Related papers: Popcorn: Accelerating Kernel K-means on GPUs throu…

Reducing the computational cost of running large scale neural networks using sparsity has attracted great attention in the deep learning community. While much success has been achieved in reducing FLOP and parameter counts while maintaining…

The K-means algorithm is arguably the most popular data clustering method, commonly applied to processed datasets in some "feature spaces", as is in spectral clustering. Highly sensitive to initializations, however, K-means encounters a…

Kernel machines often yield superior predictive performance on various tasks; however, they suffer from severe computational challenges. In this paper, we show how to overcome the important challenge of speeding up kernel machines. In…

Kernel methods provide a powerful framework for non parametric learning. They are based on kernel functions and allow learning in a rich functional space while applying linear statistical learning tools, such as Ridge Regression or Support…

We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees…

This problem was solved within the framework of the grant project "Solving of problems of cluster analysis with application of parallel algorithms and cloud technologies" in the Institute of Mathematics and Mathematical Modelling in Almaty.…

Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental operation in graph computing and analytics. However, the irregularity of real-world graphs poses significant challenges to achieving efficient SpMM operation for graph data on…

Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

One of the applications of center-based clustering algorithms such as K-Means is partitioning data points into K clusters. In some examples, the feature space relates to the underlying problem we are trying to solve, and sometimes we can…

K-means -- and the celebrated Lloyd algorithm -- is more than the clustering method it was originally designed to be. It has indeed proven pivotal to help increase the speed of many machine learning and data analysis techniques such as…

k-means has recently been recognized as one of the best algorithms for clustering unsupervised data. Since k-means depends mainly on distance calculation between all data points and the centers, the time cost will be high when the size of…

Low-rank approximation is a common tool used to accelerate kernel methods: the $n \times n$ kernel matrix $K$ is approximated via a rank-$k$ matrix $\tilde K$ which can be stored in much less space and processed more quickly. In this work…

Sparse Matrix-Vector multiplication (SpMV) is an essential computational kernel in many application scenarios. Tens of sparse matrix formats and implementations have been proposed to compress the memory storage and speed up SpMV…

Score-debiased kernel density estimation (SD-KDE) achieves improved asymptotic convergence rates over classical KDE, but its use of an empirical score has made it significantly slower in practice. We show that by re-ordering the SD-KDE…

Many recent GPUs feature matrix multiplication engines (aka Tensor Core Units or TCUs) that perform small fixed-size matrix-matrix products at very high throughput. They have been used very effectively to speed up dense matrix-matrix…

Kronecker-sparse (KS) matrices -- whose supports are Kronecker products of identity and all-ones blocks -- underpin the structure of Butterfly and Monarch matrices and offer the promise of more efficient models. However, existing GPU…

We introduce the {\it diffusion $K$-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion $K$-means constructs a random walk on the similarity…

Sparse matrix-vector products (SpMVs) are a bottleneck in many scientific codes. Due to the heavy strain on the main memory interface from loading the sparse matrix and the possibly irregular memory access pattern, SpMV typically exhibits…

Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…