Model order selection and cue combination are both difficult open problems in the area of clustering. In this work we build upon stability-based approaches to develop a new method for automatic model order selection and cue combination with applications to visual grouping. Novel features of our approach include the ability to detect multiple stable clusterings (instead of only one), a simpler means of calculating stability that does not require training a classifier, and a new characterization of the space of stabilities for a continuum of segmentations that provides for an efficient sampling scheme. Our contribution is a framework for visual grouping that frees the user from the hassles of parameter tuning and model order selection: the input is an image, the output is a shortlist of segmentations.

Classification problems abundantly arise in many computer vision tasks eing of supervised, semi-supervised or unsupervised nature. Even when class labels are not available, a user still might favor certain grouping solutions over others. This bias can be expressed either by providing a clustering criterion or cost function and, in addition to that, by specifying pairwise constraints on the assignment of objects to classes. In this work, we discuss a unifying formulation for labelled and unlabelled data that can incorporate constrained data for model fitting. Our approach models the constraint information by the maximum entropy principle. This modeling strategy allows us (i) to handle constraint violations and soft constraints, and, at the same time, (ii) to speed up the optimization process. Experimental results on face classification and image segmentation indicates that the proposed algorithm is computationally efficient and generates superior groupings when compared with alternative techniques.

Data clustering represents an important tool in exploratory data analysis. The lack of objective criteria render model selection as well as the identification of robust solutions particularly difficult. The use of a stability assessment and the combination of multiple clustering solutions represents an important ingredient to achieve the goal of finding useful partitions. In this work, we propose a novel way of combining multiple clustering solutions for both, hard and soft partitions: the approach is based on modeling the probability that two objects are grouped together. An efficient EM optimization strategy is employed in order to estimate the model parameters. Our proposal can also be extended in order to emphasize the signal more strongly by weighting individual base clustering solutions according to their consistency with the prediction for previously unseen objects. In addition to that, the probabilistic model supports an out-of-sample extension that (i) makes it possible to assign previously unseen objects to classes of the combined solution and (ii) renders the efficient aggregation of solutions possible. In this work, we also shed some light on the usefulness of such combination approaches. In the experimental result section, we demonstrate the competitive performance of our proposal in comparison with other recently proposed methods for combining multiple classifications of a finite data set.

Fusing multiple information sources can yield significant benefits to suc- cessfully accomplish learning tasks. Many studies have focussed on fus- ing information in supervised learning contexts. We present an approach to utilize multiple information sources in the form of similarity data for unsupervised learning. Based on similarity information, the clustering task is phrased as a non-negative matrix factorization problem of a mix- ture of similarity measurements. The tradeoff between the informative- ness of data sources and the sparseness of their mixture is controlled by an entropy-based weighting mechanism. For the purpose of model se- lection, a stability-based approach is employed to ensure the selection of the most self-consistent hypothesis. The experiments demonstrate the performance of the method on toy as well as real world data sets.

A network of leaky integrate-and-fire (IAF) neurons is proposed to segment gray-scale images. The network architecture with local competition between neurons that encode segment assignments of image blocks is motivated by a histogram clustering approach to image segmentation. Lateral excitatory connections between neighboring image sites yield a local smoothing of segments. The mean firing rate of class membership neurons encodes the image segmentation. A weight modification scheme is proposed that estimates segment-specific prototypical histograms. The robustness properties of the network implementation make it amenable to an analog VLSI realization. Results on synthetic and real-world images demonstrate the effectiveness of the architecture.

Data clustering describes a set of frequently employed techniques in exploratory data analysis to extract "natural" group structure in data. Such groupings need to be validated to separate the signal in the data from spurious structure. In this context, finding an appropriate number of clusters is a particularly important model selection question. We introduce a measure of cluster stability to assess the validity of a cluster model. This stability measure quantifies the reproducibility of clustering solutions on a second sample, and it can be interpreted as a classification risk with regard to class labels produced by a clustering algorithm. The preferred number of clusters is determined by minimizing this classification risk as a function of the number of clusters. Convincing results are achieved on simulated as well as gene expression data sets. Comparisons to other methods demonstrate the competitive performance of our method and its suitability as a general validation tool for clustering solutions in real-world problems.

A novel approach to combining clustering and feature selection is pre- sented. It implements a wrapper strategy for feature selection, in the sense that the features are directly selected by optimizing the discrimina- tive power of the used partitioning algorithm. On the technical side, we present an efficient optimization algorithm with guaranteed local con- vergence 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.

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 cross- validation, 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 se- lection in comparison to standard techniques in this area.