MFPCA: Multiscale Functional Principal Component Analysis


  • Zhenhua Lin University of California, Davis
  • Hongtu Zhu University of North Carolina, Chapel Hill



We consider the problem of performing dimension reduction on heteroscedastic functional data where the variance is in different scales over entire domain. The aim of this paper is to propose a novel multiscale functional principal component analysis (MFPCA) approach to address such heteroscedastic issue. The key ideas of MFPCA are to partition the whole domain into several subdomains according to the scale of variance, and then to conduct the usual functional principal component analysis (FPCA) on each individual subdomain. Both theoretically and numerically, we show that MFPCA can capture features on areas of low variance without estimating high-order principal components, leading to overall improvement of performance on dimension reduction for heteroscedastic functional data. In contrast, traditional FPCA prioritizes optimizing performance on the subdomain of larger data variance and requires a practically prohibitive number of components to characterize data in the region bearing relatively small variance.




How to Cite

Lin, Z., & Zhu, H. (2019). MFPCA: Multiscale Functional Principal Component Analysis. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01), 4320-4327.



AAAI Technical Track: Machine Learning