Kernel Matching Pursuit for Large Datasets

Kernel matching pursuit is a greedy algorithm for building an approximation of a discriminant function as a linear combination of some basis functions selected from a kernel-induced dictionary. Here we propose a modification of the kernel matching pursuit algorithm that aims at making the method practical for large datasets. Starting from an approximating algorithm, the weak greedy algorithm, we introduce a stochastic method for reducing the search space at each iteration. Then we study the implications of using an approximate algorithm and we show how one can control the trade-off between the accuracy and the need for resources. Finally, we present some experiments performed on a large dataset that support our approach and illustrate its applicability

Adaptive Kernel Matching Pursuit for Pattern Classification

A sparse classifier is guaranteed to generalize better than a denser one, given they perform identical on the training set. However, methods like Support Vector Machine, even if they produce relatively sparse models, are known to scale linearly as the number of training examples increases. A recent proposed method, the Kernel Matching Pursuit, presents a number of advantages over th

Comparing error minimized extreme learning machines and support vector sequential feed-forward neural networks

Recently, error minimized extreme learning machines (EM-ELMs) have been proposed as a simple and efficient approach to build single-hidden-layer feed-forward networks (SLFNs) sequentially. They add random hidden nodes one by one (or group by group) and update the output weights incrementally to minimize the sum-of-squares error in the training set. Other very similar methods that also construct SLFNs sequentially had been reported earlier with the main difference that their hidden-layer weights are a subset of the data instead of being random. These approaches are referred to as support vector sequential feed-forward neural networks (SV-SFNNs), and they are a particular case of the sequential approximation with optimal coefficients and interacting frequencies (SAOCIF) method. In this paper, it is firstly shown that EM-ELMs can also be cast as a particular case of SAOCIF. In particular, EM-ELMs can easily be extended to test some number of random candidates at each step and select the best of them, as SAOCIF does. Moreover, it is demonstrated that the cost of the computation of the optimal output-layer weights in the originally proposed EM-ELMs can be improved if it is replaced by the one included in SAOCIF. Secondly, we present the results of an experimental study on 10 benchmark classification and 10 benchmark regression data sets, comparing EM-ELMs and SV-SFNNs, that was carried out under the same conditions for the two models. Although both models have the same (efficient) computational cost, a statistically significant improvement in generalization performance of SV-SFNNs vs. EM-ELMs was found in 12 out of the 20 benchmark problems. © 2011 Elsevier Ltd.This work was supported in part by the Ministerio de Ciencia e Innovación (MICINN), under project TIN2009-13895-C02-01.Peer Reviewe

A Covariance Matrix Adaptation Evolution Strategy for Direct Policy Search in Reproducing Kernel Hilbert Space

The covariance matrix adaptation evolution strategy (CMA-ES) is an efficient derivative-free optimization algorithm. It optimizes a black-box objective function over a well defined parameter space. In some problems, such parameter spaces are defined using function approximation in which feature functions are manually defined. Therefore, the performance of those techniques strongly depends on the quality of chosen features. Hence, enabling CMA-ES to optimize on a more complex and general function class of the objective has long been desired. Specifically, we consider modeling the input space for black-box optimization in reproducing kernel Hilbert spaces (RKHS). This modeling leads to a functional optimization problem whose domain is a function space that enables us to optimize in a very rich function class. In addition, we propose CMA-ES-RKHS, a generalized CMA-ES framework, that performs black-box functional optimization in the RKHS. A search distribution, represented as a Gaussian process, is adapted by updating both its mean function and covariance operator. Adaptive representation of the function and covariance operator is achieved with sparsification techniques. We evaluate CMA-ES-RKHS on a simple functional optimization problem and bench-mark reinforcement learning (RL) domains. For an application in RL, we model policies for MDPs in RKHS and transform a cumulative return objective as a functional of RKHS policies, which can be optimized via CMA-ES-RKHS. This formulation results in a black-box functional policy search framework

NARX-based nonlinear system identification using orthogonal least squares basis hunting

An orthogonal least squares technique for basis hunting (OLS-BH) is proposed to construct sparse radial basis function (RBF) models for NARX-type nonlinear systems. Unlike most of the existing RBF or kernel modelling methods, whichplaces the RBF or kernel centers at the training input data points and use a fixed common variance for all the regressors, the proposed OLS-BH technique tunes the RBF center and diagonal covariance matrix of individual regressor by minimizing the training mean square error. An efficient optimization method isadopted for this basis hunting to select regressors in an orthogonal forward selection procedure. Experimental results obtained using this OLS-BH technique demonstrate that it offers a state-of-the-art method for constructing parsimonious RBF models with excellent generalization performance

Comparing error minimized extreme learning machines and support vector sequential feed-forward neural networks

Recently, error minimized extreme learning machines (EM-ELMs) have been proposed as a simple and efficient approach to build single-hidden-layer feed-forward networks (SLFNs) sequentially. They add random hidden nodes one by one (or group by group) and update the output weights incrementally to minimize the sum-of-squares error in the training set. Other very similar methods that also construct SLFNs sequentially had been reported earlier with the main difference that their hidden-layer weights are a subset of the data instead of being random. By analogy with the concept of support vectors original of support vector machines (SVMs), these approaches can be referred to as support vector sequential feed-forward neural networks (SV-SFNNs), and they are a particular case of the Sequential Approximation with Optimal Coefficients and Interacting Frequencies (SAOCIF) method. In this paper, it is firstly shown that EM-ELMs can also be cast as a particular case of SAOCIF. In particular, EM-ELMs can easily be extended to test some number of random candidates at each step and select the best of them, as SAOCIF does. Moreover, it is demonstrated that the cost of the calculation of the optimal output-layer weights in the originally proposed EM-ELMs can be improved if it is replaced by the one included in SAOCIF. Secondly, we present the results of an experimental study on 10 benchmark classification and 10 benchmark regression data sets, comparing EM-ELMs and SV-SFNNs, that was carried out under the same conditions for the two models. Although both models have the same (efficient) computational cost, a statistically significant improvement in generalization performance of SV-SFNNs vs. EM-ELMs was found in 12 out of the 20 benchmark problems.Postprint (published version

Symmetric RBF classifier for nonlinear detection in multiple-antenna aided systems

In this paper, we propose a powerful symmetric radial basis function (RBF) classifier for nonlinear detection in the so-called “overloaded” multiple-antenna-aided communication systems. By exploiting the inherent symmetry property of the optimal Bayesian detector, the proposed symmetric RBF classifier is capable of approaching the optimal classification performance using noisy training data. The classifier construction process is robust to the choice of the RBF width and is computationally efficient. The proposed solution is capable of providing a signal-to-noise ratio (SNR) gain in excess of 8 dB against the powerful linear minimum bit error rate (BER) benchmark, when supporting four users with the aid of two receive antennas or seven users with four receive antenna elements. Index Terms—Classification, multiple-antenna system, orthogonal forward selection, radial basis function (RBF), symmetry