Kernel K-médias com distâncias adaptativas para dados intervalares

Abstract

Symbolic Data Analysis (SDA) is an extension of classic data analysis that aims to develop statistical and/or computational techniques for more complex data than the usual data, usually represented by values and categories, may include variations and internal structures. Several clustering methods for classical data have already been extended for symbolic data, such as K-means and its kernelized versions. The kernel functions have been widely used in clustering algorithms due to improvements in their performance in scenarios where the clusters are non-linearly separable. Even so, these kernel-based methods consider that variables are equally important in the clustering process, which most of the time is not configured in this way, especially in the era of Big Data, where high-dimensional data sets are easily found. The objective of this work is to propose new

kernel-based clustering methods for interval-valued symbolic data with automatic weigh- ting of variables through adaptive distances that change at each iteration of the algorithm

and are obtained as the sum of the square Euclidean distances between the observations

and centroids of each group, calculated for each variable, individually. The main ad- vantage of the proposed methods over the conventional approach is the use of adaptive

distances which allows to assign weights to variables, making possible to differentiate the importance of the variables and consequently improve the performance of the algorithms. This work encompasses the hard clustering paradigm and considers two aspects used in kernel functions, when the prototypes are defined in the original data space and when the prototypes are defined in a higher dimension space, known as feature space. Experiments with simulated data and real interval-valued data shows the efficiency of the proposed methods.