In signal processing and data analytics, Wiener filter is a classical powerful tool to transform an input signal to match a desired or target signal by a linear time-invariant (LTI) filter. The input signal of a Wiener filter is one-dimensional while its associated least-squares solution, namely Wiener-Hopf equation, involves a two-dimensional data-array, or correlation matrix. However, the actual match should often be carried out between a multi-dimensional filtered signal-sequence, which is the output of a multi-channel filter characterized as a linear-time-invariant MIMO (multi-input and multi-output) system, and a multi-dimensional desired signal-sequence simultaneously. In the presence of such a multi-channel filter, the solution to the corresponding Wiener filter, which we call MIMO Wiener-Hopf equation now, involves a correlation tensor. Therefore, we call this optimal multi-channel filter Tensor Wiener Filter (TWF). Due to lack of the pertinent mathematical framework of needed tensor operations, TWF has never been investigated so far. Now we would like to make the first-ever attempt to establish a new mathematical framework for TWF, which relies on the inverse of the correlation tensor. We propose the new parallel block-Jacobi tensor-inversion algorithm for this tensor inversion. A typical application of the new TWF approach is illustrated as a multi-channel linear predictor (MCLP) built upon a multi-channel autoregressive (MCAR) filter with multi-dimensional input data. Numerical experiments pertaining to seismic data, optical images, and macroeconomic time-series are conducted in comparison with other existing methods. The memory- and computational-complexities corresponding to our proposed parallel block-Jacobi tensor-inversion algorithm are also studied in this paper.

Traffic prediction is a very important mechanism in intelligent transportation systems for applications including routing planning and traffic control. In order to infer multifarious traffic information, one/two-relational traffic data in the vector/matrix form need to be expanded to multi-relational traffic data in an arbitrary tensor form. However, none of the existing approaches is capable of performing traffic prediction by characterizing and tracking the inherent nonlinear dynamics which are often encountered in realistic time-series analysis. Although the extended Kalman filter (EKF) has been proven to be quite promising in inferring nonlinear dynamics from time series, but the current EKF approach still suffers, unfortunately, from a serious drawback that state variables have to be represented in vector form. In fact, the characteristics of multi-relational states in practice can never been manifested accurately in practice and the performance of an EKF would be greatly restricted thereby. In this work, we introduce a new tensor extended Kalman filter (TEKF) approach to accommodate arbitrary input, output, and state variables all in arbitrary tensor forms. We also propose a new tensor-based expectation-maximization (EM) algorithm to estimate the nonlinear state-transition and observation-model mappings. The computational and memory complexities of the proposed TEKF approach are also studied in this paper. Finally, numerical experiments are conducted to evaluate the traffic prediction performance of the proposed new TEKF approach over the simulated and realworld traffic datasets in comparison with three other existing deep-learning prediction methods.

This article introduces a novel physical-layer (PHY-layer) authentication scheme, called transfer learning-based PHY-layer authentication (TL-PHA), aiming to achieve fast online user authentication that is highly desired for latency-sensitive applications such as edge computing. The proposed TL-PHA scheme is characterized by incorporating with a novel convolutional neural network architecture, namely, the triple-pool network (TP-Net), for achieving lightweight and online classification, as well as effective data augmentation methods for generation of data set samples for the network model training. To assess the performance of the proposed scheme, we conducted two sets of experiments, including the one using computer-simulated channel data and the other utilizing real experiment data generated by our wireless testbed. The results demonstrate the superiority of the proposed scheme in terms of authentication accuracy, detection rate, and training complexity compared to all the considered counterparts.

Because of rapid growth of multimedia data over the Internet, the infobesity has been emerging in recent years. Many recommender systems (RSs) have been proposed using a variety of techniques, including artificial intelligence, machine learning, statistical analysis, and data mining. Nowadays, E-commerce companies such as Amazon, eBay, Netflix, etc. have applied RSs conveniently to provide better customer services than before by enabling customized multimedia-content recommendations. It is well known that classical RSs are almost all based on the user-item attribute matrices. However, this two-fold user-item relationship should be extended to the emerging many-fold relationship among an arbitrary number of attribute groups so that the corresponding new RSs may lead to better performances. Therefore, in this paper, we introduce a novel personalized multimedia recommender system (PMRS) according to our proposed new parallel higher-order tensor singular-value-decomposition (PHOTSVD) algorithm. This PHOTSVD algorithm is capable of accommodating an arbitrary number of entities such as social-media channels, users, queries, webpages, etc. in a robust RS. Furthermore, we also investigate the cold start and data bias problems critical to RSs. Finally, we compare the performances of our proposed new PMRS and three other existing tensor-based RSs over realworld data with respect to the well-adopted metric, namely normalized root-mean-square error (NRMSE). Our proposed new PMRS greatly outperforms the other three existing tensor-based RSs in terms of NRMSE.

Channel estimation (CE) in reconfigurable intelligent surfaces (RIS)-assisted wireless communication systems is challenging when using traditional CE methods due to their computational intensity and inaccuracies, especially in large-scale RIS environments. These limitations directly impact the achievable data rate, which relies heavily on accurate channel state information (CSI) obtained from CE. To overcome these challenges, we propose a novel approach that utilizes graph neural networks (GNN) with region-specific training models. The GNN is employed to obtain CSI for carefully selected regions in a given large-scale area of interest (AOI) using a trial-based method, where different system configurations and parameters are tried, and the achieved performance for different assessing region sizes is evaluated. This ensures that the chosen regions effectively act as representative samples for the entire AOI. By leveraging the GNN-based CEs for these selected regions, we can accurately predict the performance for users in any AOI region. Additionally, we optimize the placement of double RISs to further enhance system performance. Extensive simulations are conducted to validate our approach and demonstrate its effectiveness in achieving accurate system performance with reduced complexity in large-scale communication systems.

Quantization is an important technique to transform the input sample values from a large set (or a continuous range) into the output sample values in a small set (or a finite set). It has been applied broadly for lossy-data compression, pattern recognition, probability density estimation, and clustering. Vector quantization (VQ) is a prevalent image-compression technique, which treats image matrices as stretched vectors and then finds the representative stretched vectors accordingly for a given image data set. One can use tensor data representation to directly characterize the original two-dimensional image data rather than stretch the image matrix into a long vector so as to destroy the original two-dimensional data structure. In this work, we propose a new tensor quantization (TQ) framework which does not need to reduce the dimensionality of the original image data and destroy the original two-dimensional spatial relationship among data; these two serious drawbacks of vector quantization are well known. We first present tensor calculus and then propose a new parallel tensor-inversion algorithm for TQ thereupon. We also establish the pertinent theoretical proof to justify that our proposed new TQ approach is superior to the existing VQ approach especially as the image dimension becomes large. Finally, numerical experiments to evaluate the image-compression performances of VQ and TQ are demonstrated and their corresponding computational-complexities are also compared.