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This paper is concerned with developing an efficient numerical algorithm for fast implementation of the sparse grid method for computing the $d$-dimensional integral of a given function. The new algorithm, called the MDI-SG ({\em multilevel…

Unsupervised learning of time series data, also known as temporal clustering, is a challenging problem in machine learning. Here we propose a novel algorithm, Deep Temporal Clustering (DTC), to naturally integrate dimensionality reduction…

Graph clustering is a fundamental and challenging task in the field of graph mining where the objective is to group the nodes into clusters taking into consideration the topology of the graph. It has several applications in diverse domains…

We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…

In this paper, I will introduce a fast and novel clustering algorithm based on Gaussian distribution and it can guarantee the separation of each cluster centroid as a given parameter, $d_s$. The worst run time complexity of this algorithm…

This paper presents a comprehensive comparative analysis of prominent clustering algorithms K-means, DBSCAN, and Spectral Clustering on high-dimensional datasets. We introduce a novel evaluation framework that assesses clustering…

FISHDBC is a flexible, incremental, scalable, and hierarchical density-based clustering algorithm. It is flexible because it empowers users to work on arbitrary data, skipping the feature extraction step that usually transforms raw data in…

Efficient layout of large-scale graphs remains a challenging problem: the force-directed and dimensionality reduction-based methods suffer from high overhead for graph distance and gradient computation. In this paper, we present a new graph…

In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often…

3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…

This work addresses the challenge of using a deep learning model to prune graphs and the ability of this method to integrate explainability into spatio-temporal problems through a new approach. Instead of applying explainability to the…

Modern cloud databases present scaling as a binary decision: scale-out by adding nodes or scale-up by increasing per-node resources. This one-dimensional view is limiting because database performance, cost, and coordination overhead emerge…

Distance measuring is a very important task in digital geometry and digital image processing. Due to our natural approach to geometry we think of the set of points that are equally far from a given point as a Euclidean circle. Using the…

We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…

Timestamped relational datasets consisting of records between pairs of entities are ubiquitous in data and network science. For applications like peer-to-peer communication, email, social network interactions, and computer network security,…

K-means plays a vital role in data mining and is the simplest and most widely used algorithm under the Euclidean Minimum Sum-of-Squares Clustering (MSSC) model. However, its performance drastically drops when applied to vast amounts of…

Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that…

In this paper, we propose cuSLINK, a novel and state-of-the-art reformulation of the SLINK algorithm on the GPU which requires only $O(Nk)$ space and uses a parameter $k$ to trade off space and time. We also propose a set of novel and…

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…