Related papers: Analytical and statistical properties of local dep…

We give an FPTAS for computing the number of matchings of size $k$ in a graph $G$ of maximum degree $\Delta$ on $n$ vertices, for all $k \le (1-\delta)m^*(G)$, where $\delta>0$ is fixed and $m^*(G)$ is the matching number of $G$, and an…

Algorithms for clustering points in metric spaces is a long-studied area of research. Clustering has seen a multitude of work both theoretically, in understanding the approximation guarantees possible for many objective functions such as…

We introduce an extension of the partitioned local depth (PaLD) algorithm that is adapted to online applications such as semi-supervised prediction. PaLD is best known for unsupervised, parameter-free clustering, but its robustness is based…

This paper presents fault-tolerant asynchronous Stochastic Gradient Descent (SGD) algorithms. SGD is widely used for approximating the minimum of a cost function $Q$, as a core part of optimization and learning algorithms. Our algorithms…

Stochastic approximation (SA) and stochastic gradient descent (SGD) algorithms are work-horses for modern machine learning algorithms. Their constant stepsize variants are preferred in practice due to fast convergence behavior. However,…

The applicability of agglomerative clustering, for inferring both hierarchical and flat clustering, is limited by its scalability. Existing scalable hierarchical clustering methods sacrifice quality for speed and often lead to over-merging…

We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…

Using gradient descent (GD) with fixed or decaying step-size is a standard practice in unconstrained optimization problems. However, when the loss function is only locally convex, such a step-size schedule artificially slows GD down as it…

Clustering is an essential task to unsupervised learning. It tries to automatically separate instances into coherent subsets. As one of the most well-known clustering algorithms, k-means assigns sample points at the boundary to a unique…

Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…

Random partition distribution is a crucial tool for model-based clustering. This study advances the field of random partition in the context of functional spatial data, focusing on the challenges posed by hourly population data across…

Stochastic Gradient Langevin Dynamics (SGLD) has emerged as a key MCMC algorithm for Bayesian learning from large scale datasets. While SGLD with decreasing step sizes converges weakly to the posterior distribution, the algorithm is often…

We consider two parametrized random digraph families, namely, proportional-edge and central similarity proximity catch digraphs (PCDs) and compare the performance of these two PCD families in testing spatial point patterns. These PCD…

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…

We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form…

We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…

Local clustering aims to find a compact cluster near the given starting instances. This work focuses on graph local clustering, which has broad applications beyond graphs because of the internal connectivities within various modalities.…

With rapidly increasing data, clustering algorithms are important tools for data analytics in modern research. They have been successfully applied to a wide range of domains; for instance, bioinformatics, speech recognition, and financial…

The unadjusted Langevin algorithm is commonly used to sample probability distributions in extremely high-dimensional settings. However, existing analyses of the algorithm for strongly log-concave distributions suggest that, as the dimension…

In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution…