Fractal dimension for clustering and unsupervised and supervised feature selection.

Data mining refers to the automation of data analysis to extract patterns from large amounts of data. A major breakthrough in modelling natural patterns is the recognition that nature is fractal, not Euclidean. Fractals are capable of modelling self-similarity, infinite details, infinite length and the absence of smoothness. This research was aimed at simplifying the discovery and detection of groups in data using fractal dimension. These data mining tasks were addressed efficiently. The first task defines groups of instances (clustering), the second selects useful features from non-defined (unsupervised) groups of instances and the third selects useful features from pre-defined (supervised) groups of instances. Improvements are shown on two data mining classification models: hierarchical clustering and Artificial Neural Networks (ANN). For clustering tasks, a new two-phase clustering algorithm based on the Fractal Dimension (FD), compactness and closeness of clusters is presented. The proposed method, uses self-similarity properties of the data, first divides the data into sufficiently large sub-clusters with high compactness. In the second stage, the algorithm merges the sub-clusters that are close to each other and have similar complexity. The final clusters are obtained through a very natural and fully deterministic way. The selection of different feature subspaces leads to different cluster interpretations. An unsupervised embedded feature selection algorithm, able to detect relevant and redundant features, is presented. This algorithm is based on the concept of fractal dimension. The level of relevance in the features is quantified using a new proposed entropy measure, which is less complex than the current state-of-the-art technology. The proposed algorithm is able to maintain and in some cases improve the quality of the clusters in reduced feature spaces. For supervised feature selection, for classification purposes, a new algorithm is proposed that maximises the relevance and minimises the redundancy of the features simultaneously. This algorithm makes use of the FD and the Mutual Information (MI) techniques, and combines them to create a new measure of feature usefulness and to produce a simpler and non-heuristic algorithm. The similar nature of the two techniques, FD and MI, makes the proposed algorithm more suitable for a straightforward global analysis of the data