Feature selection has been recognized for long as an important preprocessing technique to reduce dimensionality and improve the performance of regression and classification tasks. The class of sequential forward feature selection methods based on Mutual Information (MI) is widely used in practice, mainly due to its computational efficiency and independence from the specific classifier. A recent work introduced a theoretical framework for this class of methods which explains the existing proposals as approximations to an optimal target objective function. Such framework made clear the advantages and drawbacks of each proposal. Methods accounting for the redundancy of candidate features using a maximization function and considering the so-called complementary effect are among the best ones. However, they still penalize the complementarity, which is an important drawback. This paper proposes the Decomposed Mutual Information Maximization (DMIM) method, which keeps the good theoretical properties of the best methods proposed so far but overcomes the complementarity penalization by applying the maximization separately to the inter-feature and class-relevant redundancies. DMIM was extensively evaluated and compared with other methods, both theoretically and using two synthetic scenarios and 20 publicly available real datasets applied to specific classifiers. Our results show that DMIM achieves a better classification performance than the remaining forward feature selection methods based on MI.

Robust statistics is a branch of statistics which includes statistical methods capable of dealing adequately with the presence of outliers. In this paper, we propose an anomaly detection method that combines a feature selection algorithm and an outlier detection method, which makes extensive use of robust statistics. Feature selection is based on a mutual information metric for which we have developed a robust estimator; it also includes a novel and automatic procedure for determining the number of relevant features. Outlier detection is based on robust Principal Component Analysis (PCA) which, opposite to classical PCA, is not sensitive to outliers and precludes the necessity of training using a reliably labeled dataset, a strong advantage from the operational point of view. To evaluate our method we designed a network scenario capable of producing a perfect ground-truth under real (but controlled) traffic conditions. Results show the significant improvements of our method over the corresponding classical ones. Moreover, despite being a largely overlooked issue in the context of anomaly detection, feature selection is found to be an important preprocessing step, allowing adaption to different network conditions and inducing significant performance gains.

Due to complexity and intractability reasons, most of the analytical studies on the reliability of communication paths in mobile ad hoc networks are based on the assumption of link independence. In this paper, an analytical framework is developed to characterize the random behavior of a multihop path and derive path metrics to characterize the reliability of paths. This is achieved through the modeling of a multihop path as a PDMP (piecewise deterministic Markov process). Two path based metrics are obtained as expectations of functionals of the process: the mean path duration and the path persistence. We show that these metrics are the unique solution of a set of integro-differential equations and provide a recursive scheme for their computation. Finally, numerical results illustrate the computation of the metrics; these results are compared with independent link approximation results.