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

A New Topology-Preserving Distance Metric with Applications to Multi-dimensional Data Clustering

Part 5: Classification - ClusteringInternational audienceIn many cases of high dimensional data analysis, data points may lie on manifolds of very complex shapes/geometries. Thus, the usual Euclidean distance may lead to suboptimal results when utilized in clustering or visualization operations. In this work, we introduce a new distance definition in multi-dimensional spaces that preserves the topology of the data point manifold. The parameters of the proposed distance are discussed and their physical meaning is explored through 2 and 3-dimensional synthetic datasets. A robust method for the parameterization of the algorithm is suggested. Finally, a modification of the well-known k-means clustering algorithm is introduced, to exploit the benefits of the proposed distance metric for data clustering. Comparative results including other established clustering algorithms are presented in terms of cluster purity and V-measure, for a number of well-known datasets