Related papers: Clustering-based Low Rank Approximation Method

Low-rank and sparse composite approximation is a natural idea to compress Large Language Models (LLMs). However, such an idea faces two primary challenges that adversely affect the performance of existing methods. The first challenge…

Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…

Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…

Clustering with incomplete views is a challenge in multi-view clustering. In this paper, we provide a novel and simple method to address this issue. Specifically, the proposed method simultaneously exploits the local information of each…

The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the…

We introduce a Generalized LU-Factorization (\textbf{GLU}) for low-rank matrix approximation. We relate this to past approaches and extensively analyze its approximation properties. The established deterministic guarantees are combined with…

Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…

Clustering, like covariate selection for classification, is an important step to compress and interpret the data. However, clustering of covariates is often performed independently of the classification step, which can lead to undesirable…

The many-light formulation provides a general framework for rendering various illumination effects using hundreds of thousands of virtual point lights (VPLs). To efficiently gather the contributions of the VPLs, lightcuts and its extensions…

A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…

Large matrix multiplication is a cornerstone of modern machine learning workloads, yet traditional approaches suffer from cubic computational complexity (e.g., $\mathcal{O}(n^3)$ for a matrix of size $n\times n$). We present Low-Rank GEMM,…

Subspace clustering discovers the clusters embedded in multiple, overlapping subspaces of high dimensional data. Many significant subspace clustering algorithms exist, each having different characteristics caused by the use of different…

Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work,…

The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…

Hierarchical clustering is a class of algorithms that seeks to build a hierarchy of clusters. It has been the dominant approach to constructing embedded classification schemes since it outputs dendrograms, which capture the hierarchical…

This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation…

This study introduces a novel technique for multi-view clustering known as the "Consensus Graph-Based Multi-View Clustering Method Using Low-Rank Non-Convex Norm" (CGMVC-NC). Multi-view clustering is a challenging task in machine learning…

Image clustering is a very useful technique that is widely applied to various areas, including remote sensing. Recently, visual representations by self-supervised learning have greatly improved the performance of image clustering. To…

Compression has emerged as one of the essential deep learning research topics, especially for the edge devices that have limited computation power and storage capacity. Among the main compression techniques, low-rank compression via matrix…