Large-Scale Subspace Clustering by Independent Distributed and Parallel Coding

Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS 2 C) problem, that is, partitioning million data points with a millon di...

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Published in:	IEEE transactions on cybernetics Vol. 52; no. 9; pp. 9090 - 9100
Main Authors:	Li, Jun, Tao, Zhiqiang, Wu, Yue, Zhong, Bineng, Fu, Yun
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.09.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Big Data Clustering Clustering methods Columns (structural) Data points Dictionaries Distributed and parallel computing Distributed databases least-squares regression (LSR) low-rank representation (LRR) Massive data points Matrix decomposition Multimedia Optimization over-high dimensional big data Regularization Sparse matrices sparse subspace clustering (SSC) subspace clustering Subspaces Video
ISSN:	2168-2267, 2168-2275, 2168-2275
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Abstract	Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS 2 C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS 2 C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/<inline-formula> <tex-math notation="LaTeX">\ell _{1} </tex-math></inline-formula>-norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS 2 C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS 2 C methods, our approach achieves better clustering results in public datasets, including a million images and videos.
AbstractList	Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS²C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS²C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/ℓ₁-norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS²C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS²C methods, our approach achieves better clustering results in public datasets, including a million images and videos. Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS2C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS2C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/[Formula Omitted]-norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS2C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS2C methods, our approach achieves better clustering results in public datasets, including a million images and videos. Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS 2 C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS 2 C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/<inline-formula> <tex-math notation="LaTeX">\ell _{1} </tex-math></inline-formula>-norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS 2 C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS 2 C methods, our approach achieves better clustering results in public datasets, including a million images and videos. Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS2C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS2C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/ l1 -norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS2C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS2C methods, our approach achieves better clustering results in public datasets, including a million images and videos.Subspace clustering is a popular method to discover underlying low-dimensional structures of high-dimensional multimedia data (e.g., images, videos, and texts). In this article, we consider a large-scale subspace clustering (LS2C) problem, that is, partitioning million data points with a millon dimensions. To address this, we explore an independent distributed and parallel framework by dividing big data/variable matrices and regularization by both columns and rows. Specifically, LS2C is independently decomposed into many subproblems by distributing those matrices into different machines by columns since the regularization of the code matrix is equal to a sum of that of its submatrices (e.g., square-of-Frobenius/ l1 -norm). Consensus optimization is designed to solve these subproblems in a parallel way for saving communication costs. Moreover, we provide theoretical guarantees that LS2C can recover consensus subspace representations of high-dimensional data points under broad conditions. Compared with the state-of-the-art LS2C methods, our approach achieves better clustering results in public datasets, including a million images and videos.
Author	Li, Jun Fu, Yun Tao, Zhiqiang Wu, Yue Zhong, Bineng
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SubjectTerms	Big Data Clustering Clustering methods Columns (structural) Data points Dictionaries Distributed and parallel computing Distributed databases least-squares regression (LSR) low-rank representation (LRR) Massive data points Matrix decomposition Multimedia Optimization over-high dimensional big data Regularization Sparse matrices sparse subspace clustering (SSC) subspace clustering Subspaces Video
Title	Large-Scale Subspace Clustering by Independent Distributed and Parallel Coding
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