In cluster analysis, it can be useful to interpret the partition built from the data in the light of external categorical variables which were not directly involved to cluster the data. An approach is proposed in the model-based clustering context to select a model and a number of clusters which both fit the data well and take advantage of the potential illustrative ability of the external variables. This approach makes use of the integrated joint likelihood of the data and the partitions at hand, namely the model-based partition and the partitions associated to the external variables. It is noteworthy that each mixture model is fitted by the maximum likelihood methodology to the data, excluding the external variables which are used to select a relevant mixture model only. Numerical experiments illustrate the promising behaviour of the derived criterion.
Abstract-Stability has been considered an important property for evaluating clustering solutions. Nevertheless, there are no conclusive studies on the relationship between this property and the capacity to recover clusters inherent to data ("ground truth"). This study focuses on this relationship, resorting to experiments on synthetic data generated under diverse scenarios (controlling relevant factors) and experiments on real data sets. Stability is evaluated using a weighted cross-validation procedure. Indices of agreement (corrected for agreement by chance) are used both to assess stability and external validation. The results obtained reveal a new perspective so far not mentioned in the literature. Despite the clear relationship between stability and external validity when a broad range of scenarios is considered, the within-scenarios conclusions deserve our special attention: faced with a specific clustering problem (as we do in practice), there is no significant relationship between clustering stability and the ability to recover data clusters
In the present paper we focus on the performance of clustering algorithms using indices of paired agreement to measure the accordance between clusters and an a priori known structure. We specifically propose a method to correct all indices considered for agreement by chance-the adjusted indices are meant to provide a realistic measure of clustering performance. The proposed method enables the correction of virtually any index-overcoming previous limitations known in the literature-and provides very precise results. We use simulated datasets under diverse scenarios and discuss the pertinence of our proposal which is particularly relevant when poorly separated clusters are considered. Finally we compare the performance of EM and K-Means algorithms, within each of the simulated scenarios and generally conclude that EM generally yields best results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.