The paper compares two popular data‑integration techniques—Stack‑SVD, which concatenates datasets before performing singular value decomposition, and SVD‑Stack, which first decomposes each dataset separately and then aggregates the leading singular vectors. By deriving exact asymptotic performance expressions and phase transitions in a proportional regime, the authors show that neither method uniformly dominates the other when unweighted, but optimally weighted Stack‑SVD outperforms optimally weighted SVD‑Stack when the low‑rank signal is fully shared. They also demonstrate that SVD‑Stack can excel with partially shared components and provide practical algorithms for estimating optimal weights, supported by simulations and genomic experiments.
By Tavor Z. Baharav, Phillip B. Nicol, Rafael A. Irizarry, Rong Ma
arXiv:2609.14815v1 Announce Type: cross
Abstract: This paper introduces a novel framework for Regularized Multivariate Functional Principal Component Analysis (ReMFPCA) via Functional Singular Value...
By Yue Zhao, Hossein Haghbin, Rebecca Sanders, Mehdi Maadooliat
arXiv:2605.15240v2 Announce Type: replace-cross
Abstract: This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalizatio...
By Yang Liu, Ernest Fokoue, Richard Lange, Daniel Krutz
The paper introduces robust multi-task procedures for principal component analysis that leverage similarity across tasks to enhance eigenspace estimation while remaining resilient to outlier tasks. It establishes non-asymptotic convergence rates and demonstrates that the methods achieve minimax optimal performance across various regimes. One procedure, based on matrix-depth, attains optimal error dependence on the proportion of outlier tasks, addressing a key challenge in robust multi-task learning.
By Dali Liu, Haolei Weng
SuperPCA is a new algorithm for high‑dimensional principal component analysis that exploits an approximate eigenspace of the sample covariance matrix. The authors show that the subspace spanned by several leading eigenvectors contains useful signal information long before individual eigenvectors converge, and they derive posteriori bounds on the angle between this subspace and the true signal subspace. By using only a small number of subsampled coordinates, SuperPCA can achieve up to a ten‑fold improvement in accuracy over classical PCA while reducing data acquisition costs, especially when the signals are approximately sparse.
By Irina-Beatrice Haas, Maike Meier, Yuji Nakatsukasa, Taejun Park
The paper introduces a new dimensionality reduction technique that enhances nearest‑neighbour relationships to estimate high‑information projections. It constructs a matrix encoding local covariance via nearest‑neighbour pairs and shows that, under standard regularity conditions, this matrix consistently estimates the Density Information Matrix (DIM), a non‑parametric analogue of the Fisher Information Matrix. The authors also demonstrate the method’s practical usefulness for clustering and outlier detection.
By David P. Hofmeyr
arXiv:2606. 11570v1 Announce Type: cross Abstract: We propose a spectral-based, unsupervised representation learning framework to derive low-dimensional embeddings for clinical concepts and patients in rare disease cohorts from electronic health records, where data are high-dimensional but sample sizes are limited.
By Feiqing Huang, Zongqi Xia, Rong Ma, Tianxi Cai
arXiv:2606. 06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques.
By Benedikt Seiter, Anya Fries, Julius von K\"ugelgen, Jonas Peters
arXiv:2505. 19925v2 Announce Type: replace-cross Abstract: The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers.
By Fabio Centofanti, Mia Hubert, Peter J. Rousseeuw
The paper introduces two randomized approaches to accelerate spectral co‑clustering of word‑document matrices: one based on randomized SVD via random projection, and another combining partial SVD with element‑wise random sampling. Experiments on real and synthetic data show both methods cut runtime compared to full SVD, with the projection technique offering more consistent performance across varied sparsity levels, while the sampling method excels on denser matrices. The study highlights that the choice of approximation should align with the data’s structural properties.
By Fateme Mazdarani, Carlos Toxtli
arXiv:2304.06522v3 Announce Type: replace-cross
Abstract: Signal extraction is difficult when the number of variables $N$ is much larger than the number of observations $M$. We address this problem u...
By Yoh-ichi Mototake, Y-h. Taguchi
arXiv:2412. 07041v4 Announce Type: replace-cross Abstract: Recovering incomplete multidimensional tensor-structured data is a fundamental task in many real-world applications.
By Mengying Lei, Lijun Sun