Online algorithms for classification often require vast amounts of memory and computation time when employed in conjunction with kernel functions. In this paper we describe and analyze a simple approach for an on-the-fly reduction of the number of past examples used for prediction. Experiments performed with real datasets show that using the proposed algorithmic approach with a single epoch is competitive with the support vector machine (SVM) although the latter, being a batch algorithm, accesses each training example multiple times.

We consider situations where training data is abundant and computing resources are comparatively scarce. We argue that suitably designed online learning algorithms asymptotically outperform any batch learning algorithm. Both theoretical and experimental evidences are presented.

We introduce an information theoretic method for nonparametric, nonlinear dimensionality reduction, based on the infinite cluster limit of rate distortion theory. By constraining the information available to manifold coordinates, a natural probabilistic map emerges that assigns original data to corresponding points on a lower dimensional manifold. With only the information-distortion trade off as a parameter, our method determines the shape of the manifold, its dimensionality, the probabilistic map and the prior that provide optimal description of the data.

Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) - a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold.

We formulate linear dimensionality reduction as a semi-parametric estimation problem, enabling us to study its asymptotic behavior. We generalize the problem beyond additive Gaussian noise to (unknown) non-Gaussian additive noise, and to unbiased non-additive models.

We consider the question of predicting nonlinear time series. Kernel Dynamical Modeling (KDM), a new method based on kernels, is proposed as an extension to linear dynamical models. The kernel trick is used twice: first, to learn the parameters of the model, and second, to compute preimages of the time series predicted in the feature space by means of Support Vector Regression. Our model shows strong connection with the classic Kalman Filter model, with the kernel feature space as hidden state space. Kernel Dynamical Modeling is tested against two benchmark time series and achieves high quality predictions.

New feature selection algorithms for linear threshold functions are described which combine backward elimination with an adaptive regularization method. This makes them particularly suitable to the classification of microarray expression data, where the goal is to obtain accurate rules depending on few genes only. Our algorithms are fast and easy to implement, since they center on an incremental (large margin) algorithm which allows us to avoid linear, quadratic or higher-order programming methods. We report on preliminary experiments with five known DNA microarray datasets. These experiments suggest that multiplicative large margin algorithms tend to outperform additive algorithms (such as SVM) on feature selection tasks.

The Minimax Probability Machine Classification (MPMC) framework [Lanckriet et al., 2002] builds classifiers by minimizing the maximum probability of misclassification, and gives direct estimates of the probabilistic accuracy bound Ω. The only assumptions that MPMC makes is that good estimates of means and covariance matrices of the classes exist. However, as with Support Vector Machines, MPMC is computationally expensive and requires extensive cross validation experiments to choose kernels and kernel parameters that give good performance. In this paper we address the computational cost of MPMC by proposing an algorithm that constructs nonlinear sparse MPMC (SMPMC) models by incrementally adding basis functions (i.e.

A new feature extraction criterion, maximum margin criterion (MMC), is proposed in this paper. This new criterion is general in the sense that, when combined with a suitable constraint, it can actually give rise to the most popular feature extractor in the literature, linear discriminate analysis (LDA).

Clustering aims at extracting hidden structure in dataset. While the problem of finding compact clusters has been widely studied in the literature, extracting arbitrarily formed elongated structures is considered a much harder problem. In this paper we present a novel clustering algorithm which tackles the problem by a two step procedure: first the data are transformed in such a way that elongated structures become compact ones. In a second step, these new objects are clustered by optimizing a compactness-based criterion. The advantages of the method over related approaches are threefold: (i) robustness properties of compactness-based criteria naturally transfer to the problem of extracting elongated structures, leading to a model which is highly robust against outlier objects; (ii) the transformed distances induce a Mercer kernel which allows us to formulate a polynomial approximation scheme to the generally N P-hard clustering problem; (iii) the new method does not contain free kernel parameters in contrast to methods like spectral clustering or mean-shift clustering.