A new fuzzy clustering algorithm for interval-valued data based on City-Block distance
Sara Inés Rizo Rodríguez, Francisco de A.T. de Carvalho · 2019
Interval-valued data are needed, for example, when an object represents a group of individuals and the variables used to describe it need to assume a value which expresses the variability inherent to the description of a group. Interval-valued data arise in practical situations such as recording monthly interval temperatures at meteorological stations, daily interval stock prices, etc. In this paper is proposed a robust partitioning fuzzy clustering algorithm for interval-valued data based on adaptive City-Block distance that takes into account the relevance of the variables according to the boundaries. This distance changes at each iteration of the algorithm and is different from one cluster to another. The method optimizes an objective function by alternating three steps to compute the representatives of each group, the fuzzy partition, as well as relevance weights for the interval-valued variables for each boundary. Experiments on synthetic and real interval-valued datasets corroborate the usefulness and robustness of the proposed algorithm.