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In this paper, a two-layer recurrent neural network is proposed to solve the nonsmooth convex optimization problem subject to convex inequality and linear equality constraints. Compared with existing neural network models, the proposed neural network has a low model complexity and avoids penalty parameters. It is proved that from any initial point, the state of the proposed neural network reaches the equality feasible region in finite time and stays there thereafter. Moreover, the state is unique if the initial point lies in the equality feasible region. The equilibrium point set of the proposed neural network is proved to be equivalent to the Karush–Kuhn–Tucker optimality set of the original optimization problem. It is further proved that the equilibrium point of the proposed neural network is stable in the sense of Lyapunov. Moreover, from any initial point, the state is proved to be convergent to an equilibrium point of the proposed neural network. Finally, as applications, the proposed neural network is used to solve nonlinear convex programming with linear constraints and L1 -norm minimization problems. [ABSTRACT FROM AUTHOR]

Dropout and DropConnect are two techniques to facilitate the regularization of neural network models, having achieved the state-of-the-art results in several benchmarks. In this paper, to improve the generalization capability of spiking neural networks (SNNs), the two drop techniques are first applied to the state-of-the-art SpikeProp learning algorithm resulting in two improved learning algorithms called SPDO (SpikeProp with Dropout) and SPDC (SpikeProp with DropConnect). In view that a higher membrane potential of a biological neuron implies a higher probability of neural activation, three adaptive drop algorithms, SpikeProp with Adaptive Dropout (SPADO), SpikeProp with Adaptive DropConnect (SPADC), and SpikeProp with Group Adaptive Drop (SPGAD), are proposed by adaptively adjusting the keep probability for training SNNs. A convergence theorem for SPDC is proven under the assumptions of the bounded norm of connection weights and a finite number of equilibria. In addition, the five proposed algorithms are carried out in a collaborative neurodynamic optimization framework to improve the learning performance of SNNs. The experimental results on the four benchmark data sets demonstrate that the three adaptive algorithms converge faster than SpikeProp, SPDO, and SPDC, and the generalization errors of the five proposed algorithms are significantly smaller than that of SpikeProp. Furthermore, the experimental results also show that the five algorithms based on collaborative neurodynamic optimization can be improved in terms of several measures. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the fuzzy constrained matrix game (MG) problems using the concepts of recurrent neural networks (RNNs). To the best of our knowledge, this paper is the first in attempting to find a solution for fuzzy game problems using RNN models. For this purpose, a fuzzy game problem is reformulated into a weighting problem. Then, the Karush–Kuhn–Tucker (KKT) optimality conditions are provided for the weighting problem. The KKT conditions are used to propose the RNN model. Moreover, the Lyapunov stability and the global convergence of the RNN model are also confirmed. Finally, three illustrative examples are presented to demonstrate the effectiveness of this approach. The obtained results are compared with the results obtained by the previous approaches for solving fuzzy constrained MG. [ABSTRACT FROM AUTHOR]

Unsupervised feature selection is fundamentally important for processing unlabeled high-dimensional data, and several methods have been proposed on this topic. Most existing embedded unsupervised methods just emphasize the data structure in the input space, which may contain large noise. Therefore, they are limited to perceive the discriminative information implied within the low-dimensional manifold. In addition, these methods always involve several parameters to be tuned, which is time-consuming. In this paper, we present a self-tuned discrimination-aware (STDA) approach for unsupervised feature selection. The main contributions of this paper are threefold: 1) it adopts the advantage of discriminant analysis technique to select the valuable features; 2) it learns the local data structure adaptively in the discriminative subspace to alleviate the effect of data noise; and 3) it performs feature selection and clustering simultaneously with an efficient optimization strategy, and saves the additional efforts to tune parameters. Experimental results on a toy data set and various real-world benchmarks justify the effectiveness of STDA on both feature selection and data clustering, and demonstrate its promising performance against the state of the arts. [ABSTRACT FROM AUTHOR]

Traffic congestion often incurs environmental problems. One of the most effective ways to mitigate this is carpooling transportation, which substantially reduces automobile demands. Due to the popularization of smartphones and mobile applications, a carpool service can be conveniently accessed via the intelligent carpool system. In this system, the service optimization required to intelligently and adaptively distribute the carpool participant resources is called the carpool service problem (CSP). Several previous studies have examined viable and preliminary solutions to the CSP by using exact and metaheuristic optimization approaches. For CSP-solving, evolutionary computation (e.g., metaheuristics) is a more promising option in comparison to exact-type approaches. However, all the previous state-of-the-art approaches use pure optimization to solve the CSP. In this paper, we employ the framework of neuroevolution to propose the self-organizing map-based neuroevolution (SOMNE) solver by which the SOM-like network represents the abstract CSP solution and is well-trained by using neural learning and evolutionary mechanism. The experimental section of this paper investigates the comparisons and analyses of two objective functions of the CSP and demonstrates that the proposed SOMNE solver achieves superior results when compared against those the other approaches produce, especially in regard to the optimization of the primary objective functions of the CSP. Finally, the visual results of the SOM are illustrated to show the effectiveness and efficiency of the evolutionary neural learning process. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new classification algorithm called the optimization of distribution differences (ODD). The algorithm aims to find a transformation from the feature space to a new space where the instances in the same class are as close as possible to one another, whereas the gravity centers of these classes are as far as possible from one another. This aim is formulated as a multiobjective optimization problem that is solved by a hybrid of an evolutionary strategy and the quasi-Newton method. The choice of the transformation function is flexible and could be any continuous space function. We experiment with a linear and a nonlinear transformation in this paper. We show that the algorithm can outperform eight other classification methods, namely naive Bayes, support vector machines, linear discriminant analysis, multilayer perceptrons, decision trees, and $k$ -nearest neighbors, and two recently proposed classification methods, in 12 standard classification data sets. Our results show that the method is less sensitive to the imbalanced number of instances compared with these methods. We also show that ODD maintains its performance better than other classification methods in these data sets and hence offers a better generalization ability. [ABSTRACT FROM AUTHOR]

The reduced-order filtering problems are investigated in this paper for static neural networks with Markovian jumping parameters and mode-dependent time-varying delays. By fully making use of integral inequalities, the designs of reduced-order $H_{\infty }$ and $L_{2}-L_{\infty }$ filters are discussed. The proper gain matrices of filters and the optimal performance indices are efficiently obtained by resolving corresponding convex optimization problems with the constraints of linear matrix inequalities. It is verified that the computational complexity for the reduced-order filter design is significantly reduced when compared with the full-order one. Furthermore, the nonfragile reduced-order filtering problems are also resolved in this paper. Two examples with simulation results are presented to demonstrate the feasibility and application of the established results. [ABSTRACT FROM AUTHOR]

Continuous-time and discrete-time forms of Zhang dynamics (ZD) for time-varying nonlinear optimization have been developed recently. In this paper, a novel discrete-time ZD (DTZD) algorithm is proposed and investigated based on the previous research. Specifically, the DTZD algorithm for time-varying nonlinear optimization is developed by adopting a new Taylor-type difference rule. This algorithm is a five-step iteration process, and thus, is referred to as the five-step DTZD algorithm in this paper. Theoretical analysis and results of the proposed five-step DTZD algorithm are presented to highlight its excellent computational performance. The geometric representation of the proposed algorithm for time-varying nonlinear optimization is also provided. Comparative numerical results are illustrated with four examples to substantiate the efficacy and superiority of the proposed five-step DTZD algorithm for time-varying nonlinear optimization compared with the previous DTZD algorithms. [ABSTRACT FROM AUTHOR]

The vast majority of dimensionality reduction (DR) techniques rely on the second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods require carefully designed regularizers and they are usually prone to outliers. In this paper, a new DR framework that can directly model the target distribution using the notion of similarity instead of distance is introduced. The proposed framework, called similarity embedding framework (SEF), can overcome the aforementioned limitations and provides a conceptually simpler way to express optimization targets similar to existing DR techniques. Deriving a new DR technique using the SEF becomes simply a matter of choosing an appropriate target similarity matrix. A variety of classical tasks, such as performing supervised DR and providing out-of-sample extensions, as well as, new novel techniques, such as providing fast linear embeddings for complex techniques, are demonstrated in this paper using the proposed framework. Six data sets from a diverse range of domains are used to evaluate the proposed method and it is demonstrated that it can outperform many existing DR techniques. [ABSTRACT FROM AUTHOR]

Hashing is emerging as a powerful tool for building highly efficient indices in large-scale search systems. In this paper, we study spectral hashing (SH), which is a classical method of unsupervised hashing. In general, SH solves for the hash codes by minimizing an objective function that tries to preserve the similarity structure of the data given. Although computationally simple, very often SH performs unsatisfactorily and lags distinctly behind the state-of-the-art methods. We observe that the inferior performance of SH is mainly due to its imperfect formulation; that is, the optimization of the minimization problem in SH actually cannot ensure that the similarity structure of the high-dimensional data is really preserved in the low-dimensional hash code space. In this paper, we, therefore, introduce reversed SH (ReSH), which is SH with its input and output interchanged. Unlike SH, which estimates the similarity structure from the given high-dimensional data, our ReSH defines the similarities between data points according to the unknown low-dimensional hash codes. Equipped with such a reversal mechanism, ReSH can seamlessly overcome the drawback of SH. More precisely, the minimization problem in our ReSH can be optimized if and only if similar data points are mapped to adjacent hash codes, and mostly important, dissimilar data points are considerably separated from each other in the code space. Finally, we solve the minimization problem in ReSH by multilayer neural networks and obtain state-of-the-art retrieval results on three benchmark data sets. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical properties of a network of neurons, each of which implements an asynchronous mapping based on polynomial growth transforms. In the first part of this paper, we present a geometric approach for visualizing the dynamics of the network where each of the neurons traverses a trajectory in a dual optimization space, whereas the network itself traverses a trajectory in an equivalent primal optimization space. We show that as the network learns to solve basic classification tasks, different choices of primal-dual mapping produce unique but interpretable neural dynamics like noise shaping, spiking, and bursting. While the proposed framework is general enough, in this paper, we demonstrate its use for designing support vector machines (SVMs) that exhibit noise-shaping properties similar to those of $\Sigma \Delta $ modulators, and for designing SVMs that learn to encode information using spikes and bursts. It is demonstrated that the emergent switching, spiking, and burst dynamics produced by each neuron encodes its respective margin of separation from a classification hyperplane whose parameters are encoded by the network population dynamics. We believe that the proposed growth transform neuron model and the underlying geometric framework could serve as an important tool to connect well-established machine learning algorithms like SVMs to neuromorphic principles like spiking, bursting, population encoding, and noise shaping. [ABSTRACT FROM AUTHOR]

This paper addresses two-stage resource allocation in the orthogonal frequency division multiplexing access system. In the subcarrier allocation stage, hysteretic noisy chaotic neural network (HNCNN) with a newly established energy function is proposed for subcarrier allocation to improve the optimization performance and reduce the computational complexity. Activation functions with both anticlockwise and clockwise hysteretic loops are applied to the HNCNN. A new energy function is established for an objective function, which can be calculated offline, resulting in a lower computational complexity in solving subcarrier allocation than the previous energy function. In the power allocation stage, the water-filling algorithm is employed to attain optimal power allocation. Simulation results show that the energy function established in this paper can decrease the runtimes of the neural networks, and that the HNCNN with both anticlockwise and clockwise hysteretic-loop activation functions can improve probabilities of feasible and optimal solutions at higher noises. The two-stage algorithm in this paper outperforms the previous algorithms in fairness, system throughput, and resource utilization. [ABSTRACT FROM AUTHOR]

Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high dimensional but sparse. This poses an imbalanced learning problem since the scale of missing entries is usually much larger than that of the observed entries, but they cannot be ignored due to the valuable negative signal. For efficiency concern, existing work typically applies a uniform weight on missing entries to allow a fast learning algorithm. However, this simplification will decrease modeling fidelity, resulting in suboptimal performance for downstream applications. In this paper, we weight the missing data nonuniformly, and more generically, we allow any weighting strategy on the missing data. To address the efficiency challenge, we propose a fast learning method, for which the time complexity is determined by the number of observed entries in the data matrix rather than the matrix size. The key idea is twofold: 1) we apply truncated singular value decomposition on the weight matrix to get a more compact representation of the weights and 2) we learn MF parameters with elementwise alternating least squares (eALS) and memorize the key intermediate variables to avoid repeating computations that are unnecessary. We conduct extensive experiments on two recommendation benchmarks, demonstrating the correctness, efficiency, and effectiveness of our fast eALS method. [ABSTRACT FROM AUTHOR]

Recent reports show that projection neural networks with a low-dimensional state space can enhance computation speed obviously. This paper proposes two projection neural networks with reduced model dimension and complexity (RDPNNs) for solving nonlinear programming (NP) problems. Compared with existing projection neural networks for solving NP, the proposed two RDPNNs have a low-dimensional state space and low model complexity. Under the condition that the Hessian matrix of the associated Lagrangian function is positive semi-definite and positive definite at each Karush–Kuhn–Tucker point, the proposed two RDPNNs are proven to be globally stable in the sense of Lyapunov and converge globally to a point satisfying the reduced optimality condition of NP. Therefore, the proposed two RDPNNs are theoretically guaranteed to solve convex NP problems and a class of nonconvex NP problems. Computed results show that the proposed two RDPNNs have a faster computation speed than the existing projection neural networks for solving NP problems. [ABSTRACT FROM AUTHOR]

Energy optimization for plug-in hybrid electric vehicles (PHEVs) is a challenging problem due to the system complexity and many physical and operational constraints in PHEVs. In this paper, we present a Q-learning-based in-vehicle learning system that is free of physical models and can robustly converge to an optimal energy control solution. The proposed machine learning algorithms combine neuro-dynamic programming (NDP) with future trip information to effectively estimate the expected future energy cost (expected cost-to-go) for a given vehicle state and control actions. The convergences of these learning algorithms were demonstrated on both fixed and randomly selected drive cycles. Based on the characteristics of these learning algorithms, we propose a two-stage deployment solution for PHEV power management applications. Furthermore, we introduce a new initialization strategy, which combines the optimal learning with a properly selected penalty function. This initialization scheme can reduce the learning convergence time by 70%, which is a significant improvement for in-vehicle implementation efficiency. Finally, we develop a neural network (NN) for predicting battery state-of-charge (SoC), rendering the proposed power management controller completely free of physical models. [ABSTRACT FROM AUTHOR]

In dynamic optimization problems (DOPs), as the environment changes through time, the optima also dynamically change. How to adapt to the dynamic environment and quickly find the optima in all environments is a challenging issue in solving DOPs. Usually, a new environment is strongly relevant to its previous environment. If we know how it changes from the previous environment to the new one, then we can transfer the information of the previous environment, e.g., past solutions, to get new promising information of the new environment, e.g., new high-quality solutions. Thus, in this paper, we propose a neural network (NN)-based information transfer method, named NNIT, to learn the transfer model of environment changes by NN and then use the learned model to reuse the past solutions. When the environment changes, NNIT first collects the solutions from both the previous environment and the new environment and then uses an NN to learn the transfer model from these solutions. After that, the NN is used to transfer the past solutions to new promising solutions for assisting the optimization in the new environment. The proposed NNIT can be incorporated into population-based evolutionary algorithms (EAs) to solve DOPs. Several typical state-of-the-art EAs for DOPs are selected for comprehensive study and evaluated using the widely used moving peaks benchmark. The experimental results show that the proposed NNIT is promising and can accelerate algorithm convergence. [ABSTRACT FROM AUTHOR]

In this paper, we study the minimization problem of a non-convex sparsity-promoting penalty function, i.e., fraction function, in compressed sensing. First, we discuss the equivalence of $\ell _{0}$ minimization and fraction function minimization. It is proved that the optimal solution to fraction function minimization solves $\ell _{0}$ minimization and the optimal solution to the regularization problem also solves fraction function minimization if the certain conditions are satisfied, which is similar to the regularization problem in a convex optimization theory. Second, we study the properties of the optimal solution to the regularization problem, including the first-order and second-order optimality conditions and the lower and upper bounds of the absolute value for its nonzero entries. Finally, we derive the closed-form representation of the optimal solution to the regularization problem and propose an iterative $FP$ thresholding algorithm to solve the regularization problem. We also provide a series of experiments to assess the performance of the $FP$ algorithm, and the experimental results show that the $FP$ algorithm performs well in sparse signal recovery with and without measurement noise. [ABSTRACT FROM AUTHOR]

Deep supervised hashing has emerged as an effective solution to large-scale semantic image retrieval problems in computer vision. Convolutional neural network-based hashing methods typically seek pairwise or triplet labels to conduct similarity-preserving learning. However, complex semantic concepts of visual contents are hard to capture by similar/dissimilar labels, which limits the retrieval performance. Generally, pairwise or triplet losses not only suffer from expensive training costs but also lack sufficient semantic information. In this paper, we propose a novel deep supervised hashing model to learn more compact class-level similarity-preserving binary codes. Our model is motivated by deep metric learning that directly takes semantic labels as supervised information in training and generates corresponding discriminant hashing code. Specifically, a novel cubic constraint loss function based on Gaussian distribution is proposed, which preserves semantic variations while penalizes the overlapping part of different classes in the embedding space. To address the discrete optimization problem introduced by binary codes, a two-step optimization strategy is proposed to provide efficient training and avoid the problem of gradient vanishing. Extensive experiments on five large-scale benchmark databases show that our model can achieve the state-of-the-art retrieval performance. [ABSTRACT FROM AUTHOR]

This paper presents a novel nonlinear dictionary learning (DL) model to address the energy disaggregation (ED) problem, i.e., decomposing the electricity signal of a home to its operating devices. First, ED is modeled as a new temporal DL problem where a set of dictionary atoms is learned to capture the most representative temporal features of electricity signals. The sparse codes corresponding to these atoms show the contribution of each device in the total electricity consumption. To learn powerful atoms, a novel deep temporal DL (DTDL) model is proposed that computes complex nonlinear dictionaries in the latent space of a long short-term memory autoencoder (LSTM-AE). While the LSTM-AE captures the deep temporal manifold of electricity signals, the DTDL model finds the most representative atoms inside this manifold. To simultaneously optimize the dictionary and the deep temporal manifold, a new optimization algorithm is proposed that alternates between finding the optimal LSTM-AE and the optimal dictionary. To the best of authors’ knowledge, DTDL is the only DL model that understands the deep temporal structures of the data. Experiments on the Reference ED Data Set show an outstanding performance compared with the recent state-of-the-art algorithms in terms of precision, recall, accuracy, and F-score. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel strategy to combine a set of compact descriptors to leverage an associated recognition task. We formulate the problem from a multiple kernel learning (MKL) perspective and solve it following a stochastic variance reduced gradient (SVRG) approach to address its scalability, currently an open issue. MKL models are ideal candidates to jointly learn the optimal combination of features along with its associated predictor. However, they are unable to scale beyond a dozen thousand of samples due to high computational and memory requirements, which severely limits their applicability. We propose SVRG-MKL, an MKL solution with inherent scalability properties that can optimally combine multiple descriptors involving millions of samples. Our solution takes place directly in the primal to avoid Gram matrices computation and memory allocation, whereas the optimization is performed with a proposed algorithm of linear complexity and hence computationally efficient. Our proposition builds upon recent progress in SVRG with the distinction that each kernel is treated differently during optimization, which results in a faster convergence than applying off-the-shelf SVRG into MKL. Extensive experimental validation conducted on several benchmarking data sets confirms a higher accuracy and a significant speedup of our solution. Our technique can be extended to other MKL problems, including visual search and transfer learning, as well as other formulations, such as group-sensitive (GMKL) and localized MKL (LMKL) in convex settings. [ABSTRACT FROM AUTHOR]

This paper deals with iterative Jacobian-based recursion technique for the root-finding problem of the vector-valued function, whose evaluations are contaminated by noise. Instead of a scalar step size, we use an iterate-dependent matrix gain to effectively weigh the different elements associated with the noisy observations. The analytical development of the matrix gain is built on an iterative-dependent linear function interfered by additive zero-mean white noise, where the dimension of the function is $ {M\ge 1}$ and the dimension of the unknown variable is $ {N\ge 1}$. Necessary and sufficient conditions for $ {M\ge N}$ algorithms are presented pertaining to algorithm stability and convergence of the estimate error covariance matrix. Two algorithms are proposed: one for the case where $ {M\ge N}$ and the second one for the antithesis. The two algorithms assume full knowledge of the Jacobian. The recursive algorithms are proposed for generating the optimal iterative-dependent matrix gain. The proposed algorithms here aim for per-iteration minimization of the mean square estimate error. We show that the proposed algorithm satisfies the presented conditions for stability and convergence of the covariance. In addition, the convergence rate of the estimation error covariance is shown to be inversely proportional to the number of iterations. For the antithesis $ {M< N}$ , contraction of the error covariance is guaranteed. This underdetermined system of equations can be helpful in training neural networks. Numerical examples are presented to illustrate the performance capabilities of the proposed multidimensional gain while considering nonlinear functions. [ABSTRACT FROM AUTHOR]

This paper addresses task assignment (TA) for multivehicle systems. Multivehicle TA problems are formulated as a combinatorial optimization problem and further as a global optimization problem. To fulfill heterogeneous tasks, cooperation among heterogeneous vehicles is incorporated in the problem formulations. A collaborative neurodynamic optimization approach is developed for solving the TA problems. Experimental results on four types of TA problems are discussed to substantiate the efficacy of the approach. [ABSTRACT FROM AUTHOR]

This paper proposes a quaternion-valued one-layer recurrent neural network approach to resolve constrained convex function optimization problems with quaternion variables. Leveraging the novel generalized Hamilton-real (GHR) calculus, the quaternion gradient-based optimization techniques are proposed to derive the optimization algorithms in the quaternion field directly rather than the methods of decomposing the optimization problems into the complex domain or the real domain. Via chain rules and Lyapunov theorem, the rigorous analysis shows that the deliberately designed quaternion-valued one-layer recurrent neural network stabilizes the system dynamics while the states reach the feasible region in finite time and converges to the optimal solution of the considered constrained convex optimization problems finally. Numerical simulations verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a robust linear discriminant analysis (RLDA) through Bhattacharyya error bound optimization. RLDA considers a nonconvex problem with the $L_{1}$ -norm operation that makes it less sensitive to outliers and noise than the $L_{2}$ -norm linear discriminant analysis (LDA). In addition, we extend our RLDA to a sparse model (RSLDA). Both RLDA and RSLDA can extract unbounded numbers of features and avoid the small sample size (SSS) problem, and an alternating direction method of multipliers (ADMM) is used to cope with the nonconvexity in the proposed formulations. Compared with the traditional LDA, our RLDA and RSLDA are more robust to outliers and noise, and RSLDA can obtain sparse discriminant directions. These findings are supported by experiments on artificial data sets as well as human face databases. [ABSTRACT FROM AUTHOR]

Convolutional sparse coding (CSC) is a useful tool in many image and audio applications. Maximizing the performance of CSC requires that the dictionary used to store the features of signals can be learned from real data. The so-called convolutional dictionary learning (CDL) problem is formulated within a nonconvex, nonsmooth optimization framework. Most existing CDL solvers alternately update the coefficients and dictionary in an iterative manner. However, these approaches are prone to running redundant iterations, and their convergence properties are difficult to analyze. Moreover, most of those methods approximate the original nonconvex sparse inducing function using a convex regularizer to promote computational efficiency. This approach to approximation may result in nonsparse representations and, thereby, hinder the performance of the applications. In this paper, we deal with the nonconvex, nonsmooth constraints of the original CDL directly using the modified forward–backward splitting approach, in which the coefficients and dictionary are simultaneously updated in each iteration. We also propose a novel parameter adaption scheme to increase the speed of the algorithm used to obtain a usable dictionary and in so doing prove convergence. We also show that the proposed approach is applicable to parallel processing to reduce the computing time required by the algorithm to achieve convergence. The experimental results demonstrate that our method requires less time than the existing methods to achieve the convergence point while using a smaller final functional value. We also applied the dictionaries learned using the proposed and existing methods to an application involving signal separation. The dictionary learned using the proposed approach provides performance superior to that of comparable methods. [ABSTRACT FROM AUTHOR]

As the main performance self-evaluation index of the Kalman filter, the estimation error covariance (EEC) has been used to design the allocation cost function of task and resources for sensor tracking networks. For nonlinear systems, the sensor allocation method based on the EEC needs to adjust the allocation plans after obtaining the filtering results. Meanwhile, recent investigations have indicated that the self-evaluation function EEC of the Kalman filtering is universally inapplicable in practical applications, for which the estimation models are generally mismatched due to difficulty in accurately training parameters and approximation of nonlinear systems. Thereby, the sensors cannot be properly allocated by using the EEC as a preliminary criterion. Alternatively, observable degree (OD) is a naturally quantitative measure on observability and can be utilized to effectively measure the estimation performance. In this paper, the OD analysis with scale transform invariance for nonlinear systems is studied by using the unscented Kalman filter, the pseudostate transition matrix, and the pseudo observation matrix on the basis of the results of linear systems. Afterward, the OD of nonlinear fusion systems, the sensor utilization efficiency, the priority of tasks, and the sensor performance and sensitivity are jointly considered to formulate the optimization problem for sensor allocation. The genetic algorithm with intelligent learning function is employed to solve the optimization problem. Moreover, extensive simulation demonstrates the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

Many machine learning problems involve learning a low-rank positive semidefinite matrix. However, existing solvers for this low-rank semidefinite program (SDP) are often expensive. In this paper, by factorizing the target matrix as a product of two matrices and using a Courant penalty to penalize for their difference, we reformulate the SDP as a biconvex optimization problem. This allows the use of multiconvex optimization techniques to define simple surrogates, which can be minimized easily by block coordinate descent. Moreover, while traditionally this biconvex problem approaches the original problem only when the penalty parameter is infinite, we show that the two problems are equivalent when the penalty parameter is sufficiently large. Experiments on a number of SDP applications in machine learning show that the proposed algorithm is as accurate as other state-of-the-art algorithms, but is much faster, especially on large data sets. [ABSTRACT FROM AUTHOR]

The limited memory version of the Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm is the most popular quasi-Newton algorithm in machine learning and optimization. Recently, it was shown that the stochastic L-BFGS (sL-BFGS) algorithm with the variance-reduced stochastic gradient converges linearly. In this paper, we propose a new sL-BFGS algorithm by importing a proper momentum. We prove an accelerated linear convergence rate under mild conditions. The experimental results on different data sets also verify this acceleration advantage. [ABSTRACT FROM AUTHOR]

For many specific applications in data mining and machine learning, we face explicit or latent size constraint for each cluster that leads to the “balanced clustering” problem. Many existing clustering algorithms perform well in partitioning but fail in producing balanced clusters and preserving the naturally balanced structure of some data. In this paper, we propose a novel balanced clustering framework that flexibly utilizes local and global information of data. First, we propose the global balanced clustering (GBC), in which a global discriminative partitioning model is combined with the minimization of the distribution entropy of data. Then, we show that the proposed GBC can be further used to globally regularize some widely used local clustering models, so as to transform them into balanced clustering that simultaneously capture local and global data. We apply our global balanced regularization to spectral clustering (SC) and local learning (LL)-based clustering, respectively, and propose another two novel balanced clustering models: the local and global balanced SC (LGB-SC) and LGB-LL. Finding the optimal balanced partition is nondeterministic polynomial-time (NP)-hard in general. We adopt the method of augmented Lagrange multipliers to help optimize our model. Comprehensive experiments on several real world benchmarks demonstrate the advantage of our framework to yield balanced clusters while preserving good clustering quality. Our proposed LGB-SC and LGB-LL also outperform SC and LL as well as other classical clustering methods. [ABSTRACT FROM AUTHOR]

Recently, there is a rapidly increasing attraction for the efficient recovery of low-rank matrix in computer vision and machine learning. The popular convex solution of rank minimization is nuclear norm-based minimization (NNM), which usually leads to a biased solution since NNM tends to overshrink the rank components and treats each rank component equally. To address this issue, some nonconvex nonsmooth rank (NNR) relaxations have been exploited widely. Different from these convex and nonconvex rank substitutes, this paper first introduces a general and flexible rank relaxation function named weighted NNR relaxation function, which is actually derived from the initial double NNR (DNNR) relaxations, i.e., DNNR relaxation function acts on the nonconvex singular values function (SVF). An iteratively reweighted SVF optimization algorithm with continuation technology through computing the supergradient values to define the weighting vector is devised to solve the DNNR minimization problem, and the closed-form solution of the subproblem can be efficiently obtained by a general proximal operator, in which each element of the desired weighting vector usually satisfies the nondecreasing order. We next prove that the objective function values decrease monotonically, and any limit point of the generated subsequence is a critical point. Combining the Kurdyka–Łojasiewicz property with some milder assumptions, we further give its global convergence guarantee. As an application in the matrix completion problem, experimental results on both synthetic data and real-world data can show that our methods are competitive with several state-of-the-art convex and nonconvex matrix completion methods. [ABSTRACT FROM AUTHOR]

Structural support vector machine (SSVM) is popular in the visual tracking field as it provides a consistent target representation for both learning and detection. However, the spatial distribution of feature is not considered in standard SSVM-based trackers, therefore leading to limited performance. To obtain a robust discriminative classifier, this paper proposes a novel tracking framework that spatially regularizes SSVM, which yields a new spatially regularized SSVM (SRSSVM). We utilize the spatial regularization prior to penalize the learning classifier with the same size as the target region. The location of classifier spatially located far from the center of region is assigned large weight and vice versa. Then, it is introduced into the SSVM model as a regularization factor to learn the robust discriminative model. Furthermore, an optimizing algorithm with dual coordination descent is presented to efficiently solve the SRSSVM tracking model. Our proposed SRSSVM tracking method has low computational cost like the traditional linear SSVM tracker while can significantly improve the robustness of the discriminative classifier. The experimental results on three popular tracking benchmark data sets show that the proposed SRSSVM tracking method performs favorably against the state-of-the-art trackers. [ABSTRACT FROM AUTHOR]

The recent studies have found that the nonconvex relaxation functions usually perform better than the convex counterparts in the $l_{0}$ -norm and rank function minimization problems. However, due to the absence of convexity in these nonconvex problems, developing efficient algorithms with convergence guarantee becomes very challenging. Inspired by the basic ideas of both the Jacobian alternating direction method of multipliers (JADMMs) for solving linearly constrained problems with separable objectives and the proximal gradient methods (PGMs) for optimizing the unconstrained problems with one variable, this paper focuses on extending the PGMs to the proximal Jacobian iteration methods (PJIMs) for handling with a family of nonconvex composite optimization problems with two splitting variables. To reduce the total computational complexity by decreasing the number of iterations, we devise the accelerated version of PJIMs through the well-known Nesterov’s acceleration strategy and further extend both to solve the multivariable cases. Most importantly, we provide a rigorous convergence analysis, in theory, to show that the generated variable sequence globally converges to a critical point by exploiting the Kurdyka–Łojasiewica (KŁ) property for a broad class of functions. Furthermore, we also establish the linear and sublinear convergence rates of the obtained variable sequence in the objective function. As the specific application to the nonconvex sparse and low-rank recovery problems, several numerical experiments can verify that the newly proposed algorithms not only keep fast convergence speed but also have high precision. [ABSTRACT FROM AUTHOR]

In this paper, we propose a framework of maximizing quadratic submodular energy with a knapsack constraint approximately, to solve certain computer vision problems. The proposed submodular maximization problem can be viewed as a generalization of the classic 0/1 knapsack problem. Importantly, maximization of our knapsack constrained submodular energy function can be solved via dynamic programing. We further introduce a range-reduction step prior to dynamic programing as a two-stage procedure for more efficient maximization. In order to demonstrate the effectiveness of the proposed energy function and its maximization algorithm, we apply it to two representative computer vision tasks: image segmentation and motion trajectory clustering. Experimental results of image segmentation demonstrate that our method outperforms the classic segmentation algorithms of graph cuts and random walks. Moreover, our framework achieves better performance than state-of-the-art methods on the motion trajectory clustering task. [ABSTRACT FROM AUTHOR]

Boosting is a learning scheme that combines weak learners to produce a strong composite learner, with the underlying intuition that one can obtain accurate learner by combining “rough” ones. This paper aims at developing a new boosting strategy, called rescaled boosting (RBoosting), to accelerate the numerical convergence rate and, consequently, improve learning performances of the original boosting. Our studies show that RBoosting possesses the almost optimal numerical convergence rate in the sense that, up to a logarithmic factor, it can reach the minimax nonlinear approximation rate. We then use RBoosting to tackle classification problems and deduce corresponding statistical consistency and tight generalization error estimates. A series of theoretical and experimental results shows that RBoosting outperforms boosting in terms of generalization. [ABSTRACT FROM AUTHOR]

Convolutional autoencoders (CAEs) have shown their remarkable performance in stacking to deep convolutional neural networks (CNNs) for classifying image data during the past several years. However, they are unable to construct the state-of-the-art CNNs due to their intrinsic architectures. In this regard, we propose a flexible CAE (FCAE) by eliminating the constraints on the numbers of convolutional layers and pooling layers from the traditional CAE. We also design an architecture discovery method by exploiting particle swarm optimization, which is capable of automatically searching for the optimal architectures of the proposed FCAE with much less computational resource and without any manual intervention. We test the proposed approach on four extensively used image classification data sets. Experimental results show that our proposed approach in this paper significantly outperforms the peer competitors including the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a two-timescale duplex neurodynamic system for constrained biconvex optimization. The two-timescale duplex neurodynamic system consists of two recurrent neural networks (RNNs) operating collaboratively at two timescales. By operating on two timescales, RNNs are able to avoid instability. In addition, based on the convergent states of the two RNNs, particle swarm optimization is used to optimize initial states of the RNNs to avoid local minima. It is proven that the proposed system is globally convergent to the global optimum with probability one. The performance of the two-timescale duplex neurodynamic system is substantiated based on the benchmark problems. Furthermore, the proposed system is applied for $L_{1}$ -constrained nonnegative matrix factorization. [ABSTRACT FROM AUTHOR]

The existing, semisupervised, spectral clustering approaches have two major drawbacks, i.e., either they cannot cope with multiple categories of supervision or they sometimes exhibit unstable effectiveness. To address these issues, two normalized affinity and penalty jointly constrained spectral clustering frameworks as well as their corresponding algorithms, referred to as type-I affinity and penalty jointly constrained spectral clustering (TI-APJCSC) and type-II affinity and penalty jointly constrained spectral clustering (TII-APJCSC), respectively, are proposed in this paper. TI refers to type-I and TII to type-II. The significance of this paper is fourfold. First, benefiting from the distinctive affinity and penalty jointly constrained strategies, both TI-APJCSC and TII-APJCSC are substantially more effective than the existing methods. Second, both TI-APJCSC and TII-APJCSC are fully compatible with the three well-known categories of supervision, i.e., class labels, pairwise constraints, and grouping information. Third, owing to the delicate framework normalization, both TI-APJCSC and TII-APJCSC are quite flexible. With a simple tradeoff factor varying in the small fixed interval (0, 1], they can self-adapt to any semisupervised scenario. Finally, both TI-APJCSC and TII-APJCSC demonstrate strong robustness, not only to the number of pairwise constraints but also to the parameter for affinity measurement. As such, the novel TI-APJCSC and TII-APJCSC algorithms are very practical for medium- and small-scale semisupervised data sets. The experimental studies thoroughly evaluated and demonstrated these advantages on both synthetic and real-life semisupervised data sets. [ABSTRACT FROM AUTHOR]

In this paper, a neurodynamic approach for image restoration is proposed. Image restoration is a process of estimating original images from blurred and/or noisy images. It can be considered as a mapping problem that can be solved by neural networks. Echo state network (ESN) is a recurrent neural network with a simplified training process, which is adopted to estimate the original images in this paper. The parameter selection is important to the performance of the ESN. Thus, the pigeon-inspired optimization (PIO) approach is employed in the training process of the ESN to obtain desired parameters. Moreover, the orthogonal design strategy is utilized in the initialization of PIO to improve the diversity of individuals. The proposed method is tested on several deteriorated images with different sorts and levels of blur and/or noise. Results obtained by the improved ESN are compared with those obtained by several state-of-the-art methods. It is verified experimentally that better image restorations can be obtained for different blurred and/or noisy instances with the proposed neurodynamic method. In addition, the performance of the orthogonal PIO algorithm is compared with that of several existing bioinspired optimization algorithms to confirm its superiority. [ABSTRACT FROM AUTHOR]

This paper develops a novel decentralized dimensionality reduction algorithm for the distributed tensor data across sensor networks. The main contributions of this paper are as follows. First, conventional centralized methods, which utilize entire data to simultaneously determine all the vectors of the projection matrix along each tensor mode, are not suitable for the network environment. Here, we relax the simultaneous processing manner into the one-vector-by-one-vector (OVBOV) manner, i.e., determining the projection vectors (PVs) related to each tensor mode one by one. Second, we prove that in the OVBOV manner each PV can be determined without modifying any tensor data, which simplifies corresponding computations. Third, we cast the decentralized PV determination problem as a set of subproblems with consensus constraints, so that it can be solved in the network environment only by local computations and information communications among neighboring nodes. Fourth, we introduce the null space and transform the PV determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint, which can be solved by the Lagrange multiplier method. Finally, experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed tensor data across the sensor networks. [ABSTRACT FROM AUTHOR]

Convolutional neural networks (CNNs) are powerful machine learning models that have become the state of the art in several problems in the areas of computer vision and image processing. Nevertheless, the knowledge of why and how these models present an impressive performance is still limited. There are visualization techniques that can help us to understand the inner working of neural networks. However, they have mostly been applied to classification models. In this paper, we evaluate the application of visualization methods to networks where the input and output are images of proportional dimensions. The results show that visualization brings visual cues associated with how these systems work, helping in their understanding and improvement. We use the knowledge obtained from the visualization of an image restoration CNN to improve the architecture’s efficiency with no significant degradation of its performance. [ABSTRACT FROM AUTHOR]

Subspace clustering is a problem of exploring the low-dimensional subspaces of high-dimensional data. State-of-the-art approaches are designed by following the model of spectral clustering-based method. These methods pay much attention to learn the representation matrix to construct a suitable similarity matrix and overlook the influence of the noise term on subspace clustering. However, the real data are always contaminated by the noise and the noise usually has a complicated statistical distribution. To alleviate this problem, in this paper, we propose a subspace clustering method based on Cauchy loss function (CLF). Particularly, it uses CLF to penalize the noise term for suppressing the large noise mixed in the real data. This is due to that the CLF’s influence function has an upper bound that can alleviate the influence of a single sample, especially the sample with a large noise, on estimating the residuals. Furthermore, we theoretically prove the grouping effect of our proposed method, which means that highly correlated data can be grouped together. Finally, experimental results on five real data sets reveal that our proposed method outperforms several representative clustering methods. [ABSTRACT FROM AUTHOR]

Multitask learning aims to improve the performance on related tasks by exploring the interdependence among them. Existing multitask learning methods explore the relatedness among tasks on the basis of the input features and the model parameters. In this paper, we focus on nonparametric multitask learning and propose to measure task relatedness from a novel perspective in a reproducing kernel Hilbert space (RKHS). Past works have shown that the objective function for a given task can be approximated using the top eigenvalues and corresponding eigenfunctions of a predefined integral operator on an RKHS. In our method, we formulate our objective for multitask learning as a linear combination of two sets of eigenfunctions, common eigenfunctions shared by different tasks and unique eigenfunctions in individual tasks, such that the eigenfunctions for one task can provide additional information on another and help to improve its performance. We present both theoretical and empirical validations of our proposed approach. The theoretical analysis demonstrates that our learning algorithm is uniformly argument stable and that the convergence rate of the generalization upper bound can be improved by learning multiple tasks. Experiments on several benchmark multitask learning data sets show that our method yields promising results. [ABSTRACT FROM AUTHOR]

Conjugate gradient (CG) methods are a class of important methods for solving linear equations and nonlinear optimization problems. In this paper, we propose a new stochastic CG algorithm with variance reduction and we prove its linear convergence with the Fletcher and Reeves method for strongly convex and smooth functions. We experimentally demonstrate that the CG with variance reduction algorithm converges faster than its counterparts for four learning models, which may be convex, nonconvex or nonsmooth. In addition, its area under the curve performance on six large-scale data sets is comparable to that of the LIBLINEAR solver for the $L2$ -regularized $L2$ -loss but with a significant improvement in computational efficiency. 1 CGVR algorithm is available on github: https://github.com/xbjin/cgvr [ABSTRACT FROM AUTHOR]

In real-world transfer learning tasks, especially in cross-modal applications, the source domain and the target domain often have different features and distributions, which are well known as the heterogeneous domain adaptation (HDA) problem. Yet, existing HDA methods focus on either alleviating the feature discrepancy or mitigating the distribution divergence due to the challenges of HDA. In fact, optimizing one of them can reinforce the other. In this paper, we propose a novel HDA method that can optimize both feature discrepancy and distribution divergence in a unified objective function. Specifically, we present progressive alignment, which first learns a new transferable feature space by dictionary-sharing coding, and then aligns the distribution gaps on the new space. Different from previous HDA methods that are limited to specific scenarios, our approach can handle diverse features with arbitrary dimensions. Extensive experiments on various transfer learning tasks, such as image classification, text categorization, and text-to-image recognition, verify the superiority of our method against several state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

In most domain adaption approaches, all features are used for domain adaption. However, often, not every feature is beneficial for domain adaption. In such cases, incorrectly involving all features might cause the performance to degrade. In other words, to make the model trained on the source domain work well on the target domain, it is desirable to find invariant features for domain adaption rather than using all features. However, invariant features across domains may lie in a higher order space, instead of in the original feature space. Moreover, the discriminative ability of some invariant features such as shared background information is weak, and needs to be further filtered. Therefore, in this paper, we propose a novel domain adaption algorithm based on an explicit feature map and feature selection. The data are first represented by a kernel-induced explicit feature map, such that high-order invariant features can be revealed. Then, by minimizing the marginal distribution difference, conditional distribution difference, and the model error, the invariant discriminative features are effectively selected. This problem is NP-hard to be solved, and we propose to relax it and solve it by a cutting plane algorithm. Experimental results on six real-world benchmarks have demonstrated the effectiveness and efficiency of the proposed algorithm, which outperforms many state-of-the-art domain adaption approaches. [ABSTRACT FROM AUTHOR]

In this paper, we propose a unified model called flexible affinity matrix learning (FAML) for unsupervised and semisupervised classification by exploiting both the relationship among data and the clustering structure simultaneously. To capture the relationship among data, we exploit the self-expressiveness property of data to learn a structured matrix in which the structures are induced by different norms. A rank constraint is imposed on the Laplacian matrix of the desired affinity matrix, so that the connected components of data are exactly equal to the cluster number. Thus, the clustering structure is explicit in the learned affinity matrix. By making the estimated affinity matrix approximate the structured matrix during the learning procedure, FAML allows the affinity matrix itself to be adaptively adjusted such that the learned affinity matrix can well capture both the relationship among data and the clustering structure. Thus, FAML has the potential to perform better than other related methods. We derive optimization algorithms to solve the corresponding problems. Extensive unsupervised and semisupervised classification experiments on both synthetic data and real-world benchmark data sets show that the proposed FAML consistently outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Previous works provide a few effective discretization formulas for zeroing neural network (ZNN), of which the precision is a square pattern. However, those formulas are separately developed via many relatively blind attempts. In this paper, general square-pattern discretization (SPD) formulas are proposed for ZNN via the idea of the second-order derivative elimination. All existing SPD formulas in previous works are included in the framework of the general SPD formulas. The connections and differences of various general formulas are also discussed. Furthermore, the general SPD formulas are used to solve future optimization under linear equality constraints, and the corresponding general discrete ZNN models are proposed. General discrete ZNN models have at least one parameter to adjust, thereby determining their zero stability. Thus, the parameter domains are obtained by restricting zero stability. Finally, numerous comparative numerical experiments, including the motion control of a PUMA560 robot manipulator, are provided to substantiate theoretical results and their superiority to conventional Euler formula. [ABSTRACT FROM AUTHOR]

In kernel methods, the kernels are often required to be positive definitethat restricts the use of many indefinite kernels. To consider those nonpositive definite kernels, in this paper, we aim to build an indefinite kernel learning framework for kernel logistic regression (KLR). The proposed indefinite KLR (IKLR) model is analyzed in the reproducing kernel Kreĭn spaces and then becomes nonconvex. Using the positive decomposition of a nonpositive definite kernel, the derived IKLR model can be decomposed into the difference of two convex functions. Accordingly, a concave-convex procedure (CCCP) is introduced to solve the nonconvex optimization problem. Since the CCCP has to solve a subproblem in each iteration, we propose a concave-inexact-convex procedure (CCICP) algorithm with an inexact solving scheme to accelerate the solving process. Besides, we propose a stochastic variant of CCICP to efficiently obtain a proximal solution, which achieves the similar purpose with the inexact solving scheme in CCICP. The convergence analyses of the above-mentioned two variants of CCCP are conducted. By doing so, our method works effectively not only in a deterministic setting but also in a stochastic setting. Experimental results on several benchmarks suggest that the proposed IKLR model performs favorably against the standard (positive definite) KLR and other competitive indefinite learning-based algorithms. [ABSTRACT FROM AUTHOR]

In this paper a self-paced learning-based probability subspace projection (SL-PSP) method is proposed for hyperspectral image classification. First, a probability label is assigned for each pixel, and a risk is assigned for each labeled pixel. Then, two regularizers are developed from a self-paced maximum margin and a probability label graph, respectively. The first regularizer can increase the discriminant ability of features by gradually involving the most confident pixels into the projection to simultaneously push away heterogeneous neighbors and pull inhomogeneous neighbors. The second regularizer adopts a relaxed clustering assumption to make avail of unlabeled samples, thus accurately revealing the affinity between mixed pixels and achieving accurate classification with very few labeled samples. Several hyperspectral data sets are used to verify the effectiveness of SL-PSP, and the experimental results show that it can achieve the state-of-the-art results in terms of accuracy and stability. [ABSTRACT FROM AUTHOR]

Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two data sets. However, all existing approaches often optimize a PLSR model in Euclidean space and take a successive strategy to calculate all the factors one by one for keeping the mutually orthogonal PLSR factors. Thus, a suboptimal solution is often generated. To overcome the shortcoming, this paper takes statistically inspired modification of PLSR (SIMPLSR) as a representative of PLSR, proposes a novel approach to transform SIMPLSR into optimization problems on Riemannian manifolds, and develops corresponding optimization algorithms. These algorithms can calculate all the PLSR factors simultaneously to avoid any suboptimal solutions. Moreover, we propose sparse SIMPLSR on Riemannian manifolds, which is simple and intuitive. A number of experiments on classification problems have demonstrated that the proposed models and algorithms can get lower classification error rates compared with other linear regression methods in Euclidean space. We have made the experimental code public at https://github.com/Haoran2014. [ABSTRACT FROM AUTHOR]