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.

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

Spectral clustering methods are common graph-based approaches to clustering of data. Spectral clustering algorithms typically start from local information encoded in a weighted graph on the data and cluster according to the global eigenvectors of the corresponding (normalized) similarity matrix. One contribution of this paper is to present fundamental limitations of this general local to global approach. We show that based only on local information, the normalized cut functional is not a suitable measure for the quality of clustering. Further, even with a suitable similarity measure, we show that the first few eigenvectors of such adjacency matrices cannot successfully cluster datasets that contain structures at different scales of size and density. Based on these findings, a second contribution of this paper is a novel diffusion based measure to evaluate the coherence of individual clusters. Our measure can be used in conjunction with any bottom-up graph-based clustering method, it is scale-free and can determine coherent clusters at all scales. We present both synthetic examples and real image segmentation problems where various spectral clustering algorithms fail. In contrast, using this coherence measure finds the expected clusters at all scales.

We describe a nonnegative variant of the "Sparse PCA" problem. The goal is to create a low dimensional representation from a collection of points which on the one hand maximizes the variance of the projected points and on the other uses only parts of the original coordinates, and thereby creating a sparse representation. What distinguishes our problem from other Sparse PCA formulations is that the projection involves only nonnegative weights of the original coordinates -- a desired quality in various fields, including economics, bioinformatics and computer vision. Adding nonnegativity contributes to sparseness, where it enforces a partitioning of the original coordinates among the new axes. We describe a simple yet efficient iterative coordinate-descent type of scheme which converges to a local optimum of our optimization criteria, giving good results on large real world datasets.

In this paper, we formalize multi-instance multi-label learning, where each training example is associated with not only multiple instances but also multiple class labels. Such a problem can occur in many real-world tasks, e.g. an image usually contains multiple patches each of which can be described by a feature vector, and the image can belong to multiple categories since its semantics can be recognized in different ways. We analyze the relationship between multi-instance multi-label learning and the learning frameworks of traditional supervised learning, multiinstance learning and multi-label learning.

In supervised learning there is a typical presumption that the training and test points are taken from the same distribution. In practice this assumption is commonly violated. The situations where the training and test data are from different distributions is called covariate shift. Recent work has examined techniques for dealing with covariate shift in terms of minimisation of generalisation error. As yet the literature lacks a Bayesian generative perspective on this problem. This paper tackles this issue for regression models. Recent work on covariate shift can be understood in terms of mixture regression. Using this view, we obtain a general approach to regression under covariate shift, which reproduces previous work as a special case. The main advantages of this new formulation over previous models for covariate shift are that we no longer need to presume the test and training densities are known, the regression and density estimation are combined into a single procedure, and previous methods are reproduced as special cases of this procedure, shedding light on the implicit assumptions the methods are making.

We propose a novel framework for the classification of single trial ElectroEncephaloGraphy (EEG), based on regularized logistic regression. Framed in this robust statistical framework no prior feature extraction or outlier removal is required.

It has been established that a neuron reproduces highly precise spike response to identical fluctuating input currents. We wish to accurately predict the firing times of a given neuron for any input current. For this purpose we adopt a model that mimics the dynamics of the membrane potential, and then take a cue from its dynamics for predicting the spike occurrence for a novel input current. It is found that the prediction is significantly improved by observing the state space of the membrane potential and its time derivative(s) in advance of a possible spike, in comparison to simply thresholding an instantaneous value of the estimated potential.

We propose a family of kernels for structured objects which is based on the bag-ofcomponents paradigm. However, rather than decomposing each complex object into the single histogram of its components, we use for each object a family of nested histograms, where each histogram in this hierarchy describes the object seen from an increasingly granular perspective. We use this hierarchy of histograms to define elementary kernels which can detect coarse and fine similarities between the objects. We compute through an efficient averaging trick a mixture of such specific kernels, to propose a final kernel value which weights efficiently local and global matches. We propose experimental results on an image retrieval experiment which show that this mixture is an effective template procedure to be used with kernels on histograms.

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.