Papers › Personalized PCA: Decoupling Shared and Unique Features
Personalized PCA: Decoupling Shared and Unique Features
Naichen Shi, Raed Al Kontar
In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining the unique features of each source. To this end, we propose personalized PCA (PerPCA), which uses mutually orthogonal global and local principal components to encode both unique and shared features. We show that, under mild conditions, both unique and shared features can be identified and recovered by a constrained optimization problem, even if the covariance matrices are immensely different. Also, we design a fully federated algorithm inspired by distributed Stiefel gradient descent to solve the problem. The algorithm introduces a new group of operations called generalized retractions to handle orthogonality constraints, and only requires global PCs to be shared across sources. We prove the linear convergence of the algorithm under suitable assumptions. Comprehensive numerical experiments highlight PerPCA's superior performance in feature extraction and prediction from heterogeneous datasets. As a systematic approach to decouple shared and unique features from heterogeneous datasets, PerPCA finds applications in several tasks, including video segmentation, topic extraction, and feature clustering.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections