A new arXiv preprint examines how Gaussian kernel similarity measures can be computed more efficiently for large sets of points. The authors build on Random Fourier Features to construct low-dimensional embeddings tailored to data lying on manifolds. The work targets applications such as kernel PCA and spectral clustering, where pairwise kernel evaluations are typically costly.
A new arXiv preprint introduces a rotation-based method for tracking subspaces when applying kernel principal component analysis to data streams. The approach targets robustness against data drift, where the underlying distribution of incoming data shifts over time. It aims to keep dimensionality reduction and feature extraction reliable in settings where datasets are not static.
Researchers introduce LORE (Low Rank Ordinal Embedding), a scalable method for recovering the structure of subjective perceptual spaces such as taste, smell, and aesthetics. Unlike prior approaches, it estimates the intrinsic dimensionality and the relative similarity relationships of items at the same time from ordinal comparisons. The work targets settings where only ranked or comparative judgments, rather than absolute numeric ratings, are available.
The paper applies a deep autoencoder to estimate the intrinsic dimensionality of high-dimensional trajectories from the Fermi-Pasta-Ulam-Tsingou beta model with 32 oscillators. The dataset spans roughly 4 million data points, and the authors take a nonlinear approach to characterize the underlying low-dimensional structure of the dynamics.
A new arXiv paper presents a framework for regularized multivariate functional principal component analysis built on a functional singular value decomposition. The approach generalizes existing MFPCA methods by adding dual penalization, which regularizes the decomposition in two ways. The work targets dimension reduction and analysis of multivariate functional data.
Researchers introduce MAPLE, a nonlinear dimensionality reduction technique that builds on UMAP by adding a self-supervised learning component to better capture manifold structure. The method aims to encode low-dimensional manifold geometry more efficiently, supporting visual analysis tasks. The work is described in an arXiv preprint in machine learning.