NDLI: Membership representation for detecting block-diagonal structure in low-rank or sparse subspace clustering

Content Provider	IEEE Xplore Digital Library
Author	Minsik Lee Jieun Lee Hyeogjin Lee Kwak, N.
Copyright Year	2015
Description	Author affiliation: Div. of EE, Hanyang Univ., Seoul, South Korea (Minsik Lee) \|\| Dept. of ECE, Ajou Univ., Suwon, South Korea (Jieun Lee) \|\| Grad. Sch. of CST, Seoul Nat. Univ., Seoul, South Korea (Hyeogjin Lee; Kwak, N.)
Abstract	Recently, there have been many proposals with state-of-the-art results in subspace clustering that take advantages of the low-rank or sparse optimization techniques. These methods are based on self-expressive models, which have well-defined theoretical aspects. They produce matrices with (approximately) block-diagonal structure, which is then applied to spectral clustering. However, there is no definitive way to construct affinity matrices from these block-diagonal matrices and it is ambiguous how the performance will be affected by the construction method. In this paper, we propose an alternative approach to detect block-diagonal structures from these matrices. The proposed method shares the philosophy of the above subspace clustering methods, in that it is a self-expressive system based on a Hadamard product of a membership matrix. To resolve the difficulty in handling the membership matrix, we solve the convex relaxation of the problem and then transform the representation to a doubly stochastic matrix, which is closely related to spectral clustering. The result of our method has eigenvalues normalized in between zero and one, which is more reliable to estimate the number of clusters and to perform spectral clustering. The proposed method shows competitive results in our experiments, even though we simply count the number of eigenvalues larger than a certain threshold to find the number of clusters.
Starting Page	1648
Ending Page	1656
File Size	239924
Page Count	9
File Format	PDF
ISSN	10636919
e-ISBN	9781467369640
DOI	10.1109/CVPR.2015.7298773
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-06-07
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Symmetric matrices Kernel Noise Eigenvalues and eigenfunctions Correlation Optimization Transforms
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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