Multisets modeling learning: an unified theory for supervised and unsupervised learning

An unified theory is proposed for putting together supervised learning and unsupervised learning (including clustering, PCA-type selforganizing and topological map) into one single frame. By this theory, different special cases will automatically lead us to supervised learning for feedforward networks and for modular architecture of local experts, to various types of unsupervised learning including data clustering, PCA and k-principal components analysis (k-PCA), minor component analysis (MCA) and k-minor components analysis (k-MCA), principal subspace analysis (PSA) and minor subspace analysis (MSA), as well as their extensions to the localized versions (e.g., local PCA, local MCA, ..., etc.). Furthermore, it is also shown that the theory can be extended to cover self-organizing topological map