On the Spectral Property of Kernel-Based Sensor Fusion Algorithms of High Dimensional Data

Xiucai Ding, Hau Tieng Wu

Research output: Contribution to journalArticlepeer-review


We apply local laws of random matrices and free probability theory to study the spectral properties of two kernel-based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), for two simultaneously recorded high dimensional datasets under the null hypothesis. The matrix of interest is the product of the kernel matrices associated with the databsets, which may not be diagonalizable in general. We prove that in the regime where dimensions of both random vectors are comparable to the sample size, if NCCA and AD are conducted using a smooth kernel function, then the first few nontrivial eigenvalues will converge to real deterministic values provided the datasets are independent Gaussian random vectors. Toward the claimed result, we also provide a convergence rate of eigenvalues of a kernel affinity matrix.

Original languageEnglish (US)
Article number9205615
Pages (from-to)640-670
Number of pages31
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 2021


  • alternating diffusion (AD)
  • eigenvalue rigidity
  • free multiplication of random matrices
  • kernel affinity matrices
  • local laws
  • nonparametric canonical correlation analysis (NCCA)
  • Sensor fusion

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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