Subspace Clustering for all Seasons

Subspace clustering is recognized as a more general and difficult task than standard clustering since it requires to identify not only objects sharing similar feature values but also the various subspaces where these similarities appear. Many approaches have been investigated for subspace clustering in the literature using various clustering paradigms. The reader is referred for instance to [5] for detailed reviews and comparisons of the best methods and main categories. Even if many evolutionary clustering approaches exist [4] very few of them address the subspace clustering problem and still include non-evolutionary stages [7,8]. According to [1], bio-inspired optimization algorithms could be improved by incorporating knowledge from molecular and evolutionary biology. A promising source of advances in optimization is one of the important phenomena in evolutionary biology: the dynamic evolution of the genome structure. Several studies showed for instance that an evolvable genome structure allows evolution to modify the effects that evolution operators (e.g., mutations) have on individuals, a phenomenon known as evolution of evolution [3]. In this paper, we present Chameleoclust, an evolutionary subspace clustering algorithm that incorporates a genome having an evolvable structure. The genome is a coarse-grained genome, inspired on [2], and defined as a list of tuples (the "genes"), each tuple containing numbers. These tuples are mapped at the phenotype level to denote core point locations in different dimensions, which are then used to collectively build the subspace clusters, by grouping the data around the core points. The biological analogy here would be that each gene codes for a molecular product and that the combination of molecular products associated together codes for a function, i.e., a cluster. To allow for evolution of evolution, Chameleo-clust genome contains a variable proportion of functional elements as , and is subject to local mutations and to large random rearrangements, namely: large deletions, duplications and translocations. Local mutations and rearrangements may thus modify the genome elements but also the genome structure. The key intuition in the design of the Chameleoclust algorithm is to take advantage of such an evolvable structure to detect various numbers of clusters in subspaces of various dimensions and to self-tune the main evolutionary parameters (e.g., levels of variability). Figure 1 illustrates Chameleoclust genome structure (genome length and proportion of functional elements) and fitness convergence on a synthetic benchmark dataset. The reader is refered to [6] for a detailed description of Chameleoclust. The algorithm has been assessed using a …