Evolutionary Self-Expressive Models for Subspace Clustering

The problem of organizing data that evolves over time into clusters is encountered in a number of practical settings. We introduce evolutionary subspace clustering, a method whose objective is to cluster a collection of evolving data points that lie on a union of low-dimensional evolving subspaces....

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Bibliographic Details
Published in:IEEE journal of selected topics in signal processing 2018-12, Vol.12 (6), p.1534-1546
Main Authors: Hashemi, Abolfazl, Vikalo, Haris
Format: Article
Language:English
Subjects:
Clustering
Clustering algorithms
Computational geometry
Convex analysis
Convexity
Data acquisition
Data collection
Data points
Evolutionary algorithms
evolutionary clustering
Optimization
Principal component analysis
real-time clustering
Real-time systems
Representations
Run time (computers)
self-expressive models
Sparse matrices
State of the art
subspace clustering
Subspace methods
Subspaces
temporal data
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Summary:The problem of organizing data that evolves over time into clusters is encountered in a number of practical settings. We introduce evolutionary subspace clustering, a method whose objective is to cluster a collection of evolving data points that lie on a union of low-dimensional evolving subspaces. To learn the parsimonious representation of the data points at each time step, we propose a non-convex optimization framework that exploits the self-expressiveness property of the evolving data while taking into account representation from the preceding time step. To find an approximate solution to the aforementioned non-convex optimization problem, we develop a scheme based on alternating minimization that both learns the parsimonious representation as well as adaptively tunes and infers a smoothing parameter reflective of the rate of data evolution. The latter addresses a fundamental challenge in evolutionary clustering-determining if and to what extent one should consider previous clustering solutions when analyzing an evolving data collection. Our experiments on both synthetic and real-world datasets demonstrate that the proposed framework outperforms state-of-the-art static subspace clustering algorithms and existing evolutionary clustering schemes in terms of both accuracy and running time, in a range of scenarios.
ISSN:1932-4553
1941-0484
DOI:10.1109/JSTSP.2018.2877478