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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2021.3052056