We present a novel algorithm called PG-means which is able to learn the number of clusters in a classical Gaussian mixture model. Our method is robust and efficient; it uses statistical hypothesis tests on one-dimensional projections of the data and model to determine if the examples are well represented by the model. In so doing, we are applying a statistical test for the entire model at once, not just on a per-cluster basis. We show that our method works well in difficult cases such as non-Gaussian data, overlapping clusters, eccentric clusters, high dimension, and many true clusters. Further, our new method provides a much more stable estimate of the number of clusters than existing methods.

The presented denoising algorithm is based on a graph-based diffusion process of the point sample. We analyze this diffusion process using recent results about the convergence of graph Laplacians. In the experiments we show that our method is capable of dealing with nontrivial high-dimensional noise. Moreover using the denoising algorithm as pre-processing method we can improve the results of a semi-supervised learning algorithm.

The standard Support Vector Machine formulation does not provide its user with the ability to explicitly control the number of support vectors used to define the generated classifier. We present a modified version of SVM that allows the user to set a budget parameter B and focuses on minimizing the loss attained by the B worst-classified examples while ignoring the remaining examples. This idea can be used to derive sparse versions of both L1-SVM and L2-SVM. Technically, we obtain these new SVM variants by replacing the 1-norm in the standard SVM formulation with various interpolation-norms. We also adapt the SMO optimization algorithm to our setting and report on some preliminary experimental results.

We describe and analyze an algorithmic framework for online classification where each online trial consists of multiple prediction tasks that are tied together. We tackle the problem of updating the online hypothesis by defining a projection problem in which each prediction task corresponds to a single linear constraint. These constraints are tied together through a single slack parameter. We then introduce a general method for approximately solving the problem by projecting simultaneously and independently on each constraint which corresponds to a prediction sub-problem, and then averaging the individual solutions. We show that this approach constitutes a feasible, albeit not necessarily optimal, solution for the original projection problem. We derive concrete simultaneous projection schemes and analyze them in the mistake bound model. We demonstrate the power of the proposed algorithm in experiments with online multiclass text categorization. Our experiments indicate that a combination of class-dependent features with the simultaneous projection method outperforms previously studied algorithms.

In this paper, we present a subspace method for learning nonlinear dynamical systems based on stochastic realization, in which state vectors are chosen using kernel canonical correlation analysis, and then state-space systems are identified through regression with the state vectors. We construct the theoretical underpinning and derive a concrete algorithm for nonlinear identification. The obtained algorithm needs no iterative optimization procedure and can be implemented on the basis of fast and reliable numerical schemes. The simulation result shows that our algorithm can express dynamics with a high degree of accuracy.

Pyramid intersection is an efficient method for computing an approximate partial matching between two sets of feature vectors. We introduce a novel pyramid embedding based on a hierarchy of non-uniformly shaped bins that takes advantage of the underlying structure of the feature space and remains accurate even for sets with high-dimensional feature vectors. The matching similarity is computed in linear time and forms a Mercer kernel. Whereas previous matching approximation algorithms suffer from distortion factors that increase linearly with the feature dimension, we demonstrate that our approach can maintain constant accuracy even as the feature dimension increases. When used as a kernel in a discriminative classifier, our approach achieves improved object recognition results over a state-of-the-art set kernel.

We present a method for localizing and separating sound sources in stereo recordings that is robust to reverberation and does not make any assumptions about the source statistics. The method consists of a probabilistic model of binaural multisource recordings and an expectation maximization algorithm for finding the maximum likelihood parameters of that model. These parameters include distributions over delays and assignments of time-frequency regions to sources. We evaluate this method against two comparable algorithms on simulations of simultaneous speech from two or three sources. Our method outperforms the others in anechoic conditions and performs as well as the better of the two in the presence of reverberation.

Our first algorithm, ILK (implicit online learning with kernels), employs a new, implicit update technique that can be applied to a wide variety of convex loss functions. We then introduce a bounded memory version, SILK (sparse ILK), that maintains a compact representation of the predictor without compromising solution quality, even in non-stationary environments. We prove loss bounds and analyze the convergence rate of both. Experimental evidence shows that our proposed algorithms outperform current methods on synthetic and real data.

Discriminative learning methods for classification perform well when training and test data are drawn from the same distribution. In many situations, though, we have labeled training data for a source domain, and we wish to learn a classifier which performs well on a target domain with a different distribution. Under what conditions can we adapt a classifier trained on the source domain for use in the target domain? Intuitively, a good feature representation is a crucial factor in the success of domain adaptation. We formalize this intuition theoretically with a generalization bound for domain adaption. Our theory illustrates the tradeoffs inherent in designing a representation for domain adaptation and gives a new justification for a recently proposed model. It also points toward a promising new model for domain adaptation: one which explicitly minimizes the difference between the source and target domains, while at the same time maximizing the margin of the training set.

Multinomial logistic regression provides the standard penalised maximumlikelihood solution to multi-class pattern recognition problems. More recently, the development of sparse multinomial logistic regression models has found application in text processing and microarray classification, where explicit identification of the most informative features is of value. In this paper, we propose a sparse multinomial logistic regression method, in which the sparsity arises from the use of a Laplace prior, but where the usual regularisation parameter is integrated out analytically. Evaluation over a range of benchmark datasets reveals this approach results in similar generalisation performance to that obtained using cross-validation, but at greatly reduced computational expense.