Leveraging Non-linear Dimension Reduction and Random Walk Co-occurrence for Node Embedding
- URL: http://arxiv.org/abs/2602.24069v1
- Date: Fri, 27 Feb 2026 14:58:49 GMT
- Title: Leveraging Non-linear Dimension Reduction and Random Walk Co-occurrence for Node Embedding
- Authors: Ryan DeWolfe,
- Abstract summary: COVE is an explainable high dimensional embedding that, when reduced to low dimension with UMAP, slightly increases performance on clustering and link prediction tasks.<n>We find that a COVE UMAP HDBSCAN pipeline performs similarly to the popular Louvain algorithm.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Leveraging non-linear dimension reduction techniques, we remove the low dimension constraint from node embedding and propose COVE, an explainable high dimensional embedding that, when reduced to low dimension with UMAP, slightly increases performance on clustering and link prediction tasks. The embedding is inspired by neural embedding methods that use co-occurrence on a random walk as an indication of similarity, and is closely related to a diffusion process. Extending on recent community detection benchmarks, we find that a COVE UMAP HDBSCAN pipeline performs similarly to the popular Louvain algorithm.
Related papers
- AGZO: Activation-Guided Zeroth-Order Optimization for LLM Fine-Tuning [8.698253005940503]
We propose Activation-Guided Zeroth-Order optimization (AGZO)<n>Unlike prior methods, AGZO extracts a compact, activation-informed subspace on the fly during the forward pass and restricts perturbations to this low-rank subspace.<n>AGZO consistently outperforms state-of-the-art ZO baselines and significantly narrows the performance gap with first-order fine-tuning.
arXiv Detail & Related papers (2026-01-24T02:28:15Z) - Learning functions through Diffusion Maps [0.6768558752130311]
We build on the Diffusion Maps framework under the manifold hypothesis.<n>We introduce a dimensionality reduction strategy based on the low-rank structure of the distance matrix.<n>Online updating mechanism enables efficient incorporation of new data.
arXiv Detail & Related papers (2025-09-03T22:57:33Z) - Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking [45.147301546565316]
This paper considers the problem of decentralized optimization on compact submanifolds.<n>We propose an algorithm where agents update variables using quantized variables.<n>To the best of our knowledge, this is the first algorithm to achieve an $mathcalO (1/K)$ convergence rate in the presence of quantization.
arXiv Detail & Related papers (2025-06-09T01:57:25Z) - Verification of Geometric Robustness of Neural Networks via Piecewise Linear Approximation and Lipschitz Optimisation [57.10353686244835]
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation.
The proposed method computes provably sound piecewise linear constraints for the pixel values by using sampling and linear approximations in combination with branch-and-bound Lipschitz.
We show that our proposed implementation resolves up to 32% more verification cases than present approaches.
arXiv Detail & Related papers (2024-08-23T15:02:09Z) - Anti-Collapse Loss for Deep Metric Learning Based on Coding Rate Metric [99.19559537966538]
DML aims to learn a discriminative high-dimensional embedding space for downstream tasks like classification, clustering, and retrieval.
To maintain the structure of embedding space and avoid feature collapse, we propose a novel loss function called Anti-Collapse Loss.
Comprehensive experiments on benchmark datasets demonstrate that our proposed method outperforms existing state-of-the-art methods.
arXiv Detail & Related papers (2024-07-03T13:44:20Z) - Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein [56.62376364594194]
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets.<n>In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem.<n>This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem.
arXiv Detail & Related papers (2024-02-03T19:00:19Z) - Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse
Problems [64.29491112653905]
We propose a novel and efficient diffusion sampling strategy that synergistically combines the diffusion sampling and Krylov subspace methods.
Specifically, we prove that if tangent space at a denoised sample by Tweedie's formula forms a Krylov subspace, then the CG with the denoised data ensures the data consistency update to remain in the tangent space.
Our proposed method achieves more than 80 times faster inference time than the previous state-of-the-art method.
arXiv Detail & Related papers (2023-03-10T07:42:49Z) - Communication-Efficient Distributed SGD with Compressed Sensing [24.33697801661053]
We consider large scale distributed optimization over a set of edge devices connected to a central server.
Inspired by recent advances in federated learning, we propose a distributed gradient descent (SGD) type algorithm that exploits the sparsity of the gradient, when possible, to reduce communication burden.
We conduct theoretical analysis on the convergence of our algorithm in the presence of noise perturbation incurred by the communication channels, and also conduct numerical experiments to corroborate its effectiveness.
arXiv Detail & Related papers (2021-12-15T02:10:45Z) - Improving Metric Dimensionality Reduction with Distributed Topology [68.8204255655161]
DIPOLE is a dimensionality-reduction post-processing step that corrects an initial embedding by minimizing a loss functional with both a local, metric term and a global, topological term.
We observe that DIPOLE outperforms popular methods like UMAP, t-SNE, and Isomap on a number of popular datasets.
arXiv Detail & Related papers (2021-06-14T17:19:44Z) - Divergence Regulated Encoder Network for Joint Dimensionality Reduction
and Classification [2.989889278970106]
We investigate performing joint dimensionality reduction and classification using a novel histogram neural network.
Motivated by a popular dimensionality reduction approach, t-Distributed Neighbor Embedding (t-SNE), our proposed method incorporates a classification loss computed on samples in a low-dimensional embedding space.
Our results show that the proposed approach maintains and/or improves classification performance and reveals characteristics of features produced by neural networks that may be helpful for other applications.
arXiv Detail & Related papers (2020-12-31T17:39:02Z) - Manifold Learning via Manifold Deflation [105.7418091051558]
dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data.
Many popular methods can fail dramatically, even on simple two-dimensional Manifolds.
This paper presents an embedding method for a novel, incremental tangent space estimator that incorporates global structure as coordinates.
Empirically, we show our algorithm recovers novel and interesting embeddings on real-world and synthetic datasets.
arXiv Detail & Related papers (2020-07-07T10:04:28Z) - IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method [64.15649345392822]
We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex.
Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method.
When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds.
arXiv Detail & Related papers (2020-06-11T18:49:06Z) - Effective Dimension Adaptive Sketching Methods for Faster Regularized
Least-Squares Optimization [56.05635751529922]
We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching.
We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform (SRHT)
arXiv Detail & Related papers (2020-06-10T15:00:09Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.