arXiv:2610.33177v1 Announce Type: new Abstract: The Gaussian Mixture Model (abbrv. GMM) is a classic generative model for clustered data, for which spectral clustering based on dimension reduction vi...
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...
arXiv:2608. 15313v1 Announce Type: cross Abstract: In this paper, we propose SHOPCA (Shape Operator-based Principal Component Analysis), a novel method for unsupervised metric learning and dimensionality reduction that incorporates differential geometric information into the covariance structure of classical PCA.
arXiv:2607. 21039v1 Announce Type: new Abstract: Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning.
arXiv:2608. 08704v1 Announce Type: cross Abstract: Kernel spectral clustering with a single bandwidth can be inadequate for data exhibiting multiple characteristic pairwise-distance scales, a problem particularly prevalent in the high-dimensional regime.
The paper investigates Partial Least Squares (PLS) in high-dimensional settings, focusing on a model where two data matrices share a low-rank latent structure plus individual-specific components. By analyzing the singular vectors of the cross‑covariance matrix with random matrix theory, the authors derive asymptotic characterizations of how well the estimated latent directions align with the true ones. They show that the PLS variant based on Singular Value Decomposition (PLS‑SVD) outperforms separate principal component analysis in detecting the common latent subspace, while also identifying regimes where PLS‑SVD behaves counter‑intuitively or reaches fundamental limits.
arXiv:2606. 05230v1 Announce Type: cross Abstract: Selecting a clustering algorithm and its hyperparameters without labels is a common difficulty in engineering machine learning pipelines that work with unsupervised analysis of sensor, image, or process data.
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.
arXiv:2610.07284v1 Announce Type: cross Abstract: Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising,...
Phase-Consistent Magnetic Spectral Learning for Multi-View Clustering proposes a new unsupervised method that uses a complex-valued magnetic affinity to capture both magnitude and phase information across multiple data views. By deriving a confidence-directed cross-view flow from anchor assignments and combining it with a nonnegative magnitude backbone, the approach constructs a Hermitian magnetic Laplacian that yields a stable shared spectral signal for representation learning and clustering. Experiments on ten public benchmarks show the method outperforms or matches leading MVC baselines on most dataset-metric combinations.
arXiv:2407. 01718v2 Announce Type: replace-cross Abstract: Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis.
arXiv:2606. 06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques.