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arXiv · 2206.05526

Quantum discriminative canonical correlation analysis

Yong-Mei Li·Hai-Ling Liu·Shi-Jie Pan·Su-Juan Qin·Fei Gao·Qiao-Yan Wen
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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.

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Yong-Mei Li, Hai-Ling Liu, Shi-Jie Pan, Su-Juan Qin, Fei Gao, Qiao-Yan Wen. 2022-06-11. Quantum discriminative canonical correlation analysis. https://arxiv.org/abs/2206.05526

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