Exploring the number of groups in robust model-based clustering

Abstract

Two key questions in Clustering problems are how to determine the number of groups properly and measure the strength of group-assignments. These questions are specially involved when the presence of certain fraction of outlying data is also expected.Any answer to these two key questions should depend on the assumed probabilisticmodel, the allowed group scatters and what we understand by noise. With this in mind, some exploratory "trimming-based" tools are presented in this work together with their justifications. The monitoring of optimal values reached when solving a robust clustering criteria and the use of some "discriminant" factors are the basis for these exploratory tools.

tclust: AnRPackage for a Trimming Approach to Cluster Analysis

“…the maximized log-likelihood (2) to increase too, and this could lead to "overestimate" the appropriate number of clusters (see García-Escudero et al 2011).…”

“…García-Escudero et al (2011) propose to monitor the "classification trimmed likelihoods" functionals…”

The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers

“…Surely, some datadependent diagnostic based on trimmed BIC notions (Neykov et al, 2007) may provide a way to select the number of groups and underlying factors, as has been shown. With reference to the choice of α, other tools can be adapted to the present case, such as silhouette plots to assess the strength of cluster assignments and the classification trimmed likelihood curves (García-Escudero et al, 2011). These curves provide helpful exploratory tools by monitoring the estimation results when moving α in [0,1] and G = 1, 2, .…”

Robust constrained fuzzy clustering

“…In this example, k = 2 is clearly a good choice for the number of clusters (once 10% of the outlying data points are trimmed). Thus, the fact of allowing for weights p j in the target function could provide interesting information about how to make sensible choices for k. This possibility was already considered in hard clustering problems in [16]. Note also that Figure 5,(a) shows many intermediate membership values due to the clear overlap between the two clusters that share one of the two normal components.…”

“…However, it is important to note that the problem of choosing α is closely related to the choice of parameters k and c [see 16]. Addressing all these determinations in a unified manner still requires an active role to be played by the researcher, as a final decision may be very subjective, and, thus, it is not clear that a fully unsupervised strategy can be found.…”