title: Sparse kernel canonical correlation analysis for discovery of nonlinear interactions in high-dimensional data.
abstract: BACKGROUND
  Advance in high-throughput technologies in genomics, transcriptomics, and metabolomics has created demand for bioinformatics tools to integrate high-dimensional data from different sources. Canonical correlation analysis (CCA) is a statistical tool for finding linear associations between different types of information. Previous extensions of CCA used to capture nonlinear associations, such as kernel CCA, did not allow feature selection or capturing of multiple canonical components. Here we propose a novel method, two-stage kernel CCA (TSKCCA) to select appropriate kernels in the framework of multiple kernel learning.
  
  
  RESULTS
  TSKCCA first selects relevant kernels based on the HSIC criterion in the multiple kernel learning framework. Weights are then derived by non-negative matrix decomposition with L1 regularization. Using artificial datasets and nutrigenomic datasets, we show that TSKCCA can extract multiple, nonlinear associations among high-dimensional data and multiplicative interactions among variables.
  
  
  CONCLUSIONS
  TSKCCA can identify nonlinear associations among high-dimensional data more reliably than previous nonlinear CCA methods.
authors.affiliation: Graduate School of Informatics, Kyoto University, Kyoto, Japan. kosuke.yoshida@oist.jp.|Neural Computation Unit, Okinawa Institute of Science and Technology, Okinawa, Japan. kosuke.yoshida@oist.jp.
authors.forename: Kosuke
authors.identifier: http://orcid.org/0000-0001-8927-913X
authors.initials: K
authors.lastname: Yoshida
authors.affiliation: Graduate School of Information Science, Nara Institute of Science and Technology, Nara, Japan.
authors.forename: Junichiro
authors.initials: J
authors.lastname: Yoshimoto
authors.affiliation: Neural Computation Unit, Okinawa Institute of Science and Technology, Okinawa, Japan.
authors.forename: Kenji
authors.initials: K
authors.lastname: Doya
mesh_terms: D000465:Algorithms; D019295:Computational Biology; D030541:Databases, Genetic; D008954:Models, Biological; D017711:Nonlinear Dynamics
keywords: Hilbert-Schmidt independent criterion; Kernel canonical correlation analysis; L1 regularization