Kernel clustering with automatic variable weighting for interval data

Abstract

Symbolic Data Analysis (SDA) is a field associated with statistics and artificial intelligence that deals with multi-valued data, such as histograms, intervals, and lists. This type of data emerges as an alternative to conventional aggregation methods (mean, median, and mode) to account for variability. It is particularly useful when analyzing groups of individuals rather than single individuals. For example, when we have information about patients but aim to describe and analyze hospitals. Kernel functions are extensively employed in clustering algorithms because they perform better when there is no linear separability between clusters and/or the clusters are not hyperspherical. This paper proposes new clustering methods based on the Gaussian kernel that weigh the interval-valued variables automatically. These methods are particularly appropriate when there are non-informative variables or variables relevant to specific clusters. We introduce four global variants, in which each variable has the same weight across all clusters, and two local variants, where variable weights differ for each cluster. Although local methods offer greater flexibility in the weighting scheme, global methods are less susceptible to local minima. Experimental evaluation over simulated and real interval-valued datasets, compared to traditional clustering methods for interval data, demonstrated the effectiveness of the introduced algorithms. The source code and datasets are available at https://github.com/Natandradesa/Kernel-Clustering-for-Interval-Data.