arXiv Machine Learning
Jul 2
FastUMAP: Scalable Dimensionality Reduction via Bipartite Landmark Sampling
arXiv:2605. 11428v2 Announce Type: replace Abstract: Exploratory analysis of high-dimensional data rarely stops at a single embedding.
How smoothing the affinity matrix affects neighborhood preservation in t-SNE
arXiv:2608. 17190v1 Announce Type: new Abstract: Dimensionality reduction methods are instrumental to visualize high-dimensional data, and t-SNE stands as one of the most widely used methods due to its emphasis on local neighborhood preservation.
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arXiv Machine Learning
Jun 3
A Nonmonotone Gradient-Based Algorithm for Symmetric Nonnegative Matrix Factorization and Graph Clustering
arXiv:2606. 02887v1 Announce Type: new Abstract: Symmetric nonnegative matrix factorization (Symmetric NMF) approximates a matrix as $WW^T$ with nonnegative rectangular factor $W$.
arXiv Machine Learning
2d ago
High-dimensional nonparametric changepoint detection via low-rank degree-two density projection
arXiv:2608. 13922v1 Announce Type: new Abstract: Detecting distributional changes in high dimension is difficult when neither the pre-change nor post-change density is parametrically specified.
arXiv Machine Learning
Jul 28
Low-Rank Dependence Decomposition via Accelerated Symmetric Non-negative Matrix Factorization
arXiv:2607. 24518v1 Announce Type: new Abstract: Symmetric non-negative matrix factorization (SymNMF) recovers latent group structure from a dependence matrix, but its dense, quadratic-memory objective has confined prior work to moderate sizes.
arXiv AI
1d ago
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
Aug 6
Breaking the Periodicity Assumption: Robust Tensorial Multi-View Clustering via Graph-Spectral Low-Rank Learning
arXiv:2607. 25295v2 Announce Type: replace Abstract: Tensorial multi-view clustering (TMC) has achieved strong performance due to its ability to capture high-order correlations across multiple views.
arXiv Machine Learning
Jun 4
On Out-of-sample Embedding in UMAP
arXiv:2606. 04451v1 Announce Type: new Abstract: Neighbor embedding algorithms reveal correlations in high-dimensional data by constructing an equivalent graph representation in a lower-dimensional space.
arXiv Machine Learning
Jul 28
Why does Greedy Search produce Optimal Clustering Outcomes? A Fixed-Core Assignment Theory
arXiv:2607. 24237v1 Announce Type: new Abstract: Many existing clustering methods are designed based on a set-oriented definition---a cluster is a set of similar points---relying a point-to-point similarity function to find similar points.
arXiv Machine Learning
Jun 30
Geometrically Principled Randomized Optimization for Efficient LLM Training
arXiv:2510. 01878v2 Announce Type: replace Abstract: Low-rank gradient optimization for large language models is currently divided into two categories: structured methods that rigorously identify subspaces, and randomized approaches employed primarily for computational efficiency.
arXiv Machine Learning
Aug 6
Stable Density Ridges: Consistency and Convergence of Subspace Constrained Mean Shift
arXiv:2608. 05112v1 Announce Type: cross Abstract: The Subspace Constrained Mean Shift (SCMS) algorithm is a popular nonparametric method for extracting density ridges, which serve as a low-dimensional representation of high-dimensional data.
arXiv AI
Jul 7
Panorama: Fast-Track Nearest Neighbors
arXiv:2510. 00566v4 Announce Type: replace-cross Abstract: Approximate Nearest-Neighbor Search (ANNS) pipelines for high-dimensional neural embeddings spend the bulk of their query time in candidate verification, making it the primary bottleneck in the search process.
arXiv AI
Jun 4
Low-Rank Decay for Grokking in Scale-Invariant Transformers: A Spectral-Geometric View
arXiv:2606. 04405v1 Announce Type: cross Abstract: Modern Transformer architectures frequently employ normalization mechanisms such as RMSNorm and Query-Key Normalization, making parts of the model approximately scale-invariant with respect to weight magnitudes.