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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]

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]

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]

Self-organizing map (SOM)-based motif mining, despite being a promising approach for problem solving, mostly fails to offer a consistent interpretation of clusters with respect to the mixed composition of signal and noise in the nodes. The main reason behind this shortcoming comes from the similarity metrics used in data assignment, specially designed with the biological interpretation for this domain, which are not meant to consider the inevitable noise mixture in the clusters. This limits the explicability of the majority of clusters that are supposedly noise dominated, degrading the overall system clarity in motif discovery. This paper aims to improve the explicability aspect of learning process by introducing a composite similarity function (CSF) that is specially designed for the k -mer-to-cluster similarity measure with respect to the degree of motif properties and embedded noise in the cluster. Our proposed motif finding algorithm in this paper is built on our previous work robust elicitation algorithms for discovering (READ) [1] and termed READ Deoxyribonucleic acid motifs using CSFs (READ _{\rm csf} ), which performs slightly better than READ and shows some remarkable improvements over SOM-based SOMBRERO and SOMEA tools in terms of F$ -measure on the testing data sets. A real data set containing multiple motifs is used to explore the potential of the READ _{\rm csf} for more challenging biological data mining tasks. Visual comparisons with the verified logos extracted from JASPAR database demonstrate that our algorithm is promising to discover multiple motifs simultaneously. [ABSTRACT FROM PUBLISHER]

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]

This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation. [ABSTRACT FROM PUBLISHER]

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]

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 propose a novel iterative optimization model for bottom-up saliency detection. By exploring bottom-up saliency principles and semisupervised learning approaches, we design a high-performance saliency analysis method for wide ranging scenes. The proposed algorithm consists of two stages: 1) we develop a boundary homogeneity model to characterize the general position and the contour of the salient objects and 2) we propose a novel iterative optimization model, termed gradual saliency optimization, for further performance improvement. Our main contribution falls on the second stage, where we propose an iterative framework with self-repairing mechanisms for refining saliency maps. In this framework, we further develop a more comprehensive optimization function applying a novel semisupervised learning scheme to enhance the traditional saliency measure. More elaborately, the iterative method can gradually improve the output in each iteration and finally converge to high-quality saliency maps. Based on our experiments on four different public data sets, it can be demonstrated that our approach significantly outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Imbalanced data with a skewed class distribution are common in many real-world applications. Deep Belief Network (DBN) is a machine learning technique that is effective in classification tasks. However, conventional DBN does not work well for imbalanced data classification because it assumes equal costs for each class. To deal with this problem, cost-sensitive approaches assign different misclassification costs for different classes without disrupting the true data sample distributions. However, due to lack of prior knowledge, the misclassification costs are usually unknown and hard to choose in practice. Moreover, it has not been well studied as to how cost-sensitive learning could improve DBN performance on imbalanced data problems. This paper proposes an evolutionary cost-sensitive deep belief network (ECS-DBN) for imbalanced classification. ECS-DBN uses adaptive differential evolution to optimize the misclassification costs based on the training data that presents an effective approach to incorporating the evaluation measure (i.e., G-mean) into the objective function. We first optimize the misclassification costs, and then apply them to DBN. Adaptive differential evolution optimization is implemented as the optimization algorithm that automatically updates its corresponding parameters without the need of prior domain knowledge. The experiments have shown that the proposed approach consistently outperforms the state of the art on both benchmark data sets and real-world data set for fault diagnosis in tool condition monitoring. [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]

This paper studies the problem of minimizing a sum of (possible nonsmooth) convex functions that are corresponding to multiple interacting nodes, subject to a convex state constraint set. Time-varying directed network is considered here. Two types of computational constraints are investigated in this paper: one where the information of gradients is not available and the other where the projection steps can only be calculated approximately. We devise a distributed zeroth-order method, the implementation of which needs only functional evaluations and approximate projection. In particular, we show that the proposed method generates expected function value sequences that converge to the optimal value, provided that the projection errors decrease at appropriate rates. [ABSTRACT FROM AUTHOR]

This paper develops a neural network architecture and a new processing method for solving in real time, the nonlinear equality constrained multiobjective optimization problem (NECMOP), where several nonlinear objective functions must be optimized in a conflicting situation. In this processing method, the NECMOP is converted to an equivalent scalar optimization problem (SOP). The SOP is then decomposed into several-separable subproblems processable in parallel and in a reasonable time by multiplexing switched capacitor circuits. The approach which we propose makes use of a decomposition–coordination principle that allows nonlinearity to be treated at a local level and where coordination is achieved through the use of Lagrange multipliers. The modularity and the regularity of the neural networks architecture herein proposed make it suitable for very large scale integration implementation. An application to the resolution of a physical problem is given to show that the approach used here possesses some advantages of the point of algorithmic view, and provides processes of resolution often simpler than the usual techniques. [ABSTRACT FROM PUBLISHER]

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]

The truncated regular $L_{1}$ -loss support vector machine can eliminate the excessive number of support vectors (SVs); thus, it has significant advantages in robustness and scalability. However, in this paper, we discover that the associated state-of-the-art solvers, such as difference convex algorithm and concave–convex procedure, not only have limited sparsity promoting property for general truncated losses especially the $L_{2}$ -loss but also have poor scalability for large-scale problems. To circumvent these drawbacks, we present a general multistage scheme with explicit interpretation regarding SVs as well as outliers. In particular, we solve the general nonconvex truncated loss minimization through a sequence of associated convex subproblems, in which the outliers are removed in advance. The proposed algorithm can be regarded as a structural optimization attempt carefully considering sparsity imposed by the nonconvex truncated losses. We show that this general multistage algorithm offers sufficient sparsity especially for the truncated $L_{2}$ -loss. To further improve the scalability, we propose a linear multistep algorithm by employing a single iteration of coordinate descent to monotonically decrease the objective function at each stage and a kernel algorithm by using the Karush–Kuhn–Tucker conditions to cheaply find most part of the outliers for the next stage. Comparison experiments demonstrate that our methods have superiority in sparsity as well as efficiency in scalability. [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]

Multitask learning (MTL) aims to learn multiple tasks simultaneously through the interdependence between different tasks. The way to measure the relatedness between tasks is always a popular issue. There are mainly two ways to measure relatedness between tasks: common parameters sharing and common features sharing across different tasks. However, these two types of relatedness are mainly learned independently, leading to a loss of information. In this paper, we propose a new strategy to measure the relatedness that jointly learns shared parameters and shared feature representations. The objective of our proposed method is to transform the features of different tasks into a common feature space in which the tasks are closely related and the shared parameters can be better optimized. We give a detailed introduction to our proposed MTL method. Additionally, an alternating algorithm is introduced to optimize the nonconvex objection. A theoretical bound is given to demonstrate that the relatedness between tasks can be better measured by our proposed MTL algorithm. We conduct various experiments to verify the superiority of the proposed joint model and feature MTL method. [ABSTRACT FROM AUTHOR]

Conventional feature selection algorithms assign a single common feature set to all regions of the sample space. In contrast, this paper proposes a novel algorithm for localized feature selection for which each region of the sample space is characterized by its individual distinct feature subset that may vary in size and membership. This approach can therefore select an optimal feature subset that adapts to local variations of the sample space, and hence offer the potential for improved performance. Feature subsets are computed by choosing an optimal coordinate space so that, within a localized region, within-class distances and between-class distances are, respectively, minimized and maximized. Distances are measured using a logistic function metric within the corresponding region. This enables the optimization process to focus on a localized region within the sample space. A local classification approach is utilized for measuring the similarity of a new input data point to each class. The proposed logistic localized feature selection (lLFS) algorithm is invariant to the underlying probability distribution of the data; hence, it is appropriate when the data are distributed on a nonlinear or disjoint manifold. lLFS is efficiently formulated as a joint convex/increasing quasi-convex optimization problem with a unique global optimum point. The method is most applicable when the number of available training samples is small. The performance of the proposed localized method is successfully demonstrated on a large variety of data sets. We demonstrate that the number of features selected by the lLFS method saturates at the number of available discriminative features. In addition, we have shown that the Vapnik-Chervonenkis dimension of the localized classifier is finite. Both these factors suggest that the lLFS method is insensitive to the overfitting issue, relative to other methods. [ABSTRACT FROM AUTHOR]

In this paper, a novel concept factorization (CF) method, called CF with adaptive neighbors (CFANs), is proposed. The idea of CFAN is to integrate an ANs regularization constraint into the CF decomposition. The goal of CFAN is to extract the representation space that maintains geometrical neighborhood structure of the data. Similar to the existing graph-regularized CF, CFAN builds a neighbor graph weights matrix. The key difference is that the CFAN performs dimensionality reduction and finds the neighbor graph weights matrix simultaneously. An efficient algorithm is also derived to solve the proposed problem. We apply the proposed method to the problem of document clustering on the 20 Newsgroups, Reuters-21578, and TDT2 document data sets. Our experiments demonstrate the effectiveness of the method. [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]

This paper presents a nearest neighbor partitioning method designed to improve the performance of a neural-network classifier. For neural-network classifiers, usually the number, positions, and labels of centroids are fixed in partition space before training. However, that approach limits the search for potential neural networks during optimization; the quality of a neural network classifier is based on how clear the decision boundaries are between classes. Although attempts have been made to generate floating centroids automatically, these methods still tend to generate sphere-like partitions and cannot produce flexible decision boundaries. We propose the use of nearest neighbor classification in conjunction with a neural-network classifier. Instead of being bound by sphere-like boundaries (such as the case with centroid-based methods), the flexibility of nearest neighbors increases the chance of finding potential neural networks that have arbitrarily shaped boundaries in partition space. Experimental results demonstrate that the proposed method exhibits superior performance on accuracy and average f-measure. [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]

Finding the optimal solution to the constrained l0 -norm minimization problems in the recovery of compressive sensed signals is an NP-hard problem and it usually requires intractable combinatorial searching operations for getting the global optimal solution, unless using other objective functions (e.g., the l1 norm or lp norm) for approximate solutions or using greedy search methods for locally optimal solutions (e.g., the orthogonal matching pursuit type algorithms). In this paper, a neurodynamic optimization method is proposed to solve the l0 -norm minimization problems for obtaining the global optimum using a recurrent neural network (RNN) model. For the RNN model, a group of modified Gaussian functions are constructed and their sum is taken as the objective function for approximating the l0 norm and for optimization. The constructed objective function sets up a convexity condition under which the neurodynamic system is guaranteed to obtain the globally convergent optimal solution. An adaptive adjustment scheme is developed for improving the performance of the optimization algorithm further. Extensive experiments are conducted to test the proposed approach in this paper and the output results validate the effectiveness of the new method. [ABSTRACT FROM PUBLISHER]

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 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]

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]

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]

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]

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]

Recently, there has been a lot of success in the development of effective binary classifiers. Although many statistical classification techniques have natural multiclass extensions, some, such as the support vector machines, do not. The existing techniques for mapping multiclass problems onto a set of simpler binary classification problems run into serious efficiency problems when there are hundreds or even thousands of classes, and these are the scenarios where this paper's contributions shine. We introduce the concept of correlation and joint probability of base binary learners. We learn these properties during the training stage, group the binary leaner's based on their independence and, with a Bayesian approach, combine the results to predict the class of a new instance. Finally, we also discuss two additional strategies: one to reduce the number of required base learners in the multiclass classification, and another to find new base learners that might best complement the existing set. We use these two new procedures iteratively to complement the initial solution and improve the overall performance. This paper has two goals: finding the most discriminative binary classifiers to solve a multiclass problem and keeping up the efficiency, i.e., small number of base learners. We validate and compare the method with a diverse set of methods of the literature in several public available datasets that range from small (10 to 26 classes) to large multiclass problems (1000 classes) always using simple reproducible scenarios. [ABSTRACT FROM PUBLISHER]

This paper presents a collective neurodynamic approach with multiple interconnected recurrent neural networks (RNNs) for distributed constrained optimization. The objective function of the distributed optimization problems to be solved is a sum of local convex objective functions, which may be nonsmooth. Subject to its local constraints, each local objective function is minimized individually by using an RNN, with consensus among others. In contrast to existing continuous-time distributed optimization methods, the proposed collective neurodynamic approach is capable of solving more general distributed optimization problems. Simulation results on three numerical examples are discussed to substantiate the effectiveness and characteristics of the proposed approach. In addition, an application to the optimal placement problem is delineated to demonstrate the viability of the approach. [ABSTRACT FROM AUTHOR]

This paper presents a two-time-scale neurodynamic approach to constrained minimax optimization using two coupled neural networks. One of the recurrent neural networks is used for minimizing the objective function and another is used for maximization. It is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization. The effectiveness and characteristics of the proposed approach are illustrated using several examples. Furthermore, the proposed approach is applied for $H_\infty $ model predictive control. [ABSTRACT FROM PUBLISHER]

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]

Face sketch–photo synthesis plays an important role in law enforcement and digital entertainment. Most of the existing methods only use pixel intensities as the feature. Since face images can be described using features from multiple aspects, this paper presents a novel multiple representations-based face sketch–photo-synthesis method that adaptively combines multiple representations to represent an image patch. In particular, it combines multiple features from face images processed using multiple filters and deploys Markov networks to exploit the interacting relationships between the neighboring image patches. The proposed framework could be solved using an alternating optimization strategy and it normally converges in only five outer iterations in the experiments. Our experimental results on the Chinese University of Hong Kong (CUHK) face sketch database, celebrity photos, CUHK Face Sketch FERET Database, IIIT-D Viewed Sketch Database, and forensic sketches demonstrate the effectiveness of our method for face sketch–photo synthesis. In addition, cross-database and database-dependent style-synthesis evaluations demonstrate the generalizability of this novel method and suggest promising solutions for face identification in forensic science. [ABSTRACT FROM PUBLISHER]

Human preferences are usually measured using ordinal variables. A system whose goal is to estimate the preferences of humans and their underlying decision mechanisms requires to learn the ordering of any given sample set. We consider the solution of this ordinal regression problem using a support vector machine algorithm. Specifically, the goal is to learn a set of classifiers with common direction vectors and different biases correctly separating the ordered classes. Current algorithms are either required to solve a quadratic optimization problem, which is computationally expensive, or based on maximizing the minimum margin (i.e., a fixed-margin strategy) between a set of hyperplanes, which biases the solution to the closest margin. Another drawback of these strategies is that they are limited to order the classes using a single ranking variable (e.g., perceived length). In this paper, we define a multiple ordinal regression algorithm based on maximizing the sum of the margins between every consecutive class with respect to one or more rankings (e.g., perceived length and weight). We provide derivations of an efficient, easy-to-implement iterative solution using a sequential minimal optimization procedure. We demonstrate the accuracy of our solutions in several data sets. In addition, we provide a key application of our algorithms in estimating human subjects’ ordinal classification of attribute associations to object categories. We show that these ordinal associations perform better than the binary one typically employed in the literature. [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]

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]

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]

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]

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]