Features Extraction Across Multi-Source Heterogeneous Data
Abstract
High-dimensional data from multiple sources often combine shared structure with source-specific variation. We study heterogeneous principal component analysis, which seeks to recover common and private principal subspaces when their dimensions are unknown. {We propose \emph{Feature Extraction (FE)}, a novel data-driven framework with two steps. First, the Eigenvector-based Spike-Count (ESC) estimator determines the number of principal components (PC) in each source using only sample eigenvector information, rather than eigenvalue-based criteria. Second, FE identifies the locations of common features by comparing bias-corrected inner products between sample eigenvectors across sources. These matches yield estimates of the common and source-specific subspaces without iterative optimization. We establish the consistency of our estimators under a spiked covariance model in a high-dimensional regime where the dimension and sample size grow proportionally. Simulations and applications to federated image data and U.S. housing prices demonstrate the performance of FE in rank recovery, subspace estimation, and data reconstruction.} Code is available at https://github.com/liwenbo-research/HeterogeneousPCA
Related
- An Explainable Multi-Criteria Decision-Making Framework for Evaluating Malware Detection Models Across Heterogeneous Datasets
- Diagonal Multi-omics Integration of Heterogeneous Datasets
- Dynamic Return Spillovers and Heterogeneous Responses Across Energy Equity Markets Under Demand–Supply Risks: A Mixed-Methods Analysis Using Chinese News Texts
- Data-Adaptive Multi-Bin Rarefying for Alpha Diversity Association Analysis under Heterogeneous Library Sizes
- Evaluating multi-season occupancy models with autocorrelation fitted to heterogeneous datasets
BibTeX
@misc{li2026features,
title = {{Features Extraction Across Multi-Source Heterogeneous Data}},
author = {Wenbo Li and Xianli Zeng and Weiming Li and Zeng Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03001},
eprint = {2611.03001},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03001},
}
RIS
TY - UNPB
TI - Features Extraction Across Multi-Source Heterogeneous Data
AU - Wenbo Li
AU - Xianli Zeng
AU - Weiming Li
AU - Zeng Li
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03001
UR - https://arxiv.org/abs/2611.03001
AB - High-dimensional data from multiple sources often combine shared structure with source-specific variation. We study heterogeneous principal component analysis, which seeks to recover common and private principal subspaces when their dimensions are unknown. {We propose \emph{Feature Extraction (FE)}, a novel data-driven framework with two steps. First, the Eigenvector-based Spike-Count (ESC) estimator determines the number of principal components (PC) in each source using only sample eigenvector information, rather than eigenvalue-based criteria. Second, FE identifies the locations of common features by comparing bias-corrected inner products between sample eigenvectors across sources. These matches yield estimates of the common and source-specific subspaces without iterative optimization. We establish the consistency of our estimators under a spiked covariance model in a high-dimensional regime where the dimension and sample size grow proportionally. Simulations and applications to federated image data and U.S. housing prices demonstrate the performance of FE in rank recovery, subspace estimation, and data reconstruction.} Code is available at https://github.com/liwenbo-research/HeterogeneousPCA
ER -