Fuzzy relational kernel clustering with Local Scaling Parameter Learning

Abstract

We introduce a new fuzzy relational clustering technique with Local Scaling Parameter Learning (LSPL). The proposed approach learns the underlying cluster dependent dissimilarity measure while finding compact clusters in the given data set. The learned measure is a Gaussian similarity function defined with respect to each cluster that allows to control the scaling of the clusters and thus, improve the final partition. We minimize one objective function for both the optimal partition and for the cluster dependent scaling parameter. This optimization is done iteratively by dynamically updating the partition and the scaling parameter in each iteration. This makes the proposed algorithm simple and fast. Moreover, as we assume that the data is available in a relational form, the proposed approach is applicable even when only the degree to which pairs of objects in the data are related is available. It is also more practical when similar objects cannot be represented by a single prototype.

An Overview of Unsupervised and Semi-Supervised Fuzzy Kernel Clustering

“…Moreover, it is not trivial to evaluate the resulting partition in order to select the optimal parameters. To overcome this limitation, the LSL algorithm [29] has been proposed. It minimizes one objective function for both the optimal partition and for cluster dependent Gaussian parameters that reflect the intra-cluster characteristics of the data.…”

“…LSL [29] and FLeCK [30] have the advantage of learning cluster dependent scaling parameters. Thus, they can be used to identify clusters of different densities.…”

“…(3). SS-LSL is an extension of the LSL algorithm [29] that incorporates partial supervision. The second term in Eq.…”

“…Setting the derivative of J with respect to σ i gives the same update equation for σ i as the LSL algorithm [29] (Refer to Eq. (16)).…”

Semi-supervised clustering and local scale learning algorithm

“…Moreover, since one global parameter is used for the entire data set, it may not be possible to find one optimal σ when there are large variations between the distributions of the different clusters in the feature space. To address this limitation, the authors in [1] introduced a fuzzy relational clustering technique with Local Scaling Parameter Learning (LSPL) that learns a scale parameter per cluster.…”