With the aim to propose a non parametric hypothesis test, this paper carries out a study on the Matching Error (ME), a comparison index of two partitions obtained from the same data set, using for example two clustering methods. This index is related to the misclassifica-tion error in supervised learning. Some properties of the ME and, especially, its distribution function for the case of two independent partitions are analyzed. Extensive simulations show the efficiency of the ME and we propose a hypothesis test based on it.
We compare the three basic algorithms for model-based clustering on high-dimensional discrete-variable datasets. All three algorithms use the same underlying model: a naive-Bayes model with a hidden root node, also known as a multinomial-mixture model. In the first part of the paper, we perform an experimental comparison between three batch algorithms that learn the parameters of this model: the Expectation–Maximization (EM) algorithm, a “winner take all” version of the EM algorithm reminiscent of the K-means algorithm, and model-based agglomerative clustering. We find that the EM algorithm significantly outperforms the other methods, and proceed to investigate the effect of various initialization methods on the final solution produced by the EM algorithm. The initializations that we consider are (1) parameters sampled from an uninformative prior, (2) random perturbations of the marginal distribution of the data, and (3) the output of agglomerative clustering. Although the methods are substantially different, they lead to learned models that are similar in quality.