Localized Functional Principal Component Analysis
Kehui Chen,Jing Lei +1 more
TL;DR: It is proved that the proposed LFPCA converges to the original functional principal component analysis (FPCA) when the tuning parameters are chosen appropriately and can almost perfectly recover the true eigenfunctions and significantly improve the estimation accuracy when the eigenFunctions are truly supported on some subdomains.
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Abstract: We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex optimization problem through a novel deflated Fantope localization method and is implemented through an efficient algorithm to obtain the global optimum. We prove that the proposed LFPCA converges to the original functional principal component analysis (FPCA) when the tuning parameters are chosen appropriately. Simulation shows that the proposed LFPCA with tuning parameters chosen by cross-validation can almost perfectly recover the true eigenfunctions and significantly improve the estimation accuracy when the eigenfunctions are truly supported on some subdomains. In the scenario that the original eigenfunctions are not localized, the proposed LFPCA also serves as a nice tool in finding orthogonal basis functions that balance between interpretability and the capability of exp...
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Citations
Weakly correlated profile monitoring based on sparse multi-channel functional principal component analysis
Chen Zhang,Hao Yan,Seungho Lee,Jianjun Shi +3 more
- 08 Jun 2018
TL;DR: This work proposes a novel Sparse Multi-channel Functional Principal Component Analysis (SMFPCA) to model multi-channel profiles and proposes an efficient convergence-guaranteed optimization algorithm to solve SMF PCA in real time based on the block coordinate descent algorithm.
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Parametric functional principal component analysis.
TL;DR: This article proposes a parametric approach to estimate the top FPCs to enhance their interpretability for users and shows that the proposed parametric FPCA is more robust when outlier curves exist.
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Fast exact conformalization of the lasso using piecewise linear homotopy
TL;DR: In this paper, the authors developed an exact and computationally efficient conformalization of the lasso and elastic net, which makes use of a piecewise linear homotopy of the Lasso solution under perturbation of a single input sample point.
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A test of weak separability for multi-way functional data, with application to brain connectivity studies
Brian Lynch,Kehui Chen +1 more
TL;DR: In this article, a concept of weak separability is introduced to model multi-way functional data where double or multiple indices are involved, and the weakly separable structure supports the use of factorization methods that decompose the signal into its spatial and temporal components.
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Hierarchical sparse functional principal component analysis for multistage multivariate profile data
Kai Wang,Fugee Tsung +1 more
- 22 Apr 2020
TL;DR: This article proposes integrating Multivariate Functional Principal Component Analysis with a three-level structured sparsity idea to develop a novel Hierarchical Sparse MFPCA (HSMFPCA), in which the stage-wise, profile-wise and element-wise sparsity are jointly investigated to clearly identify the informative stages and variables in each eigenvector.
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