Matrix-Qubit Algorithm for Semantic Analysis of Probabilistic Data

This paper presents a method for semantic data analysis by complex-valued matrix decomposition. The method is based on the quantum model of contextual decision-making, according to which observable probabilities are generated by the qubit states, representing the subjective meaning of the contexts relative to the basis decision. In the simplest three-context case, one of these qubits is decomposed into a superposition of the remaining two, mathematically encoding semantic relations between the three contexts. For use in data analysis, this model is translated to the matrix form, in which the rows and columns correspond to the contexts and samples of the experiment. The observable real-valued data then emerge from a complex-valued amplitude matrix, decomposed to a product of a real basis matrix and complex-valued matrix of superposition coefficients. This decomposition reveals stable process-semantic relations between the considered contexts, not captured by other methods of analysis. As a result, the data are approximated with higher precision and fewer parameters than singular and nonnegative matrix decompositions, truncated to the same dimension. The model is experimentally tested in the descriptive and prognostic regimes. The result opens prospects for development of nature-like computational architectures on novel logical grounds.