A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New definition of naturally reductive Finsler manifolds using geodesic graphs.
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity measure used for graph sparsification. This choice is motivated by the observation…
Paper introduces a taxonomy of reduction matrices for more efficient graph coarsening.
New method reduces spatial graphs while preserving their topological features.
Graph Signal Processing (GSP) is a promising framework to analyze multi-dimensional neuroimaging datasets, while taking into account both the spatial and functional dependencies between brain signals. In the present work, we apply dimensionality reduction techniques based on graph representations of the brain to decode…
Unified framework for graph coarsening using node features and graph matrices.
We study Riemannian nilmanifolds associated with graphs. We prove that such a nilmanifold is geodesic orbit if and only if it is naturally reductive if and only if its defining graph is the disjoint union of complete graphs and the left-invariant metric is generated by a certain naturally defined inner product.
Eigen-GNN enhances GNNs by preserving graph structures.
We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie algebra of rank at most 2, gives rise to a confluent system of reduction rules of…
New algorithms for clustering and dimension reduction using relative von Neumann entropy.
In this era of data deluge, many signal processing and machine learning tasks are faced with high-dimensional datasets, including images, videos, as well as time series generated from social, commercial and brain network interactions. Their efficient processing calls for dimensionality reduction techniques capable of p…
Introduces a probabilistic framework for dimension reduction methods.
Survey of Laplacian-based methods for data dimensionality reduction and embedding.
Paper interprets UMAP and t-SNE as probabilistic MAP inference.
Study of Betti numbers in prodsimplicial complexes for directed graphs, focusing on DNA recombination.
A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated as graph filtering operations, that enable the exploitation of data node connec…
Combines PCA and message passing for better graph node embeddings.
Graph regularized autoencoder improves anomaly detection performance.
The lattice cohomology of a plumbed 3--manifold associated with a connected negative definite plumbing graph is an important tool in the study of topological properties of , and in the comparison of the topological properties with analytic ones when is realized as complex analytic singularity link. By defini…
New findings on QHD smoothing for graphs with 3 or 4 large nodes.
Proposes a faster Isomap algorithm by reducing eigenvalue decomposition complexity.
AB-SAGA optimizes distributed optimization over directed graphs using variance reduction and stochastic weights.
Push-SAGA is a decentralized algorithm for directed graphs that converges linearly.
Improved EXACT strategy reduces GNN memory consumption and runtime.
This paper improves GNN robustness by aligning feature and adjacency matrix learning.
RP-GFRFT unifies fractional order and rotation control for graph signals.
We give a description of local and global moves on a class of locally planar trivalent graphs and we show that it contains -Scale calculus, therefore in particular untyped lambda calculus. Surprisingly, the beta reduction rule comes from a local "sewing" transformation of trivalent locally planar graphs.
A novel hypergraph partitioning method using tensor eigenvalue decomposition captures super-dyadic interactions.
Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionali…
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that produce the largest reduction in empirical conditional entropy; it is greedy in the se…
LNPE enhances local connections in embeddings using extended neighbor propagation.
This paper explains spectral clustering and its equivalence to PCA, breaking it into fully connected and multi-connected cases.
In online advertising, display ads are increasingly being placed based on real-time auctions where the advertiser who wins gets to serve the ad. This is called real-time bidding (RTB). In RTB, auctions have very tight time constraints on the order of 100ms. Therefore mechanisms for bidding intelligently such as clickth…
FEALM learns features for better nonlinear DR of hidden patterns.
The paper shows how to recover true node positions from a graph or similarity matrix.
We prove the first nontrivial worst-case lower bounds for two closely related problems. First, degree-1 reductions, series-parallel reductions, and Y transformations are required in the worst case to reduce an -vertex plane graph to a single vertex or edge. The lower bound is achieved by any planar g…
New GCNs solve graph embedding problems efficiently and interpretably.
Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised learning on graph-based datasets. For sparse graphs, linear and polynomial filter functions have yielded impressive results. For large non-sparse graphs, however, network training and evaluation becomes prohibitively expensive. B…
Structural and topological information play a key role in modeling flow and transport through fractured rock in the subsurface. Discrete fracture network (DFN) computational suites such as dfnWorks are designed to simulate flow and transport in such porous media. Flow and transport calculations reveal that a small back…
Graph embeddings, a class of dimensionality reduction techniques designed for relational data, have proven useful in exploring and modeling network structure. Most dimensionality reduction methods allow out-of-sample extensions, by which an embedding can be applied to observations not present in the training set. Appli…
Paper introduces a noise-robust classification method using hypergraph neural networks.
Graph neural network optimizes energy-efficient precoding for massive MIMO systems.
New algorithm for training GNNs with learned weights.
We introduce a nonlinear method for directly embedding large, sparse, stochastic graphs into low-dimensional spaces, without requiring vertex features to reside in, or be transformed into, a metric space. Graph data and models are prevalent in real-world applications. Direct graph embedding is fundamental to many graph…
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the jo…
A new method reduces complexity and uncertainty in neural networks.
For any collection of graphs we find the minimal dimension d such that the product of these graphs is embeddable into the d-dimensional Euclidean space. In particular, we prove that the n-th powers of the Kuratowsky graphs are not embeddable into the 2n-dimensional Euclidean space. This is a solution of a problem of Me…
We focus in this paper on dataset reduction techniques for use in k-nearest neighbor classification. In such a context, feature and prototype selections have always been independently treated by the standard storage reduction algorithms. While this certifying is theoretically justified by the fact that each subproblem …