Norm-Free Radon-Nikodym Approach to Machine Learning

For Machine Learning (ML) classification problem, where a vector of x--observations (values of attributes) is mapped to a single y value (class label), a generalized Radon--Nikodym type of solution is proposed. Quantum--mechanics --like probability states psi2(x) are considered and "Cluster Centers", corresponding to the extremums of <ypsi2(x)>/<psi2(x)>, are found from generalized eigenvalues problem. The eigenvalues give possible y[i] outcomes and corresponding to them eigenvectors psi[i](x) define "Cluster Centers". The projection of a psi state, localized at given x to classify, on these eigenvectors define the probability of y[i] outcome, thus avoiding using a norm (L2 or other types), required for "quality criteria" in a typical Machine Learning technique. A coverage of each `Cluster Center" is calculated, what potentially allows to separate system properties (described by y[i] outcomes) and system testing conditions (described by C[i] coverage). As an example of such application y distribution estimator is proposed in a form of pairs (y[i],C[i]), that can be considered as Gauss quadratures generalization. This estimator allows to perform y probability distribution estimation in a strongly non--Gaussian case.