There exist many approaches to clustering, but the important issue of feature selection, i.e., selecting the data attributes that are relevant for clustering, is rarely addressed. Feature selection for clustering is difficult due to the absence of class labels. We propose two approaches to feature selection in the context of Gaussian mixture-based clustering. In the first one, instead of making hard selections, we estimate feature saliencies. An expectation-maximization (EM) algorithm is derived for this task. The second approach extends Koller and Sahami's mutual-informationbased feature relevance criterion to the unsupervised case. Feature selection is then carried out by a backward search scheme. This scheme can be classified as a "wrapper", since it wraps mixture estimation in an outer layer that performs feature selection. Experimental results on synthetic and real data show that both methods have promising performance.

Model selection is linked to model assessment, which is the problem of comparing different models, or model parameters, for a specific learning task. For supervised learning, the standard practical technique is crossvalidation, which is not applicable for semi-supervised and unsupervised settings. In this paper, a new model assessment scheme is introduced which is based on a notion of stability. The stability measure yields an upper bound to cross-validation in the supervised case, but extends to semi-supervised and unsupervised problems. In the experimental part, the performance of the stability measure is studied for model order selection in comparison to standard techniques in this area.

Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as K-means initially fails to find one that is meaningful to a user, the only recourse may be for the user to manually tweak the metric until sufficiently good clusters are found. For these and other applications requiring good metrics, it is desirable that we provide a more systematic way for users to indicate what they consider "similar." For instance, we may ask them to provide examples.

The information bottleneck (IB) method is an information-theoretic formulation for clustering problems.

We argue that human inductive generalization is best explained in a Bayesian framework, rather than by traditional models based on similarity computations. We go beyond previous work on Bayesian concept learning by introducing an unsupervised method for constructing flexible hypothesis spaces, and we propose a version of the Bayesian Occam's razor that trades off priors and likelihoods to prevent under-or over-generalization in these flexible spaces. We analyze two published data sets on inductive reasoning as well as the results of a new behavioral study that we have carried out.

Recently the Fisher score (or the Fisher kernel) is increasingly used as a feature extractor for classification problems. The Fisher score is a vector of parameter derivatives of loglikelihood of a probabilistic model. This paper gives a theoretical analysis about how class information is preserved in the space of the Fisher score, which turns out that the Fisher score consists of a few important dimensions with class information and many nuisance dimensions. When we perform clustering with the Fisher score, K-Means type methods are obviously inappropriate because they make use of all dimensions. So we will develop a novel but simple clustering algorithm specialized for the Fisher score, which can exploit important dimensions. This algorithm is successfully tested in experiments with artificial data and real data (amino acid sequences).

Using a Markov chain perspective of spectral clustering we present an algorithm to automatically find the number of stable clusters in a dataset. The Markov chain's behaviour is characterized by the spectral properties of the matrix of transition probabilities, from which we derive eigenflows along with their halflives. An eigenflow describes the flow of probability mass due to the Markov chain, and it is characterized by its eigenvalue, or equivalently, by the halflife of its decay as the Markov chain is iterated. A ideal stable cluster is one with zero eigenflow and infinite half-life. The key insight in this paper is that bottlenecks between weakly coupled clusters can be identified by computing the sensitivity of the eigenflow's halflife to variations in the edge weights.

There exist many approaches to clustering, but the important issue of feature selection, i.e., selecting the data attributes that are relevant for clustering, is rarely addressed. Feature selection for clustering is difficult due to the absence of class labels. We propose two approaches to feature selection in the context of Gaussian mixture-based clustering. In the first one, instead of making hard selections, we estimate feature saliencies. An expectation-maximization (EM) algorithm is derived for this task. The second approach extends Koller and Sahami's mutual-informationbased feature relevance criterion to the unsupervised case. Feature selection is then carried out by a backward search scheme. This scheme can be classified as a "wrapper", since it wraps mixture estimation in an outer layer that performs feature selection. Experimental results on synthetic and real data show that both methods have promising performance.

Model selection is linked to model assessment, which is the problem of comparing different models, or model parameters, for a specific learning task. For supervised learning, the standard practical technique is crossvalidation, which is not applicable for semi-supervised and unsupervised settings. In this paper, a new model assessment scheme is introduced which is based on a notion of stability. The stability measure yields an upper bound to cross-validation in the supervised case, but extends to semi-supervised and unsupervised problems. In the experimental part, the performance of the stability measure is studied for model order selection in comparison to standard techniques in this area.

Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as K-means initially fails to find one that is meaningful to a user, the only recourse may be for the user to manually tweak the metric until sufficiently good clusters are found. For these and other applications requiring good metrics, it is desirable that we provide a more systematic way for users to indicate what they consider "similar." For instance, we may ask them to provide examples.