Randomized sketches for kernel CCA. (July 2020)

• Record Type: Journal Article
• Authors: Lian, Heng; Zhang, Fode; Lu, Wenqi
• Is Part Of: Neural networks. Volume 127(2020)
• Page Start: 29
• Page End: 37
• Publication Date: 2020-07
• Subjects: Canonical correlation analysis -- Covariance/cross-covariance operator -- Kernel method -- Random projection; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2020.04.006
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: Kernel canonical correlation analysis (KCCA) is a popular tool as a nonlinear extension of canonical correlation analysis. Consistency and optimal convergence rate have been established in the literature. However, the time complexity of KCCA scales as O ( n 3 ) and is thus prohibitive when n is large. We propose an m -dimensional randomized sketches approach for KCCA with m < < n, based on the recent work on randomized sketches for kernel ridge regression (KRR). Technically we establish our theoretical results relying on an interesting connection between KCCA and KRR by utilizing a novel "duality tracking" device that alternates between the infinite-dimensional operator-theory-based view of KCCA and the finite-dimensional kernel-matrix-based view.