The dominant eigenvector of the covariance matrix of a zero-mean data distribution describes the line wherein the variance of the projected data is maximized. In practical applications, the true covariance matrix is unknown and its dominant eigenvector is estimated by principal-component analysis (PCA) of a finite collection of coherent data points. As the size of the data collection increases, its principal component (PC) tends to the covariance eigenvector. The downside of PCA is that it is very sensitive against any outliers in the data collection. L1-PCA is an increasingly popular robust alternative to standard PCA that has demonstrated sturdy resistance against outliers in a number of applications. However, to date, the asymptotic properties of L1-PCA as an eigenvector estimator are not well understood. In this work we show for the first time that, for centered elliptical distributions, as the number of samples increases, the L1-PC tends to the eigenvector of the covariance matrix, just like the standard PC.

Detection CNN architectures often exhibit over-parameterization which results in excessive computational and storage overhead, but also undesired overfitting and reduced performance. In this work we focus on YOLOrs, a state-of-the-art CNN for target detection in remote sensing imagery, and counteract over-parameterization by enforcing Tensor-Train (TT) structure to its convolutional kernels. While TT has been successfully used before for compressing classification CNNs, this work is the first one that uses it to compress a detection CNN. We refer to the resulting network as YOLOrs-lite and compare its performance against standard YOLOrs as well as other state-of-the-art detection networks. Our numerical studies show that the proposed network attains superior detection performance, with storage savings as high as 70%. The proposed network combines light storage with real-time inference, making it quite promising for edge deployment.

Utilizing millimeter wave (mmWave) wireless communication in wireless datacenter networks, the power consumption of the networking equipment can be reduced drastically. However, security of a datacenter is one of the highest design priorities. Many studies on the security of wired datacenters including identifying the possible threats and solutions have been explored in the literature. On the contrary, being an emerging technology, no study has been conducted on the security for the wireless datacenters. Being a wireless system, it has the potential to inherit many of the threats of a typical wireless network. So, in order to successfully realize wireless datacenter architectures, it is essential to do an extensive investigation of the system from a security perspective. In this paper, we study both existing as well as novel threats and their impact on the wireless datacenter network. In addition to these conventional threats, we demonstrate the impact of a novel attack on the wireless datacenter which can be launched by leveraging its control plane.

Standard Tucker tensor decomposition seeks to maximize the L2-norm of the compressed tensor; thus, it is very responsive to outlying/high-magnitude entries among the processed data. To counteract the impact of outliers in tensor data analysis, we propose L1-Tucker: a reformulation of standard Tucker decomposition, resulting by simple substitution of the outlier-responsive L2-norm by the sturdier L1-norm. Then, we propose the L1-norm Higher Order Orthogonal Iterations (L1-HOOI) algorithm for the approximate solution to L1-Tucker. Our numerical studies on data reconstruction and classification corroborate that L1-HOOI exhibits sturdy resistance against outliers compared to standard counterparts.

We consider corruption-resistant L1-norm-based TUCKER2 (L1-TUCKER2) decomposition of a D×M×N 3-way tensor, treated (with no loss of generality) as a collection of N D×M matrices. Our contributions are as follows. First, we show that rank-1 L1-TUCKER2 can be cast as a combinatorial problem over N antipodal-binary variables; accordingly, we provide the first exact algorithm for its solution. Then, we develop an efficient (quadratic-cost/near-exact) algorithm that approximates the solution to rank-1 L1- TUCKER2 by means of a converging sequence of optimal single-bit flips; the algorithm is accompanied by formal convergence proof and complexity analysis. Finally, by means of the standard deflation technique, we generalize the developed bit - flipping algorithm for solving L1- TUCKER2 decomposition problems of general rank. Our extensive numerical studies show that the bit-flipping algorithm returns the exact L1- TUCKER2 solution with very high frequency. Moreover, the developed exact and efficient algorithms exhibit remarkable outlier resistance, outperforming some of the most popular L2-norm-based and L1-norm-based counterparts.

Sampling the physical-array autocorrelations is the initial processing step in standard direction-of-arrival (DoA) estimation with coprime arrays. These samples are then organized into an autocorrelation matrix estimate of a uniform-linear virtual coarray, which in turn is used for DoA estimation. Existing autocorrelation-sampling approaches provide the exact coarray autocorrelation matrix for asymptotically large sample support; however, they attain arbi-trary/suboptimal mean-squared estimation error (MSE) for lim-ited/low sample support. In this work, we present a minimum- MSE (MMSE) approach for autocorrelation sampling. The proposed method offers a superior autocorrelation-matrix estimate that can attain higher DoA estimation accuracy than the standard counterparts.

This letter studies the rank-1 L1-norm-based TUCKER2 (L1-TUCKER2) decomposition of 3-way tensors. First, we prove that the problem is formally NP-hard. Then, we derive the first two algorithms in the literature for its exact solution. Our algorithms are accompanied by formal complexity analysis. Finally, we conduct numerical studies to compare the performance of exact L1-TUCKER2 (proposed) with standard HOSVD, HOOI, GLRAM, PCA, L1-PCA, and TPCA-L1. In our numerical studies, L1-TUCKER2 outperforms (e.g., in tensor approximation) all the aforementioned counterparts when the processed data are outlier corrupted.

Statistically-optimal Linear Discriminant Analysis (LDA) is formulated as a maximization that involves the nominal statistics of the classes to be discriminated. In practice, however, these nominal statistics are unknown and estimated from a collection of labeled training data. Accordingly, the nominal LDA basis is approximated by the solution of the popular practical LDA problem defined upon these estimates. However, when the available training data are few, the solution to practical LDA is known to lie far from the nominal LDA basis. In this work, we propose a novel algorithm that operates on the estimated class statistics and generates a sequence of bases that converges to the solution of practical LDA. Importantly, our studies illustrate that early elements of the proposed sequence exhibit significantly higher approximation to the nominal LDA basis than the converging point and, thus, offer the means for superior classification performance.

We introduce maximum-SINR sparse-binary waveforms that modulate data information symbols from any finite alphabet and span the whole continuum of the available/device-accessible spectrum. We offer an optimal algorithm that designs the proposed waveforms by maximizing the signal-to-interference-plus-noise ratio (SINR) at the output of the maximum-SINR linear receiver. In addition, we offer a suboptimal algorithm for the same problem with significantly reduced computational complexity. The post-filtering SINR improvements attained by the proposed waveforms in a single-input single-output (SISO) communication system with colored interference are presented analytically. Simulation studies compare the proposed waveforms with their conventional non-sparse counterparts and demonstrate their superior SINR performance.

We consider Alamouti encoding that draws symbols from phase-shift keying and develop a new differential modulation scheme that attains full rate for any constellation order. In contrast to past work, the proposed scheme guarantees that the encoded matrix maintains the characteristics of the initial codebook and, at the same time, attains full rate so that all possible sequences of space-time matrices become valid. Surprisingly, although the validity of all sequences could be thought as a drawback with respect to the cost of noncoherent sequence decoding, in fact it turns out to be an advantage. Based on recent results in the context of quadratic-form maximization over finite alphabets, we exploit the full-rate property of the proposed scheme to develop a polynomial-complexity maximum-likelihood noncoherent sequence decoder whose order is solely determined by the number of receive antennas. Numerical studies show the superiority of the proposed scheme in comparison with contemporary alternatives in terms of encoding rate, decoding complexity, bandwidth efficiency, and throughput.

The K L1-norm Principal Components (L1-PCs) of a data matrix X ∈ ℝD × Ncan be found optimally with cost O(2NK), in the general case, and O(Nrank(X)K - K + 1), when rankX is a constant with respect to N [1],[2]. Certainly, in real-world applications where N is large, even the latter polynomial cost is prohibitive. In this work, we present L1-BF: a novel, near-optimal algorithm that calculates the K L1-PCs of X with cost O (NDmin{N, D} + N2(K4+ DK2) + DNK3), comparable to that of standard (L2-norm) Principal-Component Analysis. Our numerical studies illustrate that the proposed algorithm attains optimality with very high frequency while, at the same time, it outperforms on the L1-PCA metric any counterpart of comparable computational cost. The outlier-resistance of the L1-PCs calculated by L1-BF is documented with experiments on dimensionality reduction and genomic data classification for disease diagnosis.

In the past decade, there has been a growing documented effort to approximate a matrix by another of lower rank minimizing the L1-norm of the residual matrix. In this paper, we first show that the problem is NP-hard. Then, we introduce a theorem on the sparsity of the residual matrix. The theorem sets the foundation for a novel algorithm that outperforms all existing counterparts in the L1-norm error minimization metric and exhibits high outlier resistance in comparison to usual L2-norm error minimization in machine learning applications.

In the field of subpixel target detection in hyperspectral images, there is well-documented current interest for identifying preferred background covariance matrix estimates, to be used in the formation of matched-filter detectors. In this work, for the first time, we study the case of local background covariance matrix estimation from SLIC-superpixel based coherent regions. Interestingly, our experiments illustrate that the SLIC-based matched-filter detector can attain performance superior to that of contemporary alternatives which employ different, globally or locally estimated, background statistics.

We address the problem of recovering an unknown image of interest, when only few, severely corrupted copies are available. We employ, for the first time in the literature, corruption-resistant L1-Principal-Components (L1-PCs) of the image data-set at hand. Specifically, the calculated L1-PCs are used for reliability-based patch-by-patch fusion of the corrupted image copies into a single high-quality representation of the original image (L1-fusion). Our experimental studies illustrate that the proposed method offers remarkable recovery results for several common corruption types, even under high corruption rate, small number of copies, and varying corruption type among copies. An additional theoretical contribution of this work is that the L1-PC of a data matrix of non-negative entries (e.g., image data) is for the first time shown to be optimally calculable with complexity linear to the matrix dimensions - as of now, the fastest-known optimal algorithm is of polynomial complexity. In the light of this result, L1-fusion is carried out with linear cost comparable to that of the simple copy-averaging alternative. The linear-low cost of L1-fusion allows for the recovered image to be, optionally, further refined by means of sophisticated single-image restoration techniques.

Recently, Markopoulos et al. [1], [2] presented an optimal algorithm that computes the L1maximum-projection principal component of any set of N real-valued data vectors of dimension D with complexity polynomial in N, O(ND). Still, moderate to high values of the data dimension D and/or data record size N may render the optimal algorithm unsuitable for practical implementation due to its exponential in D complexity. In this paper, we present for the first time in the literature a fast greedy single-bit-flipping conditionally optimal iterative algorithm for the computation of the L1principal component with complexity O(N3). Detailed numerical studies are carried out demonstrating the effectiveness of the developed algorithm with applications to the general field of data dimensionality reduction and direction-of-arrival estimation.

We consider Alamouti encoding that draws symbols from M-ary phase-shift keying (M-PSK) and develop a new differential modulation scheme that attains full rate for any constellation order. In contrast to past work, the proposed scheme guarantees that the encoded matrix maintains the characteristics of the initial codebook and, at the same time, attains full rate so that all possible sequences of space-time matrices become valid. The latter property is exploited to develop a polynomial-complexity maximum-likelihood noncoherent sequence decoder whose order is solely determined by the number of receive antennas. We show that the proposed scheme is superior to contemporary alternatives in terms of encoding rate, decoding complexity, and performance.

Pseudo-noise (PN) masking is regarded as an effective means to combat data eavesdropping (for example in military-grade communications or positioning systems). At the same time, PN-masked data transmissions are considered vulnerable to interference/jamming due to lack of practical interference suppression solutions. In this work, (i) we derive an efficient minimum-mean-square-error (MMSE) optimal linear receiver of PN-masked data and (ii) develop an auxiliary-vector (AV) MMSE adaptive filter estimator with state-of-the-art small-sample-support estimation performance. Simulation studies included in this paper illustrate the effectiveness of the theoretical developments.

In the context of secure wireless communications, pseudo-noise (PN) masking of transferred data has proven to be an effective technique against eavesdropping (notable examples are military-grade communication and global-positioning systems). At the same time, PN-masked transmissions are thought to be vulnerable to interference/jamming due to lack of a minimum-mean-square-error (MMSE) disturbance suppressing solution. In this paper, for the first time we establish the MMSE operation for masked data in the form of a time (mask) varying linear filter, suggest an implementation that avoids repeated input autocorrelation matrix inversion, and develop an auxiliary-vector (AV) MMSE filter estimator with state-of-the-art short-data-record estimation performance. Simulation examples included herein illustrate the theoretical developments.