Quantum discriminative canonical correlation analysis
Abstract
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 of two parts: (i) mean-centering that subtracts the sample mean from the sample; (ii) solving the generalized eigenvalue problem. The cost of DCCA is expensive when dealing with a large number of high-dimensional samples. To solve this problem, here we propose a quantum DCCA algorithm. Specifically, we devise an efficient method to compute the mean of all samples, then use block-Hamiltonian simulation and quantum phase estimation to solve the generalized eigenvalue problem. Our algorithm achieves a polynomial speedup in the dimension of samples under certain conditions over its classical counterpart.
Keywords
Cite
@article{arxiv.2206.05526,
title = {Quantum discriminative canonical correlation analysis},
author = {Yong-Mei Li and Hai-Ling Liu and Shi-Jie Pan and Su-Juan Qin and Fei Gao and Qiao-Yan Wen},
journal= {arXiv preprint arXiv:2206.05526},
year = {2022}
}