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.

We prove generalization error bounds of classes of low-rank matrices with some norm constraints for collaborative filtering tasks. Our bounds are tighter, compared to known bounds using rank or the related quantity only, by taking the additional L1 and L∞ constraints into account. Also, we show that our bounds on the Rademacher complexity of the classes are optimal.

Recommender systems (RS) exploit user ratings on items and side information to make personalized recommendations. In order to recommend the right products to users, RS must accurately model the implicit preferences of each user and the properties of each product. In reality, both user preferences and item properties are changing dynamically over time, so treating the historical decisions of a user or the received comments of an item as static is inappropriate. Besides, the review text accompanied with a rating score can help us to understand why a user likes or dislikes an item, so temporal dynamics and text information in reviews are important side information for recommender systems. Moreover, compared with the large number of available items, the number of items a user can buy is very limited, which is called the sparsity problem. In order to solve this problem, utilizing item correlation provides a promising solution. Although famous methods like TimeSVD++, TopicMF and CoFactor partially take temporal dynamics, reviews and correlation into consideration, none of them combine these information together for accurate recommendation. Therefore, in this paper we propose a novel combined model called TmRevCo which is based on matrix factorization. Our model combines the dynamic user factor of TimeSVD++ with the hidden topic of each review text mined by the topic model of TopicMF through a new transformation function. Meanwhile, to support our five-scoring datasets, we use a more appropriate item correlation measure in CoFactor and associate the item factors of CoFactor with that of matrix factorization. Our model comprehensively combines the temporal dynamics, review information and item correlation simultaneously. Experimental results on three real-world datasets show that our proposed model leads to significant improvement compared with the baseline methods.

This paper presents a theoretical design of novel THz bandpass filters composed of M-PhC (metallic-photonic-crystal) point-defect-cavities (PDCs) with a centrally-loaded-rod. After a brief review of the properties of the recently-proposed M-PhC PDCs, two inline-type bandpass filters are synthesized in terms of the coupling matrix theory. The FDTD simulation results of the synthesized filters are in good agreement with the theoretical ones, which confirms the validity of the proposed filters' structures and the design scheme.

The spectrum sculpting precoder (SSP) is a precoding scheme for sidelobe suppression of frequency division multiplexing (OFDM) signals. It can form deep spectral notches at chosen frequencies and is suitable for cognitive radio systems. However, the SSP degrades the error rate as the number of notched frequencies increases. Orthogonal precoding that improves the SSP can achieve both spectrum notching and the ideal error rate, but its computational complexity is very high since the precoder matrix is large in size. This paper proposes an effective and equivalent decomposition of the precoder matrix by QR-decomposition in order to reduce the computational complexity of orthogonal precoding. Numerical experiments show that the proposed method can drastically reduce the computational complexity with no performance degradation.

The microfabrication technique based on SR (Synchrotron Radiation) direct etching process has recently been applied to construct PTFE microstructures. This paper attempts to fabricate an integrated PTFE-filled waveguide Butler matrix for short millimeter-wave by SR direct etching. First, a cruciform 3-dB directional coupler and an intersection circuit (0-dB coupler) are designed at 180 GHz. Then, a 4×4 Butler matrix with horn antennas is designed and fabricated. Finally, the measured radiation patterns of the Butler matrix are shown.

In this research, we propose an effective stability analysis method to impacting systems with periodically moving borders (periodic borders). First, we describe an n-dimensional impacting system with periodic borders. Subsequently, we present an algorithm based on a stability analysis method using the monodromy matrix for calculating stability of the waveform. This approach requires the state-transition matrix be related to the impact phenomenon, which is known as the saltation matrix. In an earlier study, the expression for the saltation matrix was derived assuming a static border (fixed border). In this research, we derive an expression for the saltation matrix for a periodic border. We confirm the performance of the proposed method, which is also applicable to systems with fixed borders, by applying it to an impacting system with a periodic border. Using this approach, we analyze the bifurcation of an impacting system with a periodic border by computing the evolution of the stable and unstable periodic waveform. We demonstrate a discontinuous change of the periodic points, which occurs when a periodic point collides with a border, in the one-parameter bifurcation diagram.

We consider online linear optimization over symmetric positive semi-definite matrices, which has various applications including the online collaborative filtering. The problem is formulated as a repeated game between the algorithm and the adversary, where in each round t the algorithm and the adversary choose matrices Xt and Lt, respectively, and then the algorithm suffers a loss given by the Frobenius inner product of Xt and Lt. The goal of the algorithm is to minimize the cumulative loss. We can employ a standard framework called Follow the Regularized Leader (FTRL) for designing algorithms, where we need to choose an appropriate regularization function to obtain a good performance guarantee. We show that the log-determinant regularization works better than other popular regularization functions in the case where the loss matrices Lt are all sparse. Using this property, we show that our algorithm achieves an optimal performance guarantee for the online collaborative filtering. The technical contribution of the paper is to develop a new technique of deriving performance bounds by exploiting the property of strong convexity of the log-determinant with respect to the loss matrices, while in the previous analysis the strong convexity is defined with respect to a norm. Intuitively, skipping the norm analysis results in the improved bound. Moreover, we apply our method to online linear optimization over vectors and show that the FTRL with the Burg entropy regularizer, which is the analogue of the log-determinant regularizer in the vector case, works well.

Neighborhood preserving embedding is a widely used manifold reduced dimensionality technique. But NPE has to encounter two problems. One problem is that it suffers from the small-sample-size (SSS) problem. Another is that the performance of NPE is seriously sensitive to the neighborhood size k. To overcome the two problems, an exponential neighborhood preserving embedding (ENPE) is proposed in this paper. The main idea of ENPE is that the matrix exponential is introduced to NPE, then the SSS problem is avoided and low sensitivity to the neighborhood size k is gotten. The experiments are conducted on ORL, Georgia Tech and AR face database. The results show that, ENPE shows advantageous performance over other unsupervised methods, such as PCA, LPP, ELPP and NPE. Another is that ENPE is much less sensitive to the neighborhood parameter k contrasted with the unsupervised manifold learning methods LPP, ELPP and NPE.

Compressed Sensing based CMOS image sensor (CS-CIS) is a new generation of CMOS image sensor that significantly reduces the power consumption. For CS-CIS, the image quality and data volume of output are two important issues to concern. In this paper, we first proposed an algorithm to generate a series of deterministic and ternary matrices, which improves the image quality, reduces the data volume and are compatible with CS-CIS. Proposed matrices are derived from the approximate DCT and trimmed in 2D-zigzag order, thus preserving the energy compaction property as DCT does. Moreover, we proposed matrix row operations adaptive to the proposed matrix to further compress data (measurements) without any image quality loss. At last, a low-cost VLSI architecture of measurements compression with proposed matrix row operations is implemented. Experiment results show our proposed matrix significantly improve the coding efficiency by BD-PSNR increase of 4.2 dB, comparing with the random binary matrix used in the-state-of-art CS-CIS. The proposed matrix row operations for measurement compression further increases the coding efficiency by 0.24 dB BD-PSNR (4.8% BD-rate reduction). The VLSI architecture is only 4.3 K gates in area and 0.3 mW in power consumption.

The separating redundancy is an important concept in the analysis of the error-and-erasure decoding of a linear block code using a parity-check matrix of the code. In this letter, we derive new constructive upper bounds on the second separating redundancies of low-density parity-check (LDPC) codes constructed from projective and Euclidean planes over the field Fq with q even.

Event-triggered control is a method that the control input is updated only when a certain triggering condition is satisfied. In networked control systems, quantization errors via A/D conversion should be considered. In this paper, a new method for quantized event-triggered control with switching triggering conditions is proposed. For a discrete-time linear system, we consider the problem of finding a state-feedback controller such that the closed-loop system is uniformly ultimately bounded in a certain ellipsoid. This problem is reduced to an LMI (Linear Matrix Inequality) optimization problem. The volume of the ellipsoid may be adjusted. The effectiveness of the proposed method is presented by a numerical example.

The problem of evaluating the matrix polynomial I+A+A2+…+AN-1 with a reduced number of matrix multiplications has long been considered. Several algorithms have been proposed for this problem, which find a procedure requiring O(log N) matrix multiplications for a given N. Among them, the hybrid algorithm based on the double-base representation of N, i.e., using mixed radices 2 and 3, proposed by Dimitrov and Cooklev is most efficient. It has been suggested by them that the use of higher radices would not bring any more efficient algorithms. In this paper, we show that we can derive more efficient algorithms by using higher radices, and propose several efficient algorithms.

As an effective method, exponential discriminant analysis (EDA) has been proposed and widely used to solve the so-called small-sample-size (SSS) problem. In this paper, a simple and effective generalization of EDA is presented and named as GEDA. In GEDA, a general exponential function, where the base of exponential function is larger than the Euler number, is used. Due to the property of general exponential function, the distance between samples belonging to different classes is larger than that of EDA, and then the discrimination property is largely emphasized. The experiment results on the Extended Yale and CMU-PIE face databases show that, GEDA gets more advantageous recognition performance compared to EDA.

In this paper, we present a new three-way split formula for binary polynomial multiplication (PM) with five recursive multiplications. The scheme is based on a recently proposed multievaluation and interpolation approach using field extension. The proposed PM formula achieves the smallest space complexity. Moreover, it has about 40% reduced time complexity compared to best known results. In addition, using developed techniques for PM formulas, we propose a three-way split formula for Toeplitz matrix vector product with five recursive products which has a considerably improved complexity compared to previous known one.

In this work, two new proposed NMF models are developed for facial expression recognition. They are called maximum volume constrained nonnegative matrix factorization (MV_NMF) and maximum volume constrained graph nonnegative matrix factorization (MV_GNMF). They achieve sparseness from a larger simplicial cone constraint and the extracted features preserve the topological structure of the original images.

This paper presents a measurement-domain intra prediction coding framework that is compatible with compressive sensing (CS)-based image sensors. In this framework, we propose a low-complexity intra prediction algorithm that can be directly applied to measurements captured by the image sensor. We proposed a structural random 0/1 measurement matrix, embedding the block boundary information that can be extracted from the measurements for intra prediction. Furthermore, a low-cost Very Large Scale Integration (VLSI) architecture is implemented for the proposed framework, by substituting the matrix multiplication with shared adders and shifters. The experimental results show that our proposed framework can compress the measurements and increase coding efficiency, with 34.9% BD-rate reduction compared to the direct output of CS-based sensors. The VLSI architecture of the proposed framework is 9.1 Kin area, and achieves the 83% reduction in size of memory bandwidth and storage for the line buffer. This could significantly reduce both the energy consumption and bandwidth in communication of wireless camera systems, which are expected to be massively deployed in the Internet of Things (IoT) era.

This work presents a new approach which derives a learned data representation method through matrix factorization on the complex domain. In particular, we introduce an encoding matrix-a new representation of data-that satisfies the simplicial constraint of the projective basis matrix on the field of complex numbers. A complex optimization framework is provided. It employs the gradient descent method and computes the derivative of the cost function based on Wirtinger's calculus.

Nonnegative Matrix Factorization (NMF) with sparseness and smoothness constraints has attracted increasing attention. When these properties are considered, NMF is usually formulated as an optimization problem in which a linear combination of an approximation error term and some regularization terms must be minimized under the constraint that the factor matrices are nonnegative. In this paper, we focus our attention on the error measure based on the Euclidean distance and propose a new iterative method for solving those optimization problems. The proposed method is based on the Hierarchical Alternating Least Squares (HALS) algorithm developed by Cichocki et al. We first present an example to show that the original HALS algorithm can increase the objective value. We then propose a new algorithm called the Gauss-Seidel HALS algorithm that decreases the objective value monotonically. We also prove that it has the global convergence property in the sense of Zangwill. We finally verify the effectiveness of the proposed algorithm through numerical experiments using synthetic and real data.

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.