with a linear classifier in the regularized framework of lasso regression. The projection matrix in conjunction with the classifier parameters are then found by solving an optimization problem over the Stiefel manifold. The experimental results on standard face databases suggest that the proposed method outperforms some recent regularized techniques when the number of training samples is small.

A sequential M-estimation algorithm is proposed as an alternative to sequential least squares (LS). Being an approximation to exact M-estimation, the proposed technique is robust to non-Gaussian noise and outperforms sequential LS. A low-cost technique is introduced for initialization. We also show that sequential LS is a special case of the proposed algorithm.

We propose a sequential M-estimation algorithm as an alternative to sequential least squares. Being an approximation of the exact M-estimator, the proposed technique is robust to nonGaussian processes and outperforms sequential least squares. Simulation results demonstrate the power of the proposed sequential M-estimator.

The problem of robust signal detection in non-Gaussian noise is revisited. In this paper, we look at some issues of robust estimators which have been discussed very little in previous works. Some robust estimators, which are adaptive in nature and asymptotically efficient, are introduced and some technical improvements are suggested. Performance of these robust estimators is given in a practical communication problem and their asymptotic properties are investigated when the parameter-to-observation ratio becomes large.

We consider the problem of joint detection and decoding for CDMA systems that employ forward error control (FEC). The main problems encountered in designing this type of receiver include high complexity and a lack of robustness in impulsive noise and contamination in the prior model. We propose that the extrinsic information may not need to be absolutely reliable as we consider impulsive interference. By allowing the judgement of confidence in using this extrinsic information, the proposed M-estimation based soft-in soft-out (SISO) detector exhibits robust performance for a low complexity.

We address the problem of multiuser signal detection in the presence of additive non-Gaussian noise, particularly the numerical procedure for solving m-equations. When the noise is modelled by the e-contaminated mixture, we show that an iteratively reweighted least squares (IRLS) technique can be readily used which offers a faster convergence than the conventional gradient approach. An alternative version of the IRLS algorithm which sacrifices optimality for computational efficiency is also introduced.

We address the problem of robust multiuser detection in heavy tailed noise. A number of multiuser detectors which have been proposed require parametric channel noise models. The rigidity in the design of these detectors can make them far from optimal when the channel noise is not close to the assumed distribution. Nonparametric detectors, on the other hand, make no assumption about the noise parameters and have been shown to be robust in different types of channel noise. In this paper, we propose a new class of detector which makes use of some a priori channel information. Simulations show that the proposed detector, under regular circumstances, exhibits robust detection over a wide range of channel noise types and outperforms the nonparametric detector at a lower computational cost.