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.

In this paper, sparse representation (factorization) of a data matrix is first discussed. An overcomplete basis matrix is estimated by using the K means method.

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.

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.

Significant progress in clustering has been achieved by algorithms that are based on pairwise affinities between the datapoints. In particular, spectral clustering methods have the advantage of being able to divide arbitrarily shaped clusters and are based on efficient eigenvector calculations. However,spectral methods lack a straightforward probabilistic interpretation which makes it difficult to automatically set parameters using trainingdata. In this paper we use the previously proposed typical cut framework for pairwise clustering. We show an equivalence between calculating the typical cut and inference in an undirected graphical model. We show that for clustering problems with hundreds of datapoints exact inference may still be possible. For more complicated datasets, we show that loopy belief propagation(BP) and generalized belief propagation (GBP) can give excellent results on challenging clustering problems. We also use graphical modelsto derive a learning algorithm for affinity matrices based on labeled data.

A novel approach to combining clustering and feature selection is presented. Itimplements a wrapper strategy for feature selection, in the sense that the features are directly selected by optimizing the discriminative powerof 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.

Spectral clustering refers to a class of techniques which rely on the eigenstructure ofa similarity matrix to partition points into disjoint clusters with points in the same cluster having high similarity and points in different clustershaving 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.

Curve data arises naturally in a variety of applications.

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. Inthis 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 thehypothesis 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 statisticalsignificance 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.

Clustering aims at extracting hidden structure in dataset. While the problem offinding compact clusters has been widely studied in the literature, extractingarbitrarily formed elongated structures is considered a much harder problem. In this paper we present a novel clustering algorithm whichtackles 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, leadingto 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.