Unsupervised learning for a clustering algorithm based on ellipsoidal calculus

Unsupervised learning is a target free methodology to classify unorganized information. This study proposes a new unsupervised learning method for classifying unlabeled targets based on convex ellipsoidal sets. The method described here uses ellipsoidal calculus tools to realize pattern classification via a clustering scheme. The algorithm consisted in adjusting the number of clusters defined by an ellipsoidal set as well as their centers, shape forms and orientation. All these processes were realized without preliminary information on the data distribution. The application of an inner gradient descent algorithm permitted the adjustment of these parameters, using the standard deviation of data in the cluster with respect to the semi-axis of ellipsoid that contains the corresponding data. A specific evaluation of the proposed algorithm used two-dimensional attributes databases. The outcomes of the classification results were compared with those produced by the K-means and DBSCAN algorithm. Comparable classification results were achieved overcoming some drawbacks of the methods.