Anchor PCA

• URL: http://arxiv.org/abs/2606.06233v1
• Date: Thu, 04 Jun 2026 14:39:09 GMT
• Title: Anchor PCA
• Abstract summary: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques.<n>We introduce Anchor PCA which trades off overall explained variance with agreement between the shared and domain-specific low-rank embeddings.<n>On simulated and real-world gas sensor data with temporal drift, we demonstrate that Anchor PCA recovers the maximally invariant subspace and yields embeddings that explain more variance on unseen domains.
• Score: 11.58762644470419
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques. We study PCA for data from multiple related domains. Since principal components generally differ across domains, one way to obtain a shared low-rank embedding is to perform PCA on the pooled data. However, this approach can focus on spurious directions that exhibit high variation in only a few domains. To find a robust embedding that still explains most variance in unseen but similar domains, we propose instead to focus on shared directions of variation. To this end, we introduce Anchor PCA which trades off overall explained variance with agreement between the shared and domain-specific low-rank embeddings. Anchor PCA amounts to PCA on a modified target matrix and thus can be solved efficiently. Moreover, we show that Anchor PCA recovers a maximal invariant subspace and admits a minimax reconstruction interpretation under bounded domain-specific covariance inflations. On simulated and real-world gas sensor data with temporal drift, we demonstrate, respectively, that Anchor PCA recovers the maximally invariant subspace and yields embeddings that explain more variance on unseen domains than the pooling baseline and a worst-case alternative. Taken together, these findings establish Anchor PCA as a promising approach to robust unsupervised dimension reduction from multi-domain data.

Related papers

• Shape Operator PCA: Curvature-Aware Projections for Geometric Machine Learning [52.452902154360565]
  SHOPCA (Shape Operator-based Principal Component Analysis) is a novel method for unsupervised metric learning and dimensionality reduction.<n>We evaluate SHOPCA on more than 50 real-world benchmark datasets.
  arXiv  Detail & Related papers  (2026-08-15T16:37:47Z)
• Curvature-Aware PCA with Geodesic Tangent Space Aggregation for Semi-Supervised Learning [52.452902154360565]
  GTSA-PCA is a geometric extension of Principal Component Analysis.<n>It integrates curvature awareness and geodesic consistency within a unified spectral framework.<n>Our results position GTSA-PCA as a principled bridge between statistical and geometric approaches to dimensionality reduction.
  arXiv  Detail & Related papers  (2026-04-20T20:36:36Z)
• The $φ$-PCA Framework: A Unified and Efficiency-Preserving Approach with Robust Variants [0.0]
  We introduce the $phi$-PCA framework which provides a unified formulation of robust and distributed PCA.<n>We show that the partition-aggregation principle underlying $phi$-PCA offers a general strategy for developing robust and efficiency-preserving methodologies.
  arXiv  Detail & Related papers  (2025-10-15T05:21:11Z)
• Fair PCA, One Component at a Time [2.5056643038238504]
  The Min-Max Fair PCA problem seeks a low-rank representation of multi-group data that is as balanced as possible across groups.<n>Existing approaches to this problem return a rank-$d$ fair subspace, but lack the fundamental containment property of standard PCA.<n>We define fair principal components as directions that minimize the maximum group-wise reconstruction error.<n>This approach preserves the containment property of standard PCA, and reduces to standard pca for data with a single group.
  arXiv  Detail & Related papers  (2025-03-27T14:47:27Z)
• Exploiting Aggregation and Segregation of Representations for Domain Adaptive Human Pose Estimation [50.31351006532924]
  Human pose estimation (HPE) has received increasing attention recently due to its wide application in motion analysis, virtual reality, healthcare, etc.<n>It suffers from the lack of labeled diverse real-world datasets due to the time- and labor-intensive annotation.<n>We introduce a novel framework that capitalizes on both representation aggregation and segregation for domain adaptive human pose estimation.
  arXiv  Detail & Related papers  (2024-12-29T17:59:45Z)
• Sparse PCA with Oracle Property [115.72363972222622]
  We propose a family of estimators based on the semidefinite relaxation of sparse PCA with novel regularizations. We prove that, another estimator within the family achieves a sharper statistical rate of convergence than the standard semidefinite relaxation of sparse PCA.
  arXiv  Detail & Related papers  (2023-12-28T02:52:54Z)
• Empirical Bayes Covariance Decomposition, and a solution to the Multiple Tuning Problem in Sparse PCA [2.5382095320488673]
  Sparse Principal Components Analysis (PCA) has been proposed as a way to improve both interpretability and reliability of PCA. We present a solution to the "multiple tuning problem" using Empirical Bayes methods.
  arXiv  Detail & Related papers  (2023-12-06T04:00:42Z)
• Off-Policy Evaluation for Large Action Spaces via Policy Convolution [60.6953713877886]
  Policy Convolution family of estimators uses latent structure within actions to strategically convolve the logging and target policies. Experiments on synthetic and benchmark datasets demonstrate remarkable mean squared error (MSE) improvements when using PC.
  arXiv  Detail & Related papers  (2023-10-24T01:00:01Z)
• Learning Feature Decomposition for Domain Adaptive Monocular Depth Estimation [51.15061013818216]
  Supervised approaches have led to great success with the advance of deep learning, but they rely on large quantities of ground-truth depth annotations. Unsupervised domain adaptation (UDA) transfers knowledge from labeled source data to unlabeled target data, so as to relax the constraint of supervised learning. We propose a novel UDA method for MDE, referred to as Learning Feature Decomposition for Adaptation (LFDA), which learns to decompose the feature space into content and style components.
  arXiv  Detail & Related papers  (2022-07-30T08:05:35Z)
• Sparse PCA on fixed-rank matrices [0.05076419064097732]
  We show that, if the rank of the covariance matrix is a fixed value, then there is an algorithm that solves sparse PCA to global optimality. We also prove a similar result for the version of sparse PCA which requires the principal components to have disjoint supports.
  arXiv  Detail & Related papers  (2022-01-07T15:05:32Z)
• FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysis [12.91948651812873]
  Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. This paper proposes a distributed PCA algorithm called FAST-PCA (Fast and exAct diSTributed PCA)
  arXiv  Detail & Related papers  (2021-08-27T16:10:59Z)
• Adaptively-Accumulated Knowledge Transfer for Partial Domain Adaptation [66.74638960925854]
  Partial domain adaptation (PDA) deals with a realistic and challenging problem when the source domain label space substitutes the target domain. We propose an Adaptively-Accumulated Knowledge Transfer framework (A$2$KT) to align the relevant categories across two domains.
  arXiv  Detail & Related papers  (2020-08-27T00:53:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.