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In this paper, we consider the composition optimization with two expected-value functions in the form of $({1}/{n})\sum _{i = 1}^{n} F_{i}\left({({1}/{m})\sum _{j = 1}^{m} G_{j}(x)}\right)+R(x)$ , which formulates many important problems in statistical learning and machine learning such as solving Bellman equations in reinforcement learning and nonlinear embedding. Full gradient- or classical stochastic gradient descent-based optimization algorithms are unsuitable or computationally expensive to solve this problem due to the inner expectation $({1}/{m})\sum _{j = 1}^{m} G_{j}(x)$. We propose a dualityfree-based stochastic composition method that combines the variance reduction methods to address the stochastic composition problem. We apply the stochastic variance reduction gradient- and stochastic average gradient algorithm-based methods to estimate the inner function and the dualityfree method to estimate the outer function. We prove the linear convergence rate not only for the convex composition problem but also for the case that the individual outer functions are nonconvex, while the objective function is strongly convex. We also provide the results of experiments that show the effectiveness of our proposed methods. [ABSTRACT FROM AUTHOR]

Growth transformations constitute a class of fixed-point multiplicative update algorithms that were originally proposed for optimizing polynomial and rational functions over a domain of probability measures. In this paper, we extend this framework to the domain of bounded real variables which can be applied towards optimizing the dual cost function of a generic support vector machine (SVM). The approach can, therefore, not only be used to train traditional soft-margin binary SVMs, one-class SVMs, and probabilistic SVMs but can also be used to design novel variants of SVMs with different types of convex and quasi-convex loss functions. In this paper, we propose an efficient training algorithm based on polynomial growth transforms, and compare and contrast the properties of different SVM variants using several synthetic and benchmark data sets. The preliminary experiments show that the proposed multiplicative update algorithm is more scalable and yields better convergence compared to standard quadratic and nonlinear programming solvers. While the formulation and the underlying algorithms have been validated in this paper only for SVM-based learning, the proposed approach is general and can be applied to a wide variety of optimization problems and statistical learning models. [ABSTRACT FROM AUTHOR]

In this paper, we propose a label-less learning for emotion cognition (LLEC) to achieve the utilization of a large amount of unlabeled data. We first inspect the unlabeled data from two perspectives, i.e., the feature layer and the decision layer. By utilizing the similarity model and the entropy model, this paper presents a hybrid label-less learning that can automatically label data without human intervention. Then, we design an enhanced hybrid label-less learning to purify the automatic labeled data. To further improve the accuracy of emotion detection model and increase the utilization of unlabeled data, we apply enhanced hybrid label-less learning for multimodal unlabeled emotion data. Finally, we build a real-world test bed to evaluate the LLEC algorithm. The experimental results show that the LLEC algorithm can improve the accuracy of emotion detection significantly. [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]

Support vector machine (SVM) is one of the most widely used learning algorithms for classification problems. Although SVM has good performance in practical applications, it has high algorithmic complexity as the size of training samples is large. In this paper, we introduce SVM classification (SVMC) algorithm based on $k$ -times Markov sampling and present the numerical studies on the learning performance of SVMC with $k$ -times Markov sampling for benchmark data sets. The experimental results show that the SVMC algorithm with $k$ -times Markov sampling not only have smaller misclassification rates, less time of sampling and training, but also the obtained classifier is more sparse compared with the classical SVMC and the previously known SVMC algorithm based on Markov sampling. We also give some discussions on the performance of SVMC with $k$ -times Markov sampling for the case of unbalanced training samples and large-scale training samples. [ABSTRACT FROM AUTHOR]

Two factors characterize a good feature selection algorithm: its accuracy and stability. This paper aims at introducing a new approach to stable feature selection algorithms. The innovation of this paper centers on a class of stable feature selection algorithms called feature weighting as regularized energy-based learning (FREL). Stability properties of FREL using L1 or L2 regularization are investigated. In addition, as a commonly adopted implementation strategy for enhanced stability, an ensemble FREL is proposed. A stability bound for the ensemble FREL is also presented. Our experiments using open source real microarray data, which are challenging high dimensionality small sample size problems demonstrate that our proposed ensemble FREL is not only stable but also achieves better or comparable accuracy than some other popular stable feature weighting methods. [ABSTRACT FROM PUBLISHER]

The large scale and complex nature of social media data raises the need to scale clustering techniques to big data and make them capable of automatically identifying data clusters with few empirical settings. In this paper, we present our investigation and three algorithms based on the fuzzy adaptive resonance theory (Fuzzy ART) that have linear computational complexity, use a single parameter, i.e., the vigilance parameter to identify data clusters, and are robust to modest parameter settings. The contribution of this paper lies in two aspects. First, we theoretically demonstrate how complement coding, commonly known as a normalization method, changes the clustering mechanism of Fuzzy ART, and discover the vigilance region (VR) that essentially determines how a cluster in the Fuzzy ART system recognizes similar patterns in the feature space. The VR gives an intrinsic interpretation of the clustering mechanism and limitations of Fuzzy ART. Second, we introduce the idea of allowing different clusters in the Fuzzy ART system to have different vigilance levels in order to meet the diverse nature of the pattern distribution of social media data. To this end, we propose three vigilance adaptation methods, namely, the activation maximization (AM) rule, the confliction minimization (CM) rule, and the hybrid integration (HI) rule. With an initial vigilance value, the resulting clustering algorithms, namely, the AM-ART, CM-ART, and HI-ART, can automatically adapt the vigilance values of all clusters during the learning epochs in order to produce better cluster boundaries. Experiments on four social media data sets show that AM-ART, CM-ART, and HI-ART are more robust than Fuzzy ART to the initial vigilance value, and they usually achieve better or comparable performance and much faster speed than the state-of-the-art clustering algorithms that also do not require a predefined number of clusters. [ABSTRACT FROM PUBLISHER]

Finite mixtures of skew distributions provide a flexible tool for modeling heterogeneous data with asymmetric distributional features. However, parameter estimation via the Expectation–Maximization (EM) algorithm can become very time consuming due to the complicated expressions involved in the E-step that are numerically expensive to evaluate. While parallelizing the EM algorithm can offer considerable speedup in time performance, current implementations focus almost exclusively on distributed platforms. In this paper, we consider instead the most typical operating environment for users of mixture models—a standalone multicore machine and the R programming environment. We develop a block implementation of the EM algorithm that facilitates the calculations on the E- and M-steps to be spread across a number of threads. We focus on the fitting of finite mixtures of multivariate skew normal and skew $t$ distributions, and show that both the E- and M-steps in the EM algorithm can be modified to allow the data to be split into blocks. Our approach is easy to implement and provides immediate benefits to users of multicore machines. Experiments were conducted on two real data sets to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider a modified error-correction learning rule for the multilayer neural network with multivalued neurons (MLMVN). This modification is based on the soft margins technique, which leads to the minimization of the distance between a cluster center and the learning samples belonging to this cluster. MLMVN has a derivative-free learning algorithm based on the error-correction learning rule and demonstrate a higher functionality and better generalization capability than a number of other machine learning techniques. The discrete $k$ -valued multivalued neuron activation function divides a complex plane into $k$ equal sectors. For more efficient and reliable solving of classification problems it is possible to modify the MLMVN learning algorithm in such a way that learning samples belonging to different classes (clusters) will be located as close as possible to the bisector of a desired sector (the cluster center) and as far as possible from each other, respectively. Such a modification based on the soft margins learning technique is considered in this paper. This modified learning algorithm improves the generalization capability of MLMVN when solving classification problems. [ABSTRACT FROM AUTHOR]

This paper addresses the robust gradient learning (RGL) problem. Gradient learning models aim at learning the gradient vector of some target functions in supervised learning problems, which can be further used to applications, such as variable selection, coordinate covariance estimation, and supervised dimension reduction. However, existing GL models are not robust to outliers or heavy-tailed noise. This paper provides an RGL framework to address this problem in both regression and classification. This is achieved by introducing a robust regression loss function and proposing a robust classification loss. Moreover, our RGL algorithm works in an instance-based kernelized dictionary instead of some fixed reproducing kernel Hilbert space, which may provide more flexibility. To solve the proposed nonconvex model, a simple computational algorithm based on gradient descent is provided and the convergence of the proposed method is also analyzed. We then apply the proposed RGL model to applications, such as nonlinear variable selection and coordinate covariance estimation. The efficiency of our proposed model is verified on both synthetic and real data sets. [ABSTRACT FROM AUTHOR]

Memory is one of the most important mechanisms in recurrent neural networks (RNNs) learning. It plays a crucial role in practical applications, such as sequence learning. With a good memory mechanism, long term history can be fused with current information, and can thus improve RNNs learning. Developing a suitable memory mechanism is always desirable in the field of RNNs. This paper proposes a novel memory mechanism for RNNs. The main contributions of this paper are: 1) an auxiliary memory unit (AMU) is proposed, which results in a new special RNN model (AMU-RNN), separating the memory and output explicitly and 2) an efficient learning algorithm is developed by employing the technique of error flow truncation. The proposed AMU-RNN model, together with the developed learning algorithm, can learn and maintain stable memory over a long time range. This method overcomes both the learning conflict problem and gradient vanishing problem. Unlike the traditional method, which mixes the memory and output with a single neuron in a recurrent unit, the AMU provides an auxiliary memory neuron to maintain memory in particular. By separating the memory and output in a recurrent unit, the problem of learning conflicts can be eliminated easily. Moreover, by using the technique of error flow truncation, each auxiliary memory neuron ensures constant error flow during the learning process. The experiments demonstrate good performance of the proposed AMU-RNNs and the developed learning algorithm. The method exhibits quite efficient learning performance with stable convergence in the AMU-RNN learning and outperforms the state-of-the-art RNN models in sequence generation and sequence classification tasks. [ABSTRACT FROM AUTHOR]

This paper presents the development of a motivated learning (ML) agent with symbolic I/O. Our earlier work on the ML agent was enhanced, giving it autonomy for interaction with other agents. Specifically, we equipped the agent with drives and pains that establish its motivations to learn how to respond to desired and undesired events and create related abstract goals. The purpose of this paper is to explore the autonomous development of motivations and memory in agents within a simulated environment. The ML agent has been implemented in a virtual environment created within the NeoAxis game engine. Additionally, to illustrate the benefits of an ML-based agent, we compared the performance of our algorithm against various reinforcement learning (RL) algorithms in a dynamic test scenario, and demonstrated that our ML agent learns better than any of the tested RL agents. [ABSTRACT FROM PUBLISHER]

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]

Class imbalance is a challenging problem in many classification tasks. It induces biased classification results for minority classes that contain less training samples than others. Most existing approaches aim to remedy the imbalanced number of instances among categories by resampling the majority and minority classes accordingly. However, the imbalanced level of difficulty of recognizing different categories is also crucial, especially for distinguishing samples with many classes. For example, in the task of clinical skin disease recognition, several rare diseases have a small number of training samples, but they are easy to diagnose because of their distinct visual properties. On the other hand, some common skin diseases, e.g., eczema, are hard to recognize due to the lack of special symptoms. To address this problem, we propose a self-paced balance learning (SPBL) algorithm in this paper. Specifically, we introduce a comprehensive metric termed the complexity of image category that is a combination of both sample number and recognition difficulty. First, the complexity is initialized using the model of the first pace, where the pace indicates one iteration in the self-paced learning paradigm. We then assign each class a penalty weight that is larger for more complex categories and smaller for easier ones, after which the curriculum is reconstructed by rearranging the training samples. Consequently, the model can iteratively learn discriminative representations via balancing the complexity in each pace. Experimental results on the SD-198 and SD-260 benchmark data sets demonstrate that the proposed SPBL algorithm performs favorably against the state-of-the-art methods. We also demonstrate the effectiveness of the SPBL algorithm’s generalization capacity on various tasks, such as indoor scene image recognition and object classification. [ABSTRACT FROM AUTHOR]

Learning from imbalanced data is among the most popular topics in the contemporary machine learning. However, the vast majority of attention in this field is given to binary problems, while their much more difficult multiclass counterparts are relatively unexplored. Handling data sets with multiple skewed classes poses various challenges and calls for a better understanding of the relationship among classes. In this paper, we propose multiclass radial-based oversampling (MC-RBO), a novel data-sampling algorithm dedicated to multiclass problems. The main novelty of our method lies in using potential functions for generating artificial instances. We take into account information coming from all of the classes, contrary to existing multiclass oversampling approaches that use only minority class characteristics. The process of artificial instance generation is guided by exploring areas where the value of the mutual class distribution is very small. This way, we ensure a smart oversampling procedure that can cope with difficult data distributions and alleviate the shortcomings of existing methods. The usefulness of the MC-RBO algorithm is evaluated on the basis of extensive experimental study and backed-up with a thorough statistical analysis. Obtained results show that by taking into account information coming from all of the classes and conducting a smart oversampling, we can significantly improve the process of learning from multiclass imbalanced data. [ABSTRACT FROM AUTHOR]

In this paper, a metacognitive octonion-valued neural network (Mc-OVNN) learning algorithm and its application to diverse time series prediction are presented. The Mc-OVNN is comprised of two components: the octonion-valued neural network that represents the cognitive component and the metacognitive component that serves to self-regulate the learning algorithm. At each epoch, the metacognitive component decides if, how, and when learning occurs. The algorithm deletes unneeded samples and only stores those that will be used. This decision is determined by the octonion magnitude and the seven phases. To evaluate the Mc-OVNN algorithm’s performance, it is applied to five real-world forecasting problems: the power consumption of a home in Honolulu, HI, USA, Box and Jenkins J series, Euro to Algerian Dinar (DZ) real-time conversion rates, the Mackey–Glass equation, and Europe Brent oil price prediction in a time series. When comparing the Mc-OVNN to other relevant techniques, Mc-OVNN displays its capability for efficient time series prediction. The real-time evaluation of the proposed algorithm is presented using the power consumption of a home in Boumerdès, Algeria, as a case study. [ABSTRACT FROM AUTHOR]

Feature selection (FS) is an important component of many pattern recognition tasks. In these tasks, one is often confronted with very high-dimensional data. FS algorithms are designed to identify the relevant feature subset from the original features, which can facilitate subsequent analysis, such as clustering and classification. Structured sparsity-inducing feature selection (SSFS) methods have been widely studied in the last few years, and a number of algorithms have been proposed. However, there is no comprehensive study concerning the connections between different SSFS methods, and how they have evolved. In this paper, we attempt to provide a survey on various SSFS methods, including their motivations and mathematical representations. We then explore the relationship among different formulations and propose a taxonomy to elucidate their evolution. We group the existing SSFS methods into two categories, i.e., vector-based feature selection (feature selection based on lasso) and matrix-based feature selection (feature selection based on lr,p -norm). Furthermore, FS has been combined with other machine learning algorithms for specific applications, such as multitask learning, multilabel learning, multiview learning, classification, and clustering. This paper not only compares the differences and commonalities of these methods based on regression and regularization strategies, but also provides useful guidelines to practitioners working in related fields to guide them how to do feature selection. [ABSTRACT FROM AUTHOR]

Many existing results on fault-tolerant algorithms focus on the single fault source situation, where a trained network is affected by one kind of weight failure. In fact, a trained network may be affected by multiple kinds of weight failure. This paper first studies how the open weight fault and the multiplicative weight noise degrade the performance of radial basis function (RBF) networks. Afterward, we define the objective function for training fault-tolerant RBF networks. Based on the objective function, we then develop two learning algorithms, one batch mode and one online mode. Besides, the convergent conditions of our online algorithm are investigated. Finally, we develop a formula to estimate the test set error of faulty networks trained from our approach. This formula helps us to optimize some tuning parameters, such as RBF width. [ABSTRACT FROM PUBLISHER]

Separable nonlinear models are very common in various research fields, such as machine learning and system identification. The variable projection (VP) approach is efficient for the optimization of such models. In this paper, we study various VP algorithms based on different matrix decompositions. Compared with the previous method, we use the analytical expression of the Jacobian matrix instead of finite differences. This improves the efficiency of the VP algorithms. In particular, based on the modified Gram–Schmidt (MGS) method, a more robust implementation of the VP algorithm is introduced for separable nonlinear least-squares problems. In numerical experiments, we compare the performance of five different implementations of the VP algorithm. Numerical results show the efficiency and robustness of the proposed MGS method-based VP algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scheme based on neural networks for predicting the packet disordering and sliding mode control (SMC) to stabilize the nonlinear networked control systems (NCSs). It is assumed that the packet disordering is unknown in the NCSs. The stochastic configuration networks (SCNs), which randomly assign the input weights and biases and analytically evaluate the output weights, are designed to solve the problem of unknown packet disordering. A new SMC scheme is developed by integrating the SCNs algorithm to learn and control the system in advance. Specifically, a novel measurement of packet disordering is constructed for the quantization of the packet disordering. In addition, the newest signal principle leads to the existence of stochastic parameters, thereby resulting in a Markovian jumping system. The effectiveness of the proposed approach is verified by some simulation 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]

Robotic control in a continuous action space has long been a challenging topic. This is especially true when controlling robots to solve compound tasks, as both basic skills and compound skills need to be learned. In this paper, we propose a hierarchical deep reinforcement learning algorithm to learn basic skills and compound skills simultaneously. In the proposed algorithm, compound skills and basic skills are learned by two levels of hierarchy. In the first level of hierarchy, each basic skill is handled by its own actor, overseen by a shared basic critic. Then, in the second level of hierarchy, compound skills are learned by a meta critic by reusing basic skills. The proposed algorithm was evaluated on a Pioneer 3AT robot in three different navigation scenarios with fully observable tasks. The simulations were built in Gazebo 2 in a robot operating system Indigo environment. The results show that the proposed algorithm can learn both high performance basic skills and compound skills through the same learning process. The compound skills learned outperform those learned by a discrete action space deep reinforcement learning algorithm. [ABSTRACT FROM AUTHOR]

The mixture of Gaussian processes (GPs) is capable of learning any general stochastic process based on a given set of (sample) curves for the regression and prediction problems. However, it is ineffective for curve clustering and prediction, when the sample curves are derived from different stochastic processes as independent sources linearly mixed together. In this paper, we propose a two-layer mixture model of GP functional regressions (GPFRs) to describe such a mixture of general stochastic processes or independent sources, especially for curve clustering and prediction. Specifically, in the lower layer, the mixture of GPFRs (MGPFRs) is developed for a cluster (or class) of curves within the input space. In the higher layer, the mixture of MGPFRs is further established to divide the curves into clusters according to its components in the output space. For the parameter estimation of the two-layer mixture of GPFRs, we develop a Monte Carlo EM algorithm based on a Monte Carlo Markov chain (MCMC) method, in short, the MCMC EM algorithm. We validate the hierarchical mixture of GPFRs and MCMC EM algorithm using synthetic and real-world data sets. Our results show that our new model outperforms the conventional mixture models in curve clustering and prediction. [ABSTRACT FROM AUTHOR]

When dealing with kernel methods, one has to decide which kernel and which values for the hyperparameters to use. Resampling techniques can address this issue but these procedures are time-consuming. This problem is particularly challenging when dealing with structured data, in particular with graphs, since several kernels for graph data have been proposed in literature, but no clear relationship among them in terms of learning properties is defined. In these cases, exhaustive search seems to be the only reasonable approach. Recently, the global Rademacher complexity (RC) and local Rademacher complexity (LRC), two powerful measures of the complexity of a hypothesis space, have shown to be suited for studying kernels properties. In particular, the LRC is able to bound the generalization error of an hypothesis chosen in a space by disregarding those ones which will not be taken into account by any learning procedure because of their high error. In this paper, we show a new approach to efficiently bound the RC of the space induced by a kernel, since its exact computation is an NP-Hard problem. Then we show for the first time that RC can be used to estimate the accuracy and expressivity of different graph kernels under different parameter configurations. The authors’ claims are supported by experimental results on several real-world graph data sets. [ABSTRACT FROM AUTHOR]

Extreme learning machine (ELM) is an emerging learning algorithm for the generalized single hidden layer feedforward neural networks, of which the hidden node parameters are randomly generated and the output weights are analytically computed. However, due to its shallow architecture, feature learning using ELM may not be effective for natural signals (e.g., images/videos), even with a large number of hidden nodes. To address this issue, in this paper, a new ELM-based hierarchical learning framework is proposed for multilayer perceptron. The proposed architecture is divided into two main components: 1) self-taught feature extraction followed by supervised feature classification and 2) they are bridged by random initialized hidden weights. The novelties of this paper are as follows: 1) unsupervised multilayer encoding is conducted for feature extraction, and an ELM-based sparse autoencoder is developed via \ell 1 constraint. By doing so, it achieves more compact and meaningful feature representations than the original ELM; 2) by exploiting the advantages of ELM random feature mapping, the hierarchically encoded outputs are randomly projected before final decision making, which leads to a better generalization with faster learning speed; and 3) unlike the greedy layerwise training of deep learning (DL), the hidden layers of the proposed framework are trained in a forward manner. Once the previous layer is established, the weights of the current layer are fixed without fine-tuning. Therefore, it has much better learning efficiency than the DL. Extensive experiments on various widely used classification data sets show that the proposed algorithm achieves better and faster convergence than the existing state-of-the-art hierarchical learning methods. Furthermore, multiple applications in computer vision further confirm the generality and capability of the proposed learning scheme. [ABSTRACT FROM AUTHOR]

In this paper, the challenging issue of estimating virtual unmodeled dynamics is addressed. A novel estimation algorithm based on historical data and the output of low-order approximation models for virtual un-modeled dynamics is presented. In particular, the virtual un-modeled dynamics are decomposed into known and unknown parts, where only the unknown part is to be estimated. The method effectively avoids the need to use the unknown control input directly, and enables the estimation of the un-modeled dynamics with a relatively simple algorithm. Moreover, it is shown that the proposed algorithm overcomes the difficulty in obtaining the control solutions caused by the fact that the controller input is embedded in un-modeled dynamics. Finally, simulation studies are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Ordinal regression (OR) is an important branch of supervised learning in between the multiclass classification and regression. In this paper, the traditional classification scheme of neural network is adapted to learn ordinal ranks. The model proposed imposes monotonicity constraints on the weights connecting the hidden layer with the output layer. To do so, the weights are transcribed using padding variables. This reformulation leads to the so-called inequality constrained least squares (ICLS) problem. Its numerical solution can be obtained by several iterative methods, for example, trust region or line search algorithms. In this proposal, the optimum is determined analytically according to the closed-form solution of the ICLS problem estimated from the Karush–Kuhn–Tucker conditions. Furthermore, following the guidelines of the extreme learning machine framework, the weights connecting the input and the hidden layers are randomly generated, so the final model estimates all its parameters without iterative tuning. The model proposed achieves competitive performance compared with the state-of-the-art neural networks methods for OR. [ABSTRACT FROM PUBLISHER]

GoDec is an efficient low-rank matrix decomposition algorithm. However, optimal performance depends on sparse errors and Gaussian noise. This paper aims to address the problem that a matrix is composed of a low-rank component and unknown corruptions. We introduce a robust local similarity measure called correntropy to describe the corruptions and, in doing so, obtain a more robust and faster low-rank decomposition algorithm: GoDec+. Based on half-quadratic optimization and greedy bilateral paradigm, we deliver a solution to the maximum correntropy criterion (MCC)-based low-rank decomposition problem. Experimental results show that GoDec+ is efficient and robust to different corruptions including Gaussian noise, Laplacian noise, salt & pepper noise, and occlusion on both synthetic and real vision data. We further apply GoDec+ to more general applications including classification and subspace clustering. For classification, we construct an ensemble subspace from the low-rank GoDec+ matrix and introduce an MCC-based classifier. For subspace clustering, we utilize GoDec+ values low-rank matrix for MCC-based self-expression and combine it with spectral clustering. Face recognition, motion segmentation, and face clustering experiments show that the proposed methods are effective and robust. In particular, we achieve the state-of-the-art performance on the Hopkins 155 data set and the first 10 subjects of extended Yale B for subspace clustering. [ABSTRACT FROM AUTHOR]

In this paper, we propose four new variants of the backpropagation algorithm to improve the generalization ability for feedforward neural networks. The basic idea of these methods stems from the Group Lasso concept which deals with the variable selection problem at the group level. There are two main drawbacks when the Group Lasso penalty has been directly employed during network training. They are numerical oscillations and theoretical challenges in computing the gradients at the origin. To overcome these obstacles, smoothing functions have then been introduced by approximating the Group Lasso penalty. Numerical experiments for classification and regression problems demonstrate that the proposed algorithms perform better than the other three classical penalization methods, Weight Decay, Weight Elimination, and Approximate Smoother, on both generalization and pruning efficiency. In addition, detailed simulations based on a specific data set have been performed to compare with some other common pruning strategies, which verify the advantages of the proposed algorithm. The pruning abilities of the proposed strategy have been investigated in detail for a relatively large data set, MNIST, in terms of various smoothing approximation cases. [ABSTRACT FROM AUTHOR]

Multitarget regression has recently generated intensive popularity due to its ability to simultaneously solve multiple regression tasks with improved performance, while great challenges stem from jointly exploring inter-target correlations and input–output relationships. In this paper, we propose multitarget sparse latent regression (MSLR) to simultaneously model intrinsic intertarget correlations and complex nonlinear input–output relationships in one single framework. By deploying a structure matrix, the MSLR accomplishes a latent variable model which is able to explicitly encode intertarget correlations via \ell 2,1 -norm-based sparse learning; the MSLR naturally admits a representer theorem for kernel extension, which enables it to flexibly handle highly complex nonlinear input-output relationships; the MSLR can be solved efficiently by an alternating optimization algorithm with guaranteed convergence, which ensures efficient multitarget regression. Extensive experimental evaluation on both synthetic data and six greatly diverse real-world data sets shows that the proposed MSLR consistently outperforms the state-of-the-art algorithms, which demonstrates its great effectiveness for multivariate prediction. [ABSTRACT FROM PUBLISHER]

In this paper, we proposed a generative model for feature selection under the unsupervised learning context. The model assumes that data are independently and identically sampled from a finite mixture of Student’s t distributions, which can reduce the sensitiveness to outliers. Latent random variables that represent the features’ salience are included in the model for the indication of the relevance of features. As a result, the model is expected to simultaneously realize clustering, feature selection, and outlier detection. Inference is carried out by a tree-structured variational Bayes algorithm. Full Bayesian treatment is adopted in the model to realize automatic model selection. Controlled experimental studies showed that the developed model is capable of modeling the data set with outliers accurately. Furthermore, experiment results showed that the developed algorithm compares favorably against existing unsupervised probability model-based Bayesian feature selection algorithms on artificial and real data sets. Moreover, the application of the developed algorithm on real leukemia gene expression data indicated that it is able to identify the discriminating genes successfully. [ABSTRACT FROM PUBLISHER]

Self-learning approaches, such as reinforcement learning, offer new possibilities for autonomous control of uncertain or time-varying systems. However, exploring an unknown environment under limited prediction capabilities is a challenge for a learning agent. If the environment is dangerous, free exploration can result in physical damage or in an otherwise unacceptable behavior. With respect to existing methods, the main contribution of this paper is the definition of a new approach that does not require global safety functions, nor specific formulations of the dynamics or of the environment, but relies on interval estimation of the dynamics of the agent during the exploration phase, assuming a limited capability of the agent to perceive the presence of incoming fatal states. Two algorithms are presented with this approach. The first is the Safety Handling Exploration with Risk Perception Algorithm (SHERPA), which provides safety by individuating temporary safety functions, called backups. SHERPA is shown in a simulated, simplified quadrotor task, for which dangerous states are avoided. The second algorithm, denominated OptiSHERPA, can safely handle more dynamically complex systems for which SHERPA is not sufficient through the use of safety metrics. An application of OptiSHERPA is simulated on an aircraft altitude control task. [ABSTRACT FROM AUTHOR]

Reducing samples through convex hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the convex hull vertices, based on the convex hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm. [ABSTRACT FROM PUBLISHER]

The lack of labeled data presents a common challenge in many computer vision and machine learning tasks. Semisupervised learning and transfer learning methods have been developed to tackle this challenge by utilizing auxiliary samples from the same domain or from a different domain, respectively. Self-taught learning, which is a special type of transfer learning, has fewer restrictions on the choice of auxiliary data. It has shown promising performance in visual learning. However, existing self-taught learning methods usually ignore the structure information in data. In this paper, we focus on building a self-taught coding framework, which can effectively utilize the rich low-level pattern information abstracted from the auxiliary domain, in order to characterize the high-level structural information in the target domain. By leveraging a high quality dictionary learned across auxiliary and target domains, the proposed approach learns expressive codings for the samples in the target domain. Since many types of visual data have been proven to contain subspace structures, a low-rank constraint is introduced into the coding objective to better characterize the structure of the given target set. The proposed representation learning framework is called self-taught low-rank (S-Low) coding, which can be formulated as a nonconvex rank-minimization and dictionary learning problem. We devise an efficient majorization–minimization augmented Lagrange multiplier algorithm to solve it. Based on the proposed S-Low coding mechanism, both unsupervised and supervised visual learning algorithms are derived. Extensive experiments on five benchmark data sets demonstrate the effectiveness of our approach. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel graph-based semisupervised learning framework, called joint sparse representation and embedding propagation learning (JSREPL). The idea of JSREPL is to join EPL with sparse representation to perform label propagation. Like most of graph-based semisupervised propagation learning algorithms, JSREPL also constructs weights graph matrix from given data. Different from classical approaches which build weights graph matrix and estimate the labels of unlabeled data in sequence, JSREPL simultaneously builds weights graph matrix and estimates the labels of unlabeled data. We also propose an efficient algorithm to solve the proposed problem. The proposed method is applied to the problem of semisupervised image clustering using the ORL, Yale, PIE, and YaleB data sets. Our experiments demonstrate the effectiveness of our proposed algorithm. [ABSTRACT FROM PUBLISHER]

It has received much attention in recent years to use Markov blankets in a Bayesian network for feature selection. The Markov blanket of a class attribute in a Bayesian network is a unique yet minimal feature subset for optimal feature selection if the probability distribution of a data set can be faithfully represented by this Bayesian network. However, if a data set violates the faithful condition, Markov blankets of a class attribute may not be unique. To tackle this issue, in this paper, we propose a new concept of representative sets and then design the selection via group alpha-investing (SGAI) algorithm to perform Markov blanket feature selection with representative sets for classification. Using a comprehensive set of real data, our empirical studies have demonstrated that SGAI outperforms the state-of-the-art Markov blanket feature selectors and other well-established feature selection methods. [ABSTRACT FROM PUBLISHER]

Several sparsity-constrained algorithms, such as orthogonal matching pursuit (OMP) or the Frank–Wolfe (FW) algorithm, with sparsity constraints work by iteratively selecting a novel atom to add to the current nonzero set of variables. This selection step is usually performed by computing the gradient and then by looking for the gradient component with maximal absolute entry. This step can be computationally expensive especially for large-scale and high-dimensional data. In this paper, we aim at accelerating these sparsity-constrained optimization algorithms by exploiting the key observation that, for these algorithms to work, one only needs the coordinate of the gradient’s top entry. Hence, we introduce algorithms based on greedy methods and randomization approaches that aim at cheaply estimating the gradient and its top entry. Another of our contribution is to cast the problem of finding the best gradient entry as a best-arm identification in a multiarmed bandit problem. Owing to this novel insight, we are able to provide a bandit-based algorithm that directly estimates the top entry in a very efficient way. Theoretical observations stating that the resulting inexact FW or OMP algorithms act, with high probability, similar to their exact versions are also given. We have carried out several experiments showing that the greedy deterministic and the bandit approaches we propose can achieve an acceleration of an order of magnitude while being as efficient as the exact gradient when used in algorithms, such as OMP, FW, or CoSaMP. [ABSTRACT FROM PUBLISHER]

Distributed learning refers to the problem of inferring a function when the training data are distributed among different nodes. While significant work has been done in the contexts of supervised and unsupervised learning, the intermediate case of Semi-supervised learning in the distributed setting has received less attention. In this paper, we propose an algorithm for this class of problems, by extending the framework of manifold regularization. The main component of the proposed algorithm consists of a fully distributed computation of the adjacency matrix of the training patterns. To this end, we propose a novel algorithm for low-rank distributed matrix completion, based on the framework of diffusion adaptation. Overall, the distributed Semi-supervised algorithm is efficient and scalable, and it can preserve privacy by the inclusion of flexible privacy-preserving mechanisms for similarity computation. The experimental results and comparison on a wide range of standard Semi-supervised benchmarks validate our proposal. [ABSTRACT FROM PUBLISHER]

Feature selection in learning to rank has recently emerged as a crucial issue. Whereas several preprocessing approaches have been proposed, only a few have focused on integrating feature selection into the learning process. In this paper, we propose a general framework for feature selection in learning to rank using support vector machines with a sparse regularization term. We investigate both classical convex regularizations, such as \ell1 or weighted \ell1 , and nonconvex regularization terms, such as log penalty, minimax concave penalty, or \ellp pseudo-norm with $p\!\!<\!\!1$ . Two algorithms are proposed: the first, an accelerated proximal approach for solving the convex problems, and, the second, a reweighted \ell1 scheme to address nonconvex regularizations. We conduct intensive experiments on nine datasets from Letor 3.0 and Letor 4.0 corpora. Numerical results show that the use of nonconvex regularizations we propose leads to more sparsity in the resulting models while preserving the prediction performance. The number of features is decreased by up to a factor of 6 compared to the \ell1 regularization. In addition, the software is publicly available on the web. 1

Available at http://remi.flamary.com/soft/soft-ranksvm-nc.html. [ABSTRACT FROM AUTHOR]

The recent literature indicates that preserving global pairwise sample similarity is of great importance for feature selection and that many existing selection criteria essentially work in this way. In this paper, we argue that besides global pairwise sample similarity, the local geometric structure of data is also critical and that these two factors play different roles in different learning scenarios. In order to show this, we propose a global and local structure preservation framework for feature selection (GLSPFS) which integrates both global pairwise sample similarity and local geometric data structure to conduct feature selection. To demonstrate the generality of our framework, we employ methods that are well known in the literature to model the local geometric data structure and develop three specific GLSPFS-based feature selection algorithms. Also, we develop an efficient optimization algorithm with proven global convergence to solve the resulting feature selection problem. A comprehensive experimental study is then conducted in order to compare our feature selection algorithms with many state-of-the-art ones in supervised, unsupervised, and semisupervised learning scenarios. The result indicates that: 1) our framework consistently achieves statistically significant improvement in selection performance when compared with the currently used algorithms; 2) in supervised and semisupervised learning scenarios, preserving global pairwise similarity is more important than preserving local geometric data structure; 3) in the unsupervised scenario, preserving local geometric data structure becomes clearly more important; and 4) the best feature selection performance is always obtained when the two factors are appropriately integrated. In summary, this paper not only validates the advantages of the proposed GLSPFS framework but also gains more insight into the information to be preserved in different feature selection tasks. [ABSTRACT FROM AUTHOR]

The spiking neural network (SNN) is the third generation of neural networks and performs remarkably well in cognitive tasks, such as pattern recognition. The temporal neural encode mechanism found in biological hippocampus enables SNN to possess more powerful computation capability than networks with other encoding schemes. However, this temporal encoding approach requires neurons to process information serially on time, which reduces learning efficiency significantly. To keep the powerful computation capability of the temporal encoding mechanism and to overcome its low efficiency in the training of SNNs, a new training algorithm, the accurate synaptic-efficiency adjustment method is proposed in this paper. Inspired by the selective attention mechanism of the primate visual system, our algorithm selects only the target spike time as attention areas, and ignores voltage states of the untarget ones, resulting in a significant reduction of training time. Besides, our algorithm employs a cost function based on the voltage difference between the potential of the output neuron and the firing threshold of the SNN, instead of the traditional precise firing time distance. A normalized spike-timing-dependent-plasticity learning window is applied to assigning this error to different synapses for instructing their training. Comprehensive simulations are conducted to investigate the learning properties of our algorithm, with input neurons emitting both single spike and multiple spikes. Simulation results indicate that our algorithm possesses higher learning performance than the existing other methods and achieves the state-of-the-art efficiency in the training of SNN. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a novel form of association rules (ARs) that do not require discretization of continuous variables or the use of intervals in either sides of the rule. This rule form captures nonlinear relationships among variables, and provides an alternative pattern representation for mining essential relations hidden in a given data set. We refer to the new rule form as a functional AR (FAR). A new neural network-based, co-operative, coevolutionary algorithm is presented for FAR mining. The algorithm is applied to both synthetic and real-world data sets, and its performance is analyzed. The experimental results show that the proposed mining algorithm is able to discover valid and essential underlying relations in the data. Comparison experiments are also carried out with the two state-of-the-art AR mining algorithms that can handle continuous variables to demonstrate the competitive performance of the proposed method. [ABSTRACT FROM PUBLISHER]

Focal underdetermined system solver (FOCUSS) is a powerful method for basis selection and sparse representation, where it employs the \ell \vphantom {Rjlp} -norm with $p\in (0,2)$ to measure the sparsity of solutions. In this paper, we give a systematical analysis on the rate of convergence of the FOCUSS algorithm with respect to $p\in (0,2)$ . We prove that the FOCUSS algorithm converges superlinearly for $0

Recently, an attractive clustering approach named multiexemplar affinity propagation (MEAP) has been proposed as an extension to the single exemplar-based AP. MEAP is able to automatically identify multiple exemplars for each cluster associated with a superexemplar. However, if the cluster number is a prior knowledge and can be specified by the user, MEAP is unable to make use of such knowledge directly in its learning process. Instead, it has to rely on rerunning the process as many times as it takes by tuning parameters until it generates the desired number of clusters. The process of MEAP rerunning may be very time-consuming. In this paper, we propose a new clustering algorithm called Multiple Exemplars Affinity Propagation with Specified K Clusters which is able to generate specified $K$ clusters directly while retaining the advantages of MEAP. Two kinds of new additional messages are introduced in K-MEAP in order to control the number of clusters in the process of message passing. Detailed problem formulation, derived messages, and in-depth analysis of the proposed K-MEAP are provided. Experimental studies on 11 real-world data sets with different kinds of applications demonstrate that K-MEAP not only generates $K$ clusters directly and efficiently without tuning parameters but also outperforms related approaches in terms of clustering accuracy. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of grouping the data points sampled from a union of multiple subspaces in the presence of outliers. Information theoretic objective functions are proposed to combine structured low-rank representations (LRRs) to capture the global structure of data and information theoretic measures to handle outliers. In theoretical part, we point out that group sparsity-induced measures ( \ell 2,1 -norm, \ell \alpha -norm, and correntropy) can be justified from the viewpoint of half-quadratic (HQ) optimization, which facilitates both convergence study and algorithmic development. In particular, a general formulation is accordingly proposed to unify HQ-based group sparsity methods into a common framework. In algorithmic part, we develop information theoretic subspace clustering methods via correntropy. With the help of Parzen window estimation, correntropy is used to handle either outliers under any distributions or sample-specific errors in data. Pairwise link constraints are further treated as a prior structure of LRRs. Based on the HQ framework, iterative algorithms are developed to solve the nonconvex information theoretic loss functions. Experimental results on three benchmark databases show that our methods can further improve the robustness of LRR subspace clustering and outperform other state-of-the-art subspace clustering methods. [ABSTRACT FROM PUBLISHER]

The identification of nonlinear spatiotemporal dynamical systems given by partial differential equations has attracted a lot of attention in the past decades. Several methods, such as searching principle-based algorithms, partially linear kernel methods, and coupled lattice methods, have been developed to address the identification problems. However, most existing methods have some restrictions on sampling processes in that the sampling intervals should usually be very small and uniformly distributed in spatiotemporal domains. These are actually not applicable for some practical applications. In this paper, to tackle this issue, a novel kernel-based learning algorithm named integral least square regularization regression (ILSRR) is proposed, which can be used to effectively achieve accurate derivative estimation for nonlinear functions in the time domain. With this technique, a discretization method named inverse meshless collocation is then developed to realize the dimensional reduction of the system to be identified. Thereafter, with this novel inverse meshless collocation model, the ILSRR, and a multiple-kernel-based learning algorithm, a multistep identification method is systematically proposed to address the identification problem of spatiotemporal systems with pointwise nonuniform observations. Numerical studies for benchmark systems with necessary discussions are presented to illustrate the effectiveness and the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a control algorithm based on adaptive dynamic programming to solve the infinite-horizon optimal control problem for known deterministic nonlinear systems with saturating actuators and nonquadratic cost functionals. The algorithm is based on an actor/critic framework, where a critic neural network (NN) is used to learn the optimal cost, and an actor NN is used to learn the optimal control policy. The adaptive control nature of the algorithm requires a persistence of excitation condition to be a priori validated, but this can be relaxed using previously stored data concurrently with current data in the update of the critic NN. A robustifying control term is added to the controller to eliminate the effect of residual errors, leading to the asymptotically stability of the closed-loop system. Simulation results show the effectiveness of the proposed approach for a controlled Van der Pol oscillator and also for a power system plant. [ABSTRACT FROM AUTHOR]

This paper presents a novel online block adaptive learning algorithm for autoregressive moving average (ARMA) controller design based on the real data measured from the plant. The method employs ARMA input–output models both for the plant and the resulting closed-loop system. In a sliding window, the plant model parameters are identified first offline using a supervised learning algorithm minimizing an $\varepsilon $ -insensitive and regularized identification error, which is the window average of the distances between the measured plant output and the model output for the input provided by the controller. The optimal controller parameters are then determined again offline for another sliding window as the solution to a constrained optimization problem, where the cost is the $\varepsilon $ -insensitive and regularized output tracking error and the constraints that are linear inequalities of the controller parameters are imposed for ensuring the closed-loop system to be Schur stable. Not only the identification phase but also the controller design phase uses the input–output samples measured from the plant during online learning. In the developed online controller design method, the controller parameters can always be kept in a parameter region providing Schur stability for the closed-loop system. The $\varepsilon $ -insensitiveness provides robustness against disturbances, so does the regularization better generalization performance in the identification and the control. The method is tested on benchmark plants, including the inverted pendulum and dc motor models. The method is also tested on an emulated and also a real dc motor by online block adaptive learning ARMA controllers, in particular, Proportional-Integral-Derivative controllers. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the learning problem of multilayer perceptrons (MLPs) formulated as the problem of minimizing a smooth error function. As well known, the learning problem of MLPs can be a difficult nonlinear nonconvex optimization problem. Typical difficulties can be the presence of extensive flat regions and steep sided valleys in the error surface, and the possible large number of training data and of free network parameters. We define a wide class of batch learning algorithms for MLP, based on the use of block decomposition techniques in the minimization of the error function. The learning problem is decomposed into a sequence of smaller and structured minimization problems in order to advantageously exploit the structure of the objective function. Theoretical convergence results are established, and a specific algorithm is constructed and evaluated through an extensive numerical experimentation. The comparisons with the state-of-the-art learning algorithms show the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

While in the learning using privileged information paradigm, privileged information may not be as informative as example features in the context of making accurate label predictions, it may be able to provide some effective comments (e.g., the values of the auxiliary function) like a human teacher on the efficacy of the learned model. In a departure from conventional static manipulations of privileged information within the support vector machine framework, this paper investigates iterative privileged learning within the context of gradient boosted decision trees (GBDTs). As the learned model evolves, the comments learned from privileged information to assess the model should also be actively upgraded instead of remaining static and passive. During the learning phase of the GBDT method, new DTs are discovered to enhance the performance of the model, and iteratively update the comments generated from the privileged information to accurately assess and coach the up-to-date model. The resulting objective function can be efficiently solved within the gradient boosting framework. Experimental results on real-world data sets demonstrate the benefits of studying privileged information in an iterative manner, as well as the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]