Comparing high dimensional partitions, with the Coclustering Adjusted Rand Index

We consider the simultaneous clustering of rows and columns of a matrix and more particularly the ability to measure the agreement between two co-clustering partitions. The new criterion we developed is based on the Adjusted Rand Index and is called the Co-clustering Adjusted Rand Index named CARI. We also suggest new improvements to existing criteria such as the Classification Error which counts the proportion of misclassified cells and the Extended Normalized Mutual Information criterion which is a generalization of the criterion based on mutual information in the case of classic classifications. We study these criteria with regard to some desired properties deriving from the co-clustering context. Experiments on simulated and real observed data are proposed to compare the behavior of these criteria.Comment: 52 page

clues: An R Package for Nonparametric Clustering Based on Local Shrinking

Determining the optimal number of clusters appears to be a persistent and controversial issue in cluster analysis. Most existing R packages targeting clustering require the user to specify the number of clusters in advance. However, if this subjectively chosen number is far from optimal, clustering may produce seriously misleading results. In order to address this vexing problem, we develop the R package clues to automate and evaluate the selection of an optimal number of clusters, which is widely applicable in the field of clustering analysis. Package clues uses two main procedures, shrinking and partitioning, to estimate an optimal number of clusters by maximizing an index function, either the CH index or the Silhouette index, rather than relying on guessing a pre-specified number. Five agreement indices (Rand index, Hubert and ArabieâÂÂs adjusted Rand index, Morey and AgrestiâÂÂs adjusted Rand index, Fowlkes and Mallows index and Jaccard index), which measure the degree of agreement between any two partitions, are also provided in clues. In addition to numerical evidence, clues also supplies a deeper insight into the partitioning process with trajectory plots.

clues: An R Package for Nonparametric Clustering Based on Local Shrinking

Determining the optimal number of clusters appears to be a persistent and controversial issue in cluster analysis. Most existing R packages targeting clustering require the user to specify the number of clusters in advance. However, if this subjectively chosen number is far from optimal, clustering may produce seriously misleading results. In order to address this vexing problem, we develop the R package clues to automate and evaluate the selection of an optimal number of clusters, which is widely applicable in the field of clustering analysis. Package clues uses two main procedures, shrinking and partitioning, to estimate an optimal number of clusters by maximizing an index function, either the CH index or the Silhouette index, rather than relying on guessing a pre-specified number. Five agreement indices (Rand index, Hubert and Arabie's adjusted Rand index, Morey and Agresti's adjusted Rand index, Fowlkes and Mallows index and Jaccard index), which measure the degree of agreement between any two partitions, are also provided in clues. In addition to numerical evidence, clues also supplies a deeper insight into the partitioning process with trajectory plots

sARI: a soft agreement measure for class partitions incorporating assignment probabilities

Agreement indices are commonly used to summarize the performance of both classification and clustering methods. The easy interpretation/intuition and desirable properties that result from the Rand and adjusted Rand indices, has led to their popularity over other available indices. While more algorithmic clustering approaches like k-means and hierarchical clustering produce hard partition assignments (assigning observations to a single cluster), other techniques like model-based clustering include information about the certainty of allocation of objects through class membership probabilities (soft partitions). To assess performance using traditional indices, e.g., the adjusted Rand index (ARI), the soft partition is mapped to a hard set of assignments, which commonly overstates the certainty of correct assignments. This paper proposes an extension of the ARI, the soft adjusted Rand index (sARI), with similar intuition and interpretation but also incorporating information from one or two soft partitions. It can be used in conjunction with the ARI, comparing the similarities of hard to soft, or soft to soft partitions to the similarities of the mapped hard partitions. Simulation study results support the intuition that in general, mapping to hard partitions tends to increase the measure of similarity between partitions. In applications, the sARI more accurately reflects the cluster boundary overlap commonly seen in real data