相关论文: Graph Metric Learning via Gershgorin Disc Alignmen…
The Gershgorin Circle Theorem is a well-known and efficient method for bounding the eigenvalues of a matrix in terms of its entries. If $A$ is a symmetric matrix, by writing $A = B + x{\bf 1}$, where ${\bf 1}$ is the matrix with unit…
An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…
Our goal is to efficiently compute low-dimensional latent coordinates for nodes in an input graph -- known as graph embedding -- for subsequent data processing such as clustering. Focusing on finite graphs that are interpreted as uniform…
This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified…
In this letter, we study distributed optimization, where a network of agents, abstracted as a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing approaches over directed graphs are…
This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Acquiring labels are often costly, whereas unlabeled data are usually easy to obtain in modern machine learning applications. Semi-supervised learning provides a principled machine learning framework to address such situations, and has been…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
A long-standing goal in deep learning has been to characterize the learning behavior of black-box models in a more interpretable manner. For graph neural networks (GNNs), considerable advances have been made in formalizing what functions…
We study distributed optimization to minimize a global objective that is a sum of smooth and strongly-convex local cost functions. Recently, several algorithms over undirected and directed graphs have been proposed that use a gradient…
We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…
We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation…
Product quantization (PQ) coupled with a space rotation, is widely used in modern approximate nearest neighbor (ANN) search systems to significantly compress the disk storage for embeddings and speed up the inner product computation.…
We develop simple and general techniques to obtain faster (near-linear time) static approximation algorithms, as well as efficient dynamic data structures, for four fundamental geometric optimization problems: minimum piercing set (MPS),…
We study faster algorithms for producing the minimum degree ordering used to speed up Gaussian elimination. This ordering is based on viewing the non-zero elements of a symmetric positive definite matrix as edges of an undirected graph, and…