Constrained locally weighted clustering

Data clustering is a difficult problem due to the complex and heterogeneous natures of multidimensional data. To improve clustering accuracy, we propose a scheme to capture the local correlation structures: associate each cluster with an independent weighting vector and embed it in the subspace spanned by an adaptive combination of the dimensions. Our clustering algorithm takes advantage of the known pairwise instance-level constraints. The data points in the constraint set are divided into groups through inference; and each group is assigned to the feasible cluster which minimizes the sum of squared distances between all the points in the group and the corresponding centroid. Our theoretical analysis shows that the probability of points being assigned to the correct clusters is much higher by the new algorithm, compared to the conventional methods. This is confirmed by our experimental results, indicating that our design indeed produces clusters which are closer to the ground truth than clusters created by the current state-ofthe-art algorithms.