The excess mass approach and the analysis of multi-modality

The excess mass approach is a general approach to statistical analysis. It can be used to formulate a probabilistic model for clustering and can be applied to the analysis of multi-modality. Intuitively, a mode is present where an excess of probability mass is concentrated. This intuitive idea can be formalized directly by means of the excess mass functional. There is no need for intervening steps like initial density estimation. The excess mass measures the local difference of a given distribution to a reference model, usually the uniform distribution. The excess mass defines a functional which can be estimated efficiently from the data and can be used to test for multi-modality.