Semi-supervised learning algorithms have been successfully applied in many applications withscarce labeled data, by utilizing the unlabeled data. One important category is graph based semi-supervised learning algorithms, for which the performance dependsconsiderably on the quality of the graph, or its hyperparameters. In this paper, we deal with the less explored problem of learning the graphs. We propose agraph learning method for the harmonic energy minimization method; this is done by minimizing the leave-one-out prediction error on labeled data points. We use a gradient based method and designed an efficient algorithm which significantly acceleratesthe calculation of the gradient by applying the matrix inversion lemma and using careful pre-computation. Experimental results show that the graph learning method is effective in improving the performance of the classification algorithm.

Multinomial logistic regression provides the standard penalised maximum-likelihood solution to multi-Class pattern recognition problems.

Large numbers of descriptors and large codebooks are needed for good results and this becomes slow using k-means. We introduce Extremely Randomized Clustering Forests - ensembles of randomly created clustering trees - and show that these provide more accurate results, much faster training and testing and good resistance to background clutter in several state-of-the-art image classification tasks.

We propose a highly efficient framework for kernel multi-class models with a large and structured set of classes. Kernel parameters are learned automatically by maximizing the cross-validation log likelihood, and predictive probabilities are estimated. We demonstrate our approach on large scale text classification tasks with hierarchical class structure, achieving state-of-the-art results in an order of magnitude less time than previous work.

We introduce two methods to improve convergence of the Kernel Hebbian Algorithm (KHA) for iterative kernel PCA. KHA has a scalar gain parameter which is either held constant or decreased as 1/t, leading to slow convergence. Our KHA/et algorithm accelerates KHA by incorporating the reciprocal of the current estimated eigenvalues as a gain vector. We then derive and apply Stochastic Meta-Descent (SMD) to KHA/et; this further speeds convergence by performing gain adaptation in RKHS. Experimental results for kernel PCA and spectral clustering of USPS digits as well as motion capture and image de-noising problems confirm that our methods converge substantially faster than conventional KHA.

The additive clustering model is widely used to infer the features of a set of stimuli from their similarities, on the assumption that similarity is a weighted linear function of common features. This paper develops a fully Bayesian formulation of the additive clustering model, using methods from nonparametric Bayesian statistics to allow the number of features to vary. We use this to explore several approaches to parameter estimation, showing that the nonparametric Bayesian approach provides a straightforward way to obtain estimates of both the number of features used in producing similarity judgments and their importance.

Finite mixture model is a powerful tool in many statistical learning problems. In this paper, we propose a general, structure-preserving approach to reduce its model complexity, which can bring significant computational benefits in many applications. The basic idea is to group the original mixture components into compact clusters, and then minimize an upper bound on the approximation error between the original and simplified models.

We examine the problem of predicting local sentiment flow in documents, and its application to several areas of text analysis. Formally, the problem is stated as predicting an ordinal sequence based on a sequence of word sets. In the spirit of isotonic regression, we develop a variant of conditional random fields that is wellsuited to handle this problem. Using the Möbius transform, we express the model as a simple convex optimization problem. Experiments demonstrate the model and its applications to sentiment prediction, style analysis, and text summarization.

While for a finite number of minimizers this result follows from multinomial distribution estimates, the case of infinite minimizers requires more refined tools.

In this paper we focus on the issue of normalization of the affinity matrix in spectral clustering.