DCG++: A data-driven metric for geometric pattern recognition.

Clustering large and complex data sets whose partitions may adopt arbitrary shapes remains a difficult challenge. Part of this challenge comes from the difficulty in defining a similarity measure between the data points that captures the underlying geometry of those data points. In this paper, we propose an algorithm, DCG++ that generates such a similarity measure that is data-driven and ultrametric. DCG++ uses Markov Chain Random Walks to capture the intrinsic geometry of data, scans possible scales, and combines all this information using a simple procedure that is shown to generate an ultrametric. We validate the effectiveness of this similarity measure within the context of clustering on synthetic data with complex geometry, on a real-world data set containing segmented audio records of frog calls described by mel-frequency cepstral coefficients, as well as on an image segmentation problem. The experimental results show a significant improvement on performance with the DCG-based ultrametric compared to using an empirical distance measure.