arXiv Machine Learning
Eigenspace-Based Clustering for Personalized System Identification
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Kernelised covariance matrices, dimension reduction and imbalanced spectral clustering
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 Machine Learning
Sep 22
On Kernel Eigen-alignments of KRR: Reconstruction and Generalization
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 AI
Aug 18
Shape Operator PCA: Curvature-Aware Projections for Geometric Machine Learning
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 Machine Learning
Jul 24
Regularized Optimization on Grassmann Manifold: Theory, Algorithm and Applications
arXiv:2607. 21039v1 Announce Type: new Abstract: Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning.
arXiv Machine Learning
Aug 11
Multi-kernel spectral clustering: Entrywise eigenvector perturbation bounds and exact recovery
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.
arXiv Machine Learning
Sep 30
High-Dimensional Partial Least Squares: Spectral Analysis and Fundamental Limitations
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.