A Variant of the K-Means Clustering Algorithm for Continuous-Nominal Data

Abstract

The core idea of the proposed algorithm is to embed the considered dataset into a metric space. Two spaces for embedding of nominal part with the Hamming metric are considered: Euclidean space (the classical approach) and the standard unit sphere $\mathbb S$ (our new approach). We proved that the distortion of embedding into the unit sphere is at least 75 % better than that of the classical approach. In our model, combinations of continuous and nominal data are interpreted as points of a cylinder $\mathbb R^p\times \mathbb S$, where p is the dimension of continuous data. We use a version of the gradient algorithm to compute centroids of finite sets on a cylinder. Experimental results show certain advances of the new algorithm. Specifically, it produces better clusters in tests with predefined groups.