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This paper addresses the problem of secure communication in a cooperative network operating in the presence of an eavesdropper as well as co-channel interference. Two opportunistic relay selection techniques are exploited for achieving physicallayer based security. The first one aims at minimizing the amount of information leaked to the eavesdropper by selecting the relay which achieves the lowest capacity to the wiretap node. In the second scheme, the relay which yields the maximum achievable capacity at the destination node, is chosen. A performance analysis, which generalizes several previous results by accounting for interference affecting the network nodes, is conducted for both schemes and considering both selection combining and maximal ratio combining, in terms of the probability of non-zero achievable secrecy capacity and the secrecy outage probability, and numerical results are provided along with comparisons.

Finding a small subset of data whose linear combination spans other data points, also called column subset selection problem (CSSP), is an important open problem in computer science with many applications in computer vision and deep learning. There are some studies that solve CSSP in a polynomial time complexity w.r.t. the size of the original dataset. A simple and efficient selection algorithm with a linear complexity order, referred to as spectrum pursuit (SP), is proposed that pursuits spectral components of the dataset using available sample points. The proposed non-greedy algorithm aims to iteratively find K data samples whose span is close to that of the first K spectral components of entire data. SP has no parameter to be fine tuned and this desirable property makes it problem-independent. The simplicity of SP enables us to extend the underlying linear model to more complex models such as nonlinear manifolds and graph-based models. The nonlinear extension of SP is introduced as kernel-SP (KSP). The superiority of the proposed algorithms is demonstrated in a wide range of applications.

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