Quantum discriminative canonical correlation analysis

Discriminative canonical correlation analysis (DCCA) is a powerful supervised feature extraction technique for two sets of multivariate data, which has wide applications in pattern recognition. DCCA consists parts: (i) mean-centering that subtracts the sample mean from and (ii) solving generalized eigenvalue problem. The cost expensive when dealing with large number high-dimensional samples. To solve this problem, here we propose quantum algorithm. Specifically, devise an efficient method to compute all samples then use block-Hamiltonian simulation phase estimation Our algorithm achieves polynomial speedup dimension under certain conditions over its classical counterpart.