Representation learning is a crucial and complex task for multivariate time series data analysis, with a wide range of applications including trend analysis, time series data search, and forecasting. In practice, unsupervised learning is strongly preferred owing to sparse labeling. However, most existing studies focus on the representation of individual subseries without considering relationships between different subseries. In certain scenarios, this may lead to downstream task failures. Here, an unsupervised representation learning model is proposed for multivariate time series that considers the semantic relationship among subseries of time series. Specifically, the covariance calculated by the Gaussian process (GP) is introduced to the self-attention mechanism, capturing relationship features of the subseries. Additionally, a novel unsupervised method is designed to learn the representation of multivariate time series. To address the challenges of variable lengths of input subseries, a temporal pyramid pooling (TPP) method is applied to construct input vectors with equal length. The experimental results show that our model has substantial advantages compared with other representation learning models. We conducted experiments on the proposed algorithm and baseline algorithms in two downstream tasks: classification and retrieval. In classification task, the proposed model demonstrated the best performance on seven of ten datasets, achieving an average accuracy of 76%. In retrieval task, the proposed algorithm achieved the best performance under different datasets and hidden sizes. The result of ablation study also demonstrates significance of semantic relationship in multivariate time series representation learning.

The estimation problem of structured clutter covariance matrix (CCM) in space-time adaptive processing (STAP) for airborne radar systems is studied in this letter. By employing the prior knowledge and the persymmetric covariance structure, a new estimation algorithm is proposed based on the whitening ability of the covariance matrix. The proposed algorithm is robust to prior knowledge of different accuracy, and can whiten the observed interference data to obtain the optimal solution. In addition, the extended factored approach (EFA) is used in the optimization for dimensionality reduction, which reduces the computational burden. Simulation results show that the proposed algorithm can effectively improve STAP performance even under the condition of some errors in prior knowledge.

Adaptive multilooking is a critical processing step in multi-temporal interferometric synthetic aperture radar (InSAR) measurement, especially in small temporal baseline subsets. Various amplitude-based adaptive multilook approaches have been proposed for the improvement of interferometric processing. However, the phase signal, which is fundamental in interferometric systems, is typically ignored in these methods. To fully exploit the information in complex SAR images, a nonlocal adaptive multilooking is proposed based on complex covariance matrix in this work. The complex signal is here exploited for the similiarity measurement between two pixels. Given the complexity of objects in SAR images, structure feature detection is introduced to adaptively estimate covariance matrix. The effectiveness and reliability of the proposed approach are demonstrated with experiments both on simulated and real data.

A robust adaptive beamforming algorithm is proposed based on the precise interference-plus-noise covariance matrix reconstruction and steering vector estimation of the desired signal, even existing large gain-phase errors. Firstly, the model of array mismatches is proposed with the first-order Taylor series expansion. Then, an iterative method is designed to jointly estimate calibration coefficients and steering vectors of the desired signal and interferences. Next, the powers of interferences and noise are estimated by solving a quadratic optimization question with the derived closed-form solution. At last, the actual interference-plus-noise covariance matrix can be reconstructed as a weighted sum of the steering vectors and the corresponding powers. Simulation results demonstrate the effectiveness and advancement of the proposed method.

A spatially “Mt. Fuji” coupled (SFC) low-density parity-check (LDPC) ensemble is a modified version of the spatially coupled (SC) LDPC ensemble. Its decoding error probability in the waterfall region has been studied only in an experimental manner. In this paper, we theoretically analyze it over the binary erasure channel by modifying the expected graph evolution (EGE) and covariance evolution (CE) that have been used to analyze the original SC-LDPC ensemble. In particular, we derive the initial condition modified for the SFC-LDPC ensemble. Then, unlike the SC-LDPC ensemble, the SFC-LDPC ensemble has a local minimum on the solution of the EGE and CE. Considering the property of it, we theoretically expect the waterfall curve of the SFC-LDPC ensemble is steeper than that of the SC-LDPC ensemble. In addition, we also confirm it by numerical experiments.

It has been reported repeatedly that discriminative learning of distance metric boosts the pattern recognition performance. Although the ITML (Information Theoretic Metric Learning)-based methods enjoy an advantage that the Bregman projection framework can be applied for optimization of distance metric, a weak point of ITML-based methods is that the distance threshold for similarity/dissimilarity constraints must be determined manually, onto which the generalization performance is sensitive. In this paper, we present a new formulation of metric learning algorithm in which the distance threshold is optimized together. Since the optimization is still in the Bregman projection framework, the Dykstra algorithm can be applied for optimization. A nonlinear equation has to be solved to project the solution onto a half-space in each iteration. We have developed an efficient technique for projection onto a half-space. We empirically show that although the distance threshold is automatically tuned for the proposed metric learning algorithm, the accuracy of pattern recognition for the proposed algorithm is comparable, if not better, to the existing metric learning methods.

In this paper, we propose an online antenna-pulse selection method in space time adaptive processing, while maintaining considerable performance and low computational complexity. The proposed method considers the antenna-pulse selection and covariance matrix estimation at the same time by exploiting the structured clutter covariance matrix. Such prior knowledge can enhance the covariance matrix estimation accuracy and thus can provide a better objective function for antenna-pulse selection. Simulations also validate the effectiveness of the proposed method.

Spectrum sensing is the first task performed by cognitive radio (CR) networks. In this paper we propose a spectrum sensing algorithm for orthogonal frequency division multiplex (OFDM) signal based on deep learning and covariance matrix graph. The advantage of deep learning in image processing is applied to the spectrum sensing of OFDM signals. We start by building the spectrum sensing model of OFDM signal, and then analyze structural characteristics of covariance matrix (CM). Once CM has been normalized and transformed into a gray level representation, the gray scale map of covariance matrix (GSM-CM) is established. Then, the convolutional neural network (CNN) is designed based on the LeNet-5 network, which is used to learn the training data to obtain more abstract features hierarchically. Finally, the test data is input into the trained spectrum sensing network model, based on which spectrum sensing of OFDM signals is completed. Simulation results show that this method can complete the spectrum sensing task by taking advantage of the GSM-CM model, which has better spectrum sensing performance for OFDM signals under low SNR than existing methods.

Using local time frames to treat non-stationary real world signals as stationary yields Quasi-Stationary Signals (QSS). In this paper, direction of arrival (DOA) estimation of uncorrelated non-circular QSS is analyzed by applying a novel technique to achieve larger consecutive lags using coprime array. A scheme of virtual extension of coprime array is proposed that exploits the difference and sum co-array which can increase consecutive co-array lags in remarkable number by using less number of sensors. In the proposed method, cross lags as well as self lags are exploited for virtual extension of co-arrays both for differences and sums. The method offers higher degrees of freedom (DOF) with a larger number of non-negative consecutive lags equal to MN+2M+1 by using only M+N-1 number of sensors where M and N are coprime with congenial interelement spacings. A larger covariance matrix can be achieved by performing covariance like computations with the Khatri-Rao (KR) subspace based approach which can operate in undetermined cases and even can deal with unknown noise covariances. This paper concentrates on only non-negative consecutive lags and subspace based method like Multiple Signal Classification (MUSIC) based approach has been executed for DOA estimation. Hence, the proposed method, named Virtual Extension of Coprime Array imbibing Difference and Sum (VECADS), in this work is promising to create larger covariance matrix with higher DOF for high resolution DOA estimation. The coprime distribution yielded by the proposed approach can yield higher resolution DOA estimation while avoiding the mutual coupling effect. Simulation results demonstrate its effectiveness in terms of the accuracy of DOA estimation even with tightly aligned sources using fewer sensors compared with other techniques like prototype coprime, conventional coprime, Coprime Array with Displaced Subarrays (CADiS), CADiS after Coprime Array with Compressed Inter-element Spacing (CACIS) and nested array seizing only difference co-array.

In statistical approaches such as statistical static timing analysis, the distribution of the maximum of plural distributions is computed by repeating a maximum operation of two distributions. Moreover, since each distribution is represented by a linear combination of several explanatory random variables so as to handle correlations efficiently, sensitivity of the maximum of two distributions to each explanatory random variable, that is, covariance between the maximum and an explanatory random variable, must be calculated in every maximum operation. Since distribution of the maximum of two Gaussian distributions is not a Gaussian, Gaussian mixture model is used for representing a distribution. However, if Gaussian mixture models are used, then it is not always possible to make both variance and covariance of the maximum correct simultaneously. We propose a new algorithm to determine covariance without deteriorating the accuracy of variance of the maximum, and show experimental results to evaluate its performance.

An improved beamformer, which uses joint estimation of the reconstructed interference-plus-noise (IPN) covariance matrix and array steering vector (ASV), is proposed. It can mitigate the problem of performance degradation in situations where the desired signal exists in the sample covariance matrix and the steering vector pointing has large errors. In the proposed method, the covariance matrix is reconstructed by weighted sum of the exterior products of the interferences' ASV and their individual power to reject the desired signal component, the coefficients of which can be accurately estimated by the compressed sensing (CS) and total least squares (TLS) techniques. Moreover, according to the theorem of sequential vector space projection, the actual ASV is estimated from an intersection of two subspaces by applying the alternating projection algorithm. Simulation results are provided to demonstrate the performance of the proposed beamformer, which is clearly better than the existing robust adaptive beamformers.

Based on the reconstruction of the augmented interference-plus-noise (IPN) covariance matrix (CM) and the estimation of the desired signal's extended steering vector (SV), we propose a novel robust widely linear (WL) beamforming algorithm. Firstly, an extension of the iterative adaptive approach (IAA) algorithm is employed to acquire the spatial spectrum. Secondly, the IAA spatial spectrum is adopted to reconstruct the augmented signal-plus-noise (SPN) CM and the augmented IPNCM. Thirdly, the extended SV of the desired signal is estimated by using the iterative robust Capon beamformer with adaptive uncertainty level (AU-IRCB). Compared with several representative robust WL beamforming algorithms, simulation results are provided to confirm that the proposed method can achieve a better performance and has a much lower complexity.

In this paper, we study robust Principal Component Analysis (PCA)-based anomaly detection techniques in network traffic, which can detect traffic anomalies by projecting measured traffic data onto a normal subspace and an anomalous subspace. In a PCA-based anomaly detection, outliers, anomalies with excessively large traffic volume, may contaminate the subspaces and degrade the performance of the detector. To solve this problem, robust PCA methods have been studied. In a robust PCA-based anomaly detection scheme, outliers can be removed from the measured traffic data before constructing the subspaces. Although the robust PCA methods are promising, they incure high computational cost to obtain the optimal location vector and scatter matrix for the subspace. We propose a novel anomaly detection scheme by extending the minimum covariance determinant (MCD) estimator, a robust PCA method. The proposed scheme utilizes the daily periodicity in traffic volume and attempts to detect anomalies for every period of measured traffic. In each period, before constructing the subspace, outliers are removed from the measured traffic data by using a location vector and a scatter matrix obtained in the preceding period. We validate the proposed scheme by applying it to measured traffic data in the Abiline network. Numerical results show that the proposed scheme provides robust anomaly detection with less computational cost.

In recent years, covariance descriptors have received considerable attention as a strong representation of a set of points. In this research, we propose a new metric learning algorithm for covariance descriptors based on the Dykstra algorithm, in which the current solution is projected onto a half-space at each iteration, and which runs in O(n3) time. We empirically demonstrate that randomizing the order of half-spaces in the proposed Dykstra-based algorithm significantly accelerates convergence to the optimal solution. Furthermore, we show that the proposed approach yields promising experimental results for pattern recognition tasks.

In this letter, a novel mainlobe anti-jamming method via eigen-projection processing and covariance matrix reconstruction is proposed. The present work mainly focuses on two aspects: the first aspect is to obtain the eigenvector of the mainlobe interference accurately in order to form the eigen-projection matrix to suppress the mainlobe interference. The second aspect is to reconstruct the covariance matrix which is uesd to calculate the adaptive weight vector for forming an ideal beam pattern. Additionally, the self-null effect caused by the signal of interest and the sidelobe interferences elimination are also considered in the proposed method. Theoretical analysis and simulation results demonstrate that the proposed method can suppress the mainlobe interference effectively and achieve a superior performance.

In this letter, a novel robust adaptive beamforming algorithm is addressed to improve the robustness against steering vector random errors (SVREs), which eliminates the signal of interest (SOI) component from the sample covariance matrix (SCM), based on interference-plus-noise covariance matrix (IPNCM) reconstruction over annulus uncertainty sets. Firstly, several annulus uncertainty sets are used to constrain the steering vectors (SVs) of both interferences and the SOI. Additionally the IPNCM is reconstructed according to its definition by estimating each interference SV over its own annulus uncertainty set via the subspace projection algorithm. Meanwhile, the SOI SV is estimated as the prime eigenvector of the SOI covariance matrix term calculated over its own annulus uncertainty set. Finally, a novel robust beamformer is formulated based on the new IPNCM and the SOI SV, and it outperforms other existing reconstruction-based beamformers when the SVREs exist, especially in low input signal-to-noise ratio (SNR) cases, which is proved through the simulation results.

Recent studies have obtained superior performance in image recognition tasks by using, as an image representation, the fully connected layer activations of Convolutional Neural Networks (CNN) trained with various kinds of images. However, the CNN representation is not very suitable for fine-grained image recognition tasks involving food image recognition. For improving performance of the CNN representation in food image recognition, we propose a novel image representation that is comprised of the covariances of convolutional layer feature maps. In the experiment on the ETHZ Food-101 dataset, our method achieved 58.65% averaged accuracy, which outperforms the previous methods such as the Bag-of-Visual-Words Histogram, the Improved Fisher Vector, and CNN-SVM.

This paper proposes an appearance-based novel descriptor for estimating head orientation. Our descriptor is inspired by the Weber-based feature, which has been successfully implemented for robust texture analysis, and the gradient which performs well for shape analysis. To further enhance the orientation differences, we combine them with an analysis of the intensity deviation. The position of a pixel and its intrinsic intensity are also considered. All features are then composed as a feature vector of a pixel. The information carried by each pixel is combined using a covariance matrix to alleviate the influence caused by rotations and illumination. As the result, our descriptor is compact and works at high speed. We also apply a weighting scheme, called Block Importance Feature using Genetic Algorithm (BIF-GA), to improve the performance of our descriptor by selecting and accentuating the important blocks. Experiments on three head pose databases demonstrate that the proposed method outperforms the current state-of-the-art methods. Also, we can extend the proposed method by combining it with a head detection and tracking system to enable it to estimate human head orientation in real applications.

We propose a novel sparse representation-based direction-of-arrival (DOA) estimation method. In contrast to those that approximate l0-norm minimization by l1-norm minimization, our method designs a reweighted l1 norm to substitute the l0 norm. The capability of the reweighted l1 norm to bridge the gap between the l0- and l1-norm minimization is then justified. In addition, an array covariance vector without redundancy is utilized to extend the aperture. It is proved that the degree of freedom is increased as such. The simulation results show that the proposed method performs much better than l1-type methods when the signal-to-noise ratio (SNR) is low and when the number of snapshots is small.

We address a robust algorithm for the interference-plus-noise covariance matrix reconstruction (RA-INCMR) against random arbitrary steering vector mismatches (RASVMs) of the interferences, which lead to substantial degradation of the original INCMR beamformer performance. Firstly, using the worst-case performance optimization (WCPO) criteria, we model these RASVMs as uncertainty sets and then propose the RA-INCMR to obtain the robust INCM (RINCM) based on the Robust Capon Beamforming (RCB) algorithm. Finally, we substitute the RINCM back into the original WCPO beamformer problem for the sample covariance matrix to formulate the new RA-INCM-WCPO beamformer problem. Simulation results demonstrate that the performance of the proposed beamformer is much better than the original INCMR beamformer when there exist RASVMs, especially at low signal-to-noise ratio (SNR).