Quantum-inspired canonical correlation analysis for exponentially large dimensional data

Canonical correlation analysis (CCA) is a technique to find statistical dependencies between pair of multivariate data. However, its application high dimensional data limited due the resulting time complexity. While conventional CCA algorithm requires polynomial time, we have developed an that approximates with computational proportional logarithm input dimensionality using quantum-inspired computation. The efficiency and approximation performance proposed (qiCCA) are experimentally demonstrated. Furthermore, fast computation qiCCA allows us directly apply even after nonlinearly mapping raw into very spaces. Experiments performed benchmark dataset demonstrated that, by spaces second-order monomials, extracted more correlations than linear was comparable deep kernel CCA. These results suggest considerably useful has potential unlock new field in which exponentially large can be analyzed.