Geometric Associative Memories and Their Applications to Pattern Classification

A New Unsupervised Learning for Clustering Using Geometric Associative Memories

“…where C is the center point of the sphere in conformal notation as defined in (2), γ is the radius of the sphere and c is the Euclidean point of C.…”

“…Then a minimum function is used to obtain an index class. GAMs can perfectly operate when the classes are spherically separable [2]. A GAM is precisely a matrix whose components are spheres, it can be seen in (7), where m is the total number of classes.…”

“…The proposed algorithm is based on the previous ideas, but the Conformal Geometric Algebra paradigm will be used. Different to the k-means algorithm the clusters in this method will be found by separating the points of the associated centroid of the others points (the main advantage is that the new centroids are found automatically) solving an optimization problem, it is described in [2].…”

“…The associative memories models developed until now can be categorized in three groups, those based on traditional vector algebra operations, those based on mathematical morphology operations, and those based on Geometric Algebra paradigm. The third group make use of Geometric Algebra [1] for their operations an operators, the so-called Geometric Associative Memories [2] (GAMs) are an example of memories that falls into this group. The goal of GAMs is the classification of a pattern as belonging to a specific class if and only if the pattern is inside of the support region (hyper-sphere) of that class.…”