Semantic integration focuses on discovering, representing, and manipulating correspondences between entities in disparate data sources. The topic has been widely studied in the context of structured data, with problems being considered including ontology and schema matching, matching relational tuples, and reconciling inconsistent data values. In recent years, however, semantic integration over text has also received increasing attention. This article studies a key challenge in semantic integration over text: identifying whether different mentions of real-world entities, such as "JFK" and "John Kennedy," within and across natural language text documents, actually represent the same concept. We present a machine-learning study of this problem. The first approach is a discriminative approach -- a pairwise local classifier is trained in a supervised way to determine whether two given mentions represent the same real-world entity. This is followed, potentially, by a global clustering algorithm that uses the classifier as its similarity metric. Our second approach is a global generative model, at the heart of which is a view on how documents are generated and how names (of different entity types) are "sprinkled" into them. In its most general form, our model assumes (1) a joint distribution over entities (for example, a document that mentions "President Kennedy" is more likely to mention "Oswald" or "White House" than "Roger Clemens"), and (2) an "author" model that assumes that at least one mention of an entity in a document is easily identifiable and then generates other mentions via (3) an "appearance" model that governs how mentions are transformed from the "representative" mention. We show that both approaches perform very accurately, in the range of 90-95 percent. F1 measure for different entity types, much better than previous approaches to some aspects of this problem. Finally, we discuss how our solution for mention matching in text can be potentially applied to matching relational tuples, as well as to linking entities across databases and text.

We describe a procedure which finds a hierarchical clustering by hillclimbing. The cost function we use is a hierarchical extension of the k-means cost; our local moves are tree restructurings and node reorderings. We show these can be accomplished efficiently, by exploiting special properties of squared Euclidean distances and by using techniques from scheduling algorithms.

We propose an information-theoretic clustering approach that incorporates a pre-known partition of the data, aiming to identify common clusters that cut across the given partition. In the standard clustering setting the formation of clusters is guided by a single source of feature information. The newly utilized pre-partition factor introduces an additional bias that counterbalances the impact of the features whenever they become correlated with this known partition. The resulting algorithmic framework was applied successfully to synthetic data, as well as to identifying text-based cross-religion correspondences.

When clustering a dataset, the right number k of clusters to use is often not obvious, and choosing k automatically is a hard algorithmic problem. In this paper we present an improved algorithm for learning k while clustering. The G-means algorithm is based on a statistical test for the hypothesis that a subset of data follows a Gaussian distribution. G-means runs k-means with increasing k in a hierarchical fashion until the test accepts the hypothesis that the data assigned to each k-means center are Gaussian. Two key advantages are that the hypothesis test does not limit the covariance of the data and does not compute a full covariance matrix. Additionally, G-means only requires one intuitive parameter, the standard statistical significance level α. We present results from experiments showing that the algorithm works well, and better than a recent method based on the BIC penalty for model complexity. In these experiments, we show that the BIC is ineffective as a scoring function, since it does not penalize strongly enough the model's complexity.

Spectral clustering refers to a class of techniques which rely on the eigenstructure of a similarity matrix to partition points into disjoint clusters with points in the same cluster having high similarity and points in different clusters having low similarity. In this paper, we derive a new cost function for spectral clustering based on a measure of error between a given partition and a solution of the spectral relaxation of a minimum normalized cut problem. Minimizing this cost function with respect to the partition leads to a new spectral clustering algorithm. Minimizing with respect to the similarity matrix leads to an algorithm for learning the similarity matrix. We develop a tractable approximation of our cost function that is based on the power method of computing eigenvectors.

This paper is concerned with transductive learning. Although transduction appears to be an easier task than induction, there have not been many provably useful algorithms and bounds for transduction. We present explicit error bounds for transduction and derive a general technique for devising bounds within this setting. The technique is applied to derive error bounds for compression schemes such as (transductive) SVMs and for transduction algorithms based on clustering.

A novel approach to combining clustering and feature selection is presented. It implements a wrapper strategy for feature selection, in the sense that the features are directly selected by optimizing the discriminative power of the used partitioning algorithm. On the technical side, we present an efficient optimization algorithm with guaranteed local convergence property. The only free parameter of this method is selected by a resampling-based stability analysis. Experiments with real-world datasets demonstrate that our method is able to infer both meaningful partitions and meaningful subsets of features.

We describe a procedure which finds a hierarchical clustering by hillclimbing. The cost function we use is a hierarchical extension of the k-means cost; our local moves are tree restructurings and node reorderings. We show these can be accomplished efficiently, by exploiting special properties of squared Euclidean distances and by using techniques from scheduling algorithms.

We propose a functional mixture model for simultaneous clustering and alignment of sets of curves measured on a discrete time grid. The model is specifically tailored to gene expression time course data. Each functional cluster center is a nonlinear combination of solutions of a simple linear differential equation that describes the change of individual mRNA levels when the synthesis and decay rates are constant. The mixture of continuous time parametric functional forms allows one to (a) account for the heterogeneity in the observed profiles, (b) align the profiles in time by estimating real-valued time shifts, (c) capture the synthesis and decay of mRNA in the course of an experiment, and (d) regularize noisy profiles by enforcing smoothness in the mean curves. We derive an EM algorithm for estimating the parameters of the model, and apply the proposed approach to the set of cycling genes in yeast. The experiments show consistent improvement in predictive power and within cluster variance compared to regular Gaussian mixtures.

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.