H CM – Harmonic Contractive Map (Semeion©)
The Harmonic CM is a fundamental variation of regular Auto CM. The main difference is the sine function in the contractive equations, learning law for the full matrix “w” evolution and the global cost function. The topology, instead, is the same of the regular Auto CM.
Another specificity of H CM is that the mono-dedicated weights, “v”, do not converge to “C”, but they converge to π.
Here is an application of H CM to a dataset of alpha numeric digits (see the figure below).
Figure: the dataset of alpha numeric digits (input 7×7).
The MST graph below shows the capability of H CM to organize the global similarities of the dataset.
Figure: MST generated from the trained weights matrix of H CM.