We describe a way of using multiple different types of similarity relationship tolearn a low-dimensional embedding of a dataset. Our method chooses different, possibly overlapping representations of similarity by individually reweighting the dimensions of a common underlying latent space. When applied to a single similarity relation that is based on Euclidean distancesbetween the input data points, the method reduces to simple dimensionality reduction. If additional information is available about the dataset or about subsets of it, we can use this information to clean up or otherwise improve the embedding. We demonstrate the potential usefulnessof this form of semi-supervised dimensionality reduction on some simple examples.

We propose the hierarchical Dirichlet process (HDP), a nonparametric Bayesian model for clustering problems involving multiple groups of data. Each group of data is modeled with a mixture, with the number of components being open-ended and inferred automatically by the model. Further, components can be shared across groups, allowing dependencies across groups to be modeled effectively as well as conferring generalization tonew groups. Such grouped clustering problems occur often in practice, e.g. in the problem of topic discovery in document corpora. We report experimental results on three text corpora showing the effective and superior performance of the HDP over previous models.

A novel linear feature selection algorithm is presented based on the global minimization of a data-dependent generalization error bound. Feature selection and scaling algorithms often lead to non-convex optimization problems,which in many previous approaches were addressed through gradient descent procedures that can only guarantee convergence to a local minimum. We propose an alternative approach, whereby the global solution of the non-convex optimization problem is derived via an equivalent optimization problem. Moreover, the convex optimization task is reduced to a conic quadratic programming problem for which efficient solversare available. Highly competitive numerical results on both artificial and real-world data sets are reported.

We describe semi-Markov conditional random fields (semi-CRFs), a conditionally trainedversion of semi-Markov chains. Intuitively, a semi-CRF on an input sequence x outputs a "segmentation" of x, in which labels are assigned to segments (i.e., subsequences) of x rather than to individual elements x

Regularization plays a central role in the analysis of modern data, where non-regularized fitting is likely to lead to over-fitted models, useless for both prediction and interpretation. We consider the design of incremental algorithmswhich follow paths of regularized solutions, as the regularization varies.These approaches often result in methods which are both efficient and highly flexible. We suggest a general path-following algorithm based on second-order approximations, prove that under mild conditions it remains "very close" to the path of optimal solutions and illustrate it with examples.

High retrieval precision in content-based image retrieval can be attained by adopting relevance feedback mechanisms. These mechanisms require that the user judges the quality of the results of the query by marking all the retrieved images as being either relevant or not. Then, the search engine exploits this information to adapt the search to better meet user's needs. At present, the vast majority of proposed relevance feedback mechanisms are formulated in terms of search model that has to be optimized. Such an optimization involves the modification of some search parameters so that the nearest neighbor of the query vector contains the largest number of relevant images.

An important aspect of clustering algorithms is whether the partitions constructed on finite samples converge to a useful clustering of the whole data space as the sample size increases. This paper investigates this question for normalized and unnormalized versions of the popular spectral clusteringalgorithm. Surprisingly, the convergence of unnormalized spectral clustering is more difficult to handle than the normalized case. Even though recently some first results on the convergence of normalized spectralclustering have been obtained, for the unnormalized case we have to develop a completely new approach combining tools from numerical integration, spectral and perturbation theory, and probability. It turns out that while in the normalized case, spectral clustering usually converges to a nice partition of the data space, in the unnormalized case the same only holds under strong additional assumptions which are not always satisfied. We conclude that our analysis gives strong evidence for the superiority of normalized spectral clustering. It also provides a basis for future exploration of other Laplacian-based methods.

The context in which a name appears in a caption provides powerful cues as to who is depicted in the associated image. We obtain 44,773 face images, usinga face detector, from approximately half a million captioned news images and automatically link names, obtained using a named entity recognizer,with these faces. A simple clustering method can produce fairresults. We improve these results significantly by combining the clustering process with a model of the probability that an individual is depicted given its context. Once the labeling procedure is over, we have an accurately labeled set of faces, an appearance model for each individual depicted, and a natural language model that can produce accurate resultson captions in isolation.

We establish a mistake bound for an ensemble method for classification based on maximizing the entropy of voting weights subject to margin constraints. The bound is the same as a general bound proved for the Weighted Majority Algorithm, and similar to bounds for other variants of Winnow. We prove a more refined bound that leads to a nearly optimal algorithmfor learning disjunctions, again, based on the maximum entropy principle. We describe a simplification of the online maximum entropy method in which, after each iteration, the margin constraints are replaced with a single linear inequality. The simplified algorithm, which takes a similar form to Winnow, achieves the same mistake bounds.

Given a directed graph in which some of the nodes are labeled, we investigate thequestion of how to exploit the link structure of the graph to infer the labels of the remaining unlabeled nodes. To that extent we propose a regularization framework for functions defined over nodes of a directed graph that forces the classification function to change slowly on densely linked subgraphs. A powerful, yet computationally simple classification algorithm is derived within the proposed framework. The experimental evaluation on real-world Web classification problems demonstrates encouraging resultsthat validate our approach.