Semi-supervised model-based clustering with controlled clusters leakage

In this paper, we focus on finding clusters in partially categorized data sets. We propose a semi-supervised version of Gaussian mixture model, called C3L, which retrieves natural subgroups of given categories. In contrast to other semi-supervised models, C3L is parametrized by user-defined leakage level, which controls maximal inconsistency between initial categorization and resulting clustering. Our method can be implemented as a module in practical expert systems to detect clusters, which combine expert knowledge with true distribution of data. Moreover, it can be used for improving the results of less flexible clustering techniques, such as projection pursuit clustering. The paper presents extensive theoretical analysis of the model and fast algorithm for its efficient optimization. Experimental results show that C3L finds high quality clustering model, which can be applied in discovering meaningful groups in partially classified data

Minimum Density Hyperplanes

Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classification which is motivated by this objective. The proposed minimum density hyperplane minimises the integral of the empirical probability density function along it, thereby avoiding intersection with high density clusters. We show that the minimum density and the maximum margin hyperplanes are asymptotically equivalent, thus linking this approach to maximum margin clustering and semi-supervised support vector classifiers. We propose a projection pursuit formulation of the associated optimisation problem which allows us to find minimum density hyperplanes efficiently in practice, and evaluate its performance on a range of benchmark datasets. The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification

Data clustering using a model granular magnet

We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures it is completely ordered; all spins are aligned. At very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.Comment: 46 pages, postscript, 15 ps figures include

In Search of Non-Gaussian Components of a High-Dimensional Distribution

Finding non-Gaussian components of high-dimensional data is an important preprocessing step for effcient information processing. This article proposes a new linear method to identify the ``non-Gaussian subspace´´ within a very general semi-parametric framework. Our proposed method, called NGCA (Non-Gaussian Component Analysis), is essentially based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector which belongs to the low dimensional non-Gaussian target subspace up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method.non-Gaussian components, dimension reduction