Fractal consistency in clusters detection

Cluster analysis is a widely adopted class of methods addressing the investigation of patterns in many areas of biomedical interest such as public health management and location of spatial clustering of disease cases (1). Many clustering algorithms are available and an increasing amount are continuously devised addressing issues, among others, of computational complexity and the need for robust performances (2). Recently algorithms for clustering stemming from fractals appeared, referring to available set of fractal dimensions. The idea is just to add an object to a class if it changes significantly the fractal dimension. The algorithm clusters points in such a way that data points in the same cluster are more self-affine among themselves than to points in other clusters, without asking for a prior fractal structure of the data sets themselves (3). Although this approach deals with clustering getting the way around pitfalls like the traditional favour to spherical shapes (i.e. centroids methods based) it faces up problems at least in the initialization step, where it still requires somehow a traditional approach to get a critical sample size of the clusters allowing the fractal dimension computation, getting a bit of logical circularity. Given this drawback in the direct use of this fractal application, we use fractals devising a strategy to cope with the issue of getting consistent results from any clustering procedure just computing fractal dimensions.