Quantum-probabilistic SVD: complex-valued factorization of matrix data

The paper reports a method for compressed representation of matrix data on the principles quantum theory. is formalized as complex-valued factorization based standard singular value decomposition. developed approach establishes bridge between methods semantic analysis and models cognition decision. According to theory, real-valued observable quantities are generated by wavefunctions being vectors in multidimensional Hilbert-space. Wavefunctions defined superpositions basis encoding composition factors. Basis found decomposition initial transformed amplitude form. Phase-dependent superposition amplitudes optimize approximation source data. resulting model represents observed from small number superposed with coefficients. tested random matrices sizes 3 × 12 dimensionality latent Hilbert-space 2 4. best achieved factors normalized interpreted generating In terms fitness, surpasses truncated SVD same dimensionality. mean advantage over considered range parameters 22 %. permits cognitive interpretation accord existing can be integrated algorithms including natural language processing. these tasks, obtained improvement translates increased precision similarity measures, principal component analysis, classification, document ranking methods. Integration decision expected boost artificial intelligence machine learning improving imitation thinking.