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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]

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]

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]

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]

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]

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 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]

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]

Nonnegative matrix factorization (NMF) and symmetric NMF (SymNMF) have been shown to be effective for clustering linearly separable data and nonlinearly separable data, respectively. Nevertheless, many practical applications demand constrained algorithms in which a small number of constraints in the form of must-link and cannot-link are available. In this paper, we propose an NMF-based constrained clustering framework in which the similarity between two points on a must-link is enforced to approximate 1 and the similarity between two points on a cannot-link is enforced to approximate 0. We then formulate the framework using NMF and SymNMF to deal with clustering of linearly separable data and nonlinearly separable data, respectively. Furthermore, we present multiplicative update rules to solve them and show the correctness and convergence. Experimental results on various text data sets, University of California, Irvine (UCI) data sets, and gene expression data sets demonstrate the superiority of our algorithms over existing constrained clustering algorithms. [ABSTRACT FROM AUTHOR]

For support vector machine (SVM) learning, least squares SVM (LSSVM), derived by duality LSSVM (D-LSSVM), is a widely used model, because it has an explicit solution. One obvious limitation of the model is that the solution lacks sparseness, which limits it from training large-scale problems efficiently. In this paper, we derive an equivalent LSSVM model in primal space LSSVM (P-LSSVM) by the representer theorem and prove that P-LSSVM can be solved exactly at some sparse solutions for problems with low-rank kernel matrices. Two algorithms are proposed for finding the sparse (approximate) solution of P-LSSVM by Cholesky factorization. One is based on the decomposition of the kernel matrix K as ${{P}} {{P}}^\top $ with the best low-rank matrix $ {{P}}$ approximately by pivoting Cholesky factorization. The other is based on solving P-LSSVM by approximating the Cholesky factorization of the Hessian matrix with rank-one update scheme. For linear learning problems, theoretical analysis and experimental results support that P-LSSVM can give the sparsest solutions in all SVM learners. Experimental results on some large-scale nonlinear training problems show that our algorithms, based on P-LSSVM, can converge to acceptable test accuracies at very sparse solutions with a sparsity level <1%, and even as little as 0.01%. Hence, our algorithms are a better choice for large-scale training problems. [ABSTRACT FROM AUTHOR]

This paper presents a complex-valued interval type-2 neuro-fuzzy inference system (CIT2FIS) and derive its metacognitive projection-based learning (PBL) algorithm. Metacognitive CIT2FIS (Mc-CIT2FIS) consists of a CIT2FIS, which realizes Takagi-Sugeno-Kang type inference mechanism, as its cognitive component. A PBL with self-regulation is its metacognitive component. The rules of CIT2FIS employ interval type- \(2~q\) -Gaussian membership functions that can represent different radial basis functions for different values of \(q\) . As each sample is presented to the network, the metacognitive component monitors the hinge-loss error and class-specific knowledge potential of the current sample to efficiently decide on what-to-learn, when-to-learn, and how-to-learn it. When a new rule is added or existing rules are updated, the optimal parameters of CIT2FIS corresponding to the minimum of the hinge-loss error function are computed using a PBL algorithm derived using the Wirtinger calculus. The performance of Mc-CIT2FIS is evaluated on a set of benchmark real-valued classification problems from the UCI machine learning repository. A circular transformation is used to convert the real-valued features to the complex-valued features in these problems. The performance comparison and statistical study clearly show the superior classification ability of Mc-CIT2FIS. Finally, the proposed complex-valued network is used to solve a practical human action recognition problem that is represented by complex-valued optical flow-based feature set, and a human emotion recognition problem represented using complex-valued Gabor filter-based features. The performance results on these problems substantiate the superior classification ability of Mc-CIT2FIS. [ABSTRACT FROM AUTHOR]

Over the past few years, multiple kernel learning (MKL) has received significant attention among data-driven feature selection techniques in the context of kernel-based learning. MKL formulations have been devised and solved for a broad spectrum of machine learning problems, including multitask learning (MTL). Solving different MKL formulations usually involves designing algorithms that are tailored to the problem at hand, which is, typically, a nontrivial accomplishment. In this paper we present a general multitask multiple kernel learning (MT-MKL) framework that subsumes well-known MT-MKL formulations, as well as several important MKL approaches on single-task problems. We then derive a simple algorithm that can solve the unifying framework. To demonstrate the flexibility of the proposed framework, we formulate a new learning problem, namely partially-shared common space MT-MKL, and demonstrate its merits through experimentation. [ABSTRACT FROM AUTHOR]

It has been widely acknowledged that learning- and reconstruction-based super-resolution (SR) methods are effective to generate a high-resolution (HR) image from a single low-resolution (LR) input. However, learning-based methods are prone to introduce unexpected details into resultant HR images. Although reconstruction-based methods do not generate obvious artifacts, they tend to blur fine details and end up with unnatural results. In this paper, we propose a new SR framework that seamlessly integrates learning- and reconstruction-based methods for single image SR to: 1) avoid unexpected artifacts introduced by learning-based SR and 2) restore the missing high-frequency details smoothed by reconstruction-based SR. This integrated framework learns a single dictionary from the LR input instead of from external images to hallucinate details, embeds nonlocal means filter in the reconstruction-based SR to enhance edges and suppress artifacts, and gradually magnifies the LR input to the desired high-quality SR result. We demonstrate both visually and quantitatively that the proposed framework produces better results than previous methods from the literature. [ABSTRACT FROM AUTHOR]

Undirected latent variable models represent an important class of graphical models that have been successfully developed to deal with various tasks. One common challenge in learning such models is to determine the number of hidden units that are unknown a priori. Although Bayesian nonparametrics have provided promising results in bypassing the model selection problem in learning directed Bayesian Networks, very little effort has been made toward applying Bayesian nonparametrics to learn undirected latent variable models. In this paper, we present the infinite exponential family Harmonium (iEFH), a bipartite undirected latent variable model that automatically determines the number of latent units from an unbounded pool. We also present two important extensions of iEFH to 1) multiview iEFH for dealing with heterogeneous data, and 2) infinite maximum-margin Harmonium (iMMH) for incorporating supervising side information to learn predictive latent features. We develop variational inference algorithms to learn model parameters. Our methods are computationally competitive because of the avoidance of selecting the number of latent units. Our extensive experiments on real image datasets and text datasets appear to demonstrate the benefits of iEFH and iMMH inherited from Bayesian nonparametrics and max-margin learning. Such results were not available until now and contribute to expanding the scope of Bayesian nonparametrics to learn the structures of undirected latent variable models. [ABSTRACT FROM AUTHOR]

This article develops a communication-efficient algorithm to solve the stochastic optimization problem defined over a distributed network, aiming at reducing the burdensome communication in applications, such as distributed machine learning. Different from the existing works based on quantization and sparsification, we introduce a communication-censoring technique to reduce the transmissions of variables, which leads to our communication-censored distributed stochastic gradient descent (CSGD) algorithm. Specifically, in CSGD, the latest minibatch stochastic gradient at a worker will be transmitted to the server if and only if it is sufficiently informative. When the latest gradient is not available, the stale one will be reused at the server. To implement this communication-censoring strategy, the batch size is increasing in order to alleviate the effect of stochastic gradient noise. Theoretically, CSGD enjoys the same order of convergence rate as that of SGD but effectively reduces communication. Numerical experiments demonstrate the sizable communication saving of CSGD. [ABSTRACT FROM AUTHOR]

In this article, distributed algorithms are proposed for training a group of neural networks with private data sets. Stochastic gradients are utilized in order to eliminate the requirement for true gradients. To obtain a universal model of the distributed neural networks trained using local data sets only, consensus tools are introduced to derive the model toward the optimum. Most of the existing works employ diminishing learning rates, which are often slow and impracticable for online learning, while constant learning rates are studied in some recent works, but the principle for choosing the rates is not well established. In this article, constant learning rates are adopted to empower the proposed algorithms with tracking ability. Under mild conditions, the convergence of the proposed algorithms is established by exploring the error dynamics of the connected agents, which provides an upper bound for selecting the constant learning rates. Performances of the proposed algorithms are analyzed with and without gradient noises, in the sense of mean square error (MSE). It is proved that the MSE converges with bounded errors determined by the gradient noises, and the MSE converges to zero if the gradient noises are absent. Simulation results are provided to validate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Conventional artificial neural network (ANN) learning algorithms for classification tasks, either derivative-based optimization algorithms or derivative-free optimization algorithms work by training ANN first (or training and validating ANN) and then testing ANN, which are a two-stage and one-pass learning mechanism. Thus, this learning mechanism may not guarantee the generalization ability of a trained ANN. In this article, a novel bilevel learning model is constructed for self-organizing feed-forward neural network (FFNN), in which the training and testing processes are integrated into a unified framework. In this bilevel model, the upper level optimization problem is built for testing error on testing data set and network architecture based on network complexity, whereas the lower level optimization problem is constructed for network weights based on training error on training data set. For the bilevel framework, an interactive learning algorithm is proposed to optimize the architecture and weights of an FFNN with consideration of both training error and testing error. In this interactive learning algorithm, a hybrid binary particle swarm optimization (BPSO) taken as an upper level optimizer is used to self-organize network architecture, whereas the Levenberg–Marquardt (LM) algorithm as a lower level optimizer is utilized to optimize the connection weights of an FFNN. The bilevel learning model and algorithm have been tested on 20 benchmark classification problems. Experimental results demonstrate that the bilevel learning algorithm can significantly produce more compact FFNNs with more excellent generalization ability when compared with conventional learning algorithms. [ABSTRACT FROM AUTHOR]

The proximal inertial gradient descent (PIGD) is efficient for the composite minimization and applicable for broad of machine learning problems. In this article, we revisit the computational complexity of this algorithm and present other novel results, especially on the convergence rates of the objective function values. The nonergodic $O(1/k)$ rate is proved for PIGD with constant step size when the objective function is coercive. When the objective function fails to promise coercivity, we prove the sublinear rate with diminishing inertial parameters. In the case that the objective function satisfies the Polyak– Lojasiewicz (PŁ) property, the linear convergence is proved with much larger and general step size than the previous literature. We also extend our results to the multiblock version and present the computational complexity. Both cyclic and stochastic index selection strategies are considered. [ABSTRACT FROM AUTHOR]

In this article, a novel learning methodology is introduced for the problem of classification in the context of high-dimensional data. In particular, the challenges introduced by high-dimensional data sets are addressed by formulating a $L_{1}$ regularized zero-sum game where optimal sparsity is estimated through a two-player game between the penalty coefficients/sparsity parameters and the deep neural network weights. In order to solve this game, a distributed learning methodology is proposed where additional variables are utilized to derive layerwise cost functions. Finally, an alternating minimization approach developed to solve the problem where the Nash solution provides optimal sparsity and compensation through the classifier. The proposed learning approach is implemented in a parallel and distributed environment through a novel computational algorithm. The efficiency of the approach is demonstrated both theoretically and empirically with nine data sets. [ABSTRACT FROM AUTHOR]

The aim of unsupervised domain adaptation is to leverage the knowledge in a labeled (source) domain to improve a model’s learning performance with an unlabeled (target) domain—the basic strategy being to mitigate the effects of discrepancies between the two distributions. Most existing algorithms can only handle unsupervised closed set domain adaptation (UCSDA), i.e., where the source and target domains are assumed to share the same label set. In this article, we target a more challenging but realistic setting: unsupervised open set domain adaptation (UOSDA), where the target domain has unknown classes that are not found in the source domain. This is the first study to provide learning bound for open set domain adaptation, which we do by theoretically investigating the risk of the target classifier on unknown classes. The proposed learning bound has a special term, namely, open set difference, which reflects the risk of the target classifier on unknown classes. Furthermore, we present a novel and theoretically guided unsupervised algorithm for open set domain adaptation, called distribution alignment with open difference (DAOD), which is based on regularizing this open set difference bound. The experiments on several benchmark data sets show the superior performance of the proposed UOSDA method compared with the state-of-the-art methods in the literature. [ABSTRACT FROM AUTHOR]

This work studies the class of algorithms for learning with side-information that emerges by extending generative models with embedded context-related variables. Using finite mixture models (FMMs) as the prototypical Bayesian network, we show that maximum-likelihood estimation (MLE) of parameters through expectation–maximization (EM) improves over the regular unsupervised case and can approach the performances of supervised learning, despite the absence of any explicit ground-truth data labeling. By direct application of the missing information principle (MIP), the algorithms’ performances are proven to range between the conventional supervised and unsupervised MLE extremities proportionally to the information content of the contextual assistance provided. The acquired benefits regard higher estimation precision, smaller standard errors, faster convergence rates, and improved classification accuracy or regression fitness shown in various scenarios while also highlighting important properties and differences among the outlined situations. Applicability is showcased with three real-world unsupervised classification scenarios employing Gaussian mixture models. Importantly, we exemplify the natural extension of this methodology to any type of generative model by deriving an equivalent context-aware algorithm for variational autoencoders (VAs), thus broadening the spectrum of applicability to unsupervised deep learning with artificial neural networks. The latter is contrasted with a neural-symbolic algorithm exploiting side information. [ABSTRACT FROM AUTHOR]

Domain adaptation is becoming increasingly important for learning systems in recent years, especially with the growing diversification of data domains in real-world applications, such as the genetic data from various sequencing platforms and video feeds from multiple surveillance cameras. Traditional domain adaptation approaches target to design transformations for each individual domain so that the twisted data from different domains follow an almost identical distribution. In many applications, however, the data from diversified domains are simply dumped to an archive even without clear domain labels. In this article, we discuss the possibility of learning domain adaptations even when the data does not contain domain labels. Our solution is based on our new model, named domain adaption using cross-domain homomorphism (DACH in short), to identify intrinsic homomorphism hidden in mixed data from all domains. DACH is generally compatible with existing deep learning frameworks, enabling the generation of nonlinear features from the original data domains. Our theoretical analysis not only shows the universality of the homomorphism, but also proves the convergence of DACH for significant homomorphism structures over the data domains is preserved. Empirical studies on real-world data sets validate the effectiveness of DACH on merging multiple data domains for joint machine learning tasks and the scalability of our algorithm to domain dimensionality. [ABSTRACT FROM AUTHOR]

The probabilistic classification vector machine (PCVM) synthesizes the advantages of both the support vector machine and the relevant vector machine, delivering a sparse Bayesian solution to classification problems. However, the PCVM is currently only applicable to binary cases. Extending the PCVM to multiclass cases via heuristic voting strategies such as one-vs-rest or one-vs-one often results in a dilemma where classifiers make contradictory predictions, and those strategies might lose the benefits of probabilistic outputs. To overcome this problem, we extend the PCVM and propose a multiclass PCVM (mPCVM). Two learning algorithms, i.e., one top-down algorithm and one bottom-up algorithm, have been implemented in the mPCVM. The top-down algorithm obtains the maximum a posteriori (MAP) point estimates of the parameters based on an expectation–maximization algorithm, and the bottom-up algorithm is an incremental paradigm by maximizing the marginal likelihood. The superior performance of the mPCVMs, especially when the investigated problem has a large number of classes, is extensively evaluated on the synthetic and benchmark data sets. [ABSTRACT FROM AUTHOR]

We analyze an online learning algorithm that adaptively combines outputs of two constituent algorithms (or the experts) running in parallel to estimate an unknown desired signal. This online learning algorithm is shown to achieve and in some cases outperform the mean-square error (MSE) performance of the best constituent algorithm in the steady state. However, the MSE analysis of this algorithm in the literature uses approximations and relies on statistical models on the underlying signals. Hence, such an analysis may not be useful or valid for signals generated by various real-life systems that show high degrees of nonstationarity, limit cycles and that are even chaotic in many cases. In this brief, we produce results in an individual sequence manner. In particular, we relate the time-accumulated squared estimation error of this online algorithm at any time over any interval to the one of the optimal convex mixture of the constituent algorithms directly tuned to the underlying signal in a deterministic sense without any statistical assumptions. In this sense, our analysis provides the transient, steady-state, and tracking behavior of this algorithm in a strong sense without any approximations in the derivations or statistical assumptions on the underlying signals such that our results are guaranteed to hold. We illustrate the introduced results through examples. [ABSTRACT FROM PUBLISHER]

Recently, distance metric learning (DML) has attracted much attention in image retrieval, but most previous methods only work for image classification and clustering tasks. In this brief, we focus on designing ordinal DML algorithms for image ranking tasks, by which the rank levels among the images can be well measured. We first present a linear ordinal Mahalanobis DML model that tries to preserve both the local geometry information and the ordinal relationship of the data. Then, we develop a nonlinear DML method by kernelizing the above model, considering of real-world image data with nonlinear structures. To further improve the ranking performance, we finally derive a multiple kernel DML approach inspired by the idea of multiple-kernel learning that performs different kernel operators on different kinds of image features. Extensive experiments on four benchmarks demonstrate the power of the proposed algorithms against some related state-of-the-art methods. [ABSTRACT FROM PUBLISHER]