Averaging on Riemannian manifolds and unsupervised learning using neural associative memory

This paper is dedicated to the new algorithm for unsupervised learning and clustering. This algorithm is based on Hopfield-type pseudoinverse associative memory. We propose to represent synaptic matrices of this type of neural network as points on the Grassmann manifold. Then we establish the procedure of generalized averaging on this manifold. This procedure enables us to endow the associative memory with ability of data generalization. In the paper we provide experimental testing for the algorithm using simulated random data. After the synthesis of associative memory containing generalized data. Cluster centers are retrieved using procedure of associative recall with random starts.