On Machine Learning Knowledge Representation In The Form Of Partially Unitary Operator. Knowledge Generalizing Operator

A new form of ML knowledge representation with high generalization power is developed and implemented numerically. Initial mathitIN attributes and mathitOUT class label are transformed into the corresponding Hilbert spaces by considering localized wavefunctions. A partially unitary operator optimally converting a state from mathitIN Hilbert space into mathitOUT Hilbert space is then built from an optimization problem of transferring maximal possible probability from mathitIN to mathitOUT, this leads to the formulation of a new algebraic problem. Constructed Knowledge Generalizing Operator U can be considered as a mathitIN to mathitOUT quantum channel; it is a partially unitary rectangular matrix of the dimension dim(mathitOUT) × dim(mathitIN) transforming operators as A^mathitOUT=U A^mathitIN Udagger. Whereas only operator U projections squared are observable leftlanglemathitOUT|U|mathitINrightrangle2 (probabilities), the fundamental equation is formulated for the operator U itself. This is the reason of high generalizing power of the approach; the situation is the same as for the Schr"odinger equation: we can only measure psi2, but the equation is written for psi itself.