TY - JOUR
T1 - Laplacian regularized low-rank representation and its applications
AU - Yin, Ming
AU - Gao, Junbin
AU - Lin, Zhouchen
N1 - Includes bibliographical references.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - Low-rank representation (LRR) has recently attracted a great deal of attention due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. For a given set of observed data corrupted with sparse errors, LRR aims at learning a lowest-rank representation of all data jointly. LRR has broad applications in pattern recognition, computer vision and signal processing. In the real world, data often reside on low-dimensional manifolds embedded in a high-dimensional ambient space. However, the LRR method does not take into account the non-linear geometric structures within data, thus the locality and similarity information among data may be missing in the learning process. To improve LRR in this regard, we propose a general Laplacian regularized low-rank representation framework for data representation where a hypergraph Laplacian regularizer can be readily introduced into, i.e., a Non-negative Sparse Hyper-Laplacian regularized LRR model (NSHLRR). By taking advantage of the graph regularizer, our proposed method not only can represent the global low-dimensional structures, but also capture the intrinsic non-linear geometric information in data. The extensive experimental results on image clustering, semi-supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method.
AB - Low-rank representation (LRR) has recently attracted a great deal of attention due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. For a given set of observed data corrupted with sparse errors, LRR aims at learning a lowest-rank representation of all data jointly. LRR has broad applications in pattern recognition, computer vision and signal processing. In the real world, data often reside on low-dimensional manifolds embedded in a high-dimensional ambient space. However, the LRR method does not take into account the non-linear geometric structures within data, thus the locality and similarity information among data may be missing in the learning process. To improve LRR in this regard, we propose a general Laplacian regularized low-rank representation framework for data representation where a hypergraph Laplacian regularizer can be readily introduced into, i.e., a Non-negative Sparse Hyper-Laplacian regularized LRR model (NSHLRR). By taking advantage of the graph regularizer, our proposed method not only can represent the global low-dimensional structures, but also capture the intrinsic non-linear geometric information in data. The extensive experimental results on image clustering, semi-supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method.
KW - Graph
KW - Hyper- Laplacian
KW - Laplacian Matrix
KW - Low-Rank Representation
KW - Manifold Structure
KW - Regularization
UR - http://www.scopus.com/inward/record.url?scp=84962090301&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84962090301&partnerID=8YFLogxK
U2 - 10.1109/TPAMI.2015.2462360
DO - 10.1109/TPAMI.2015.2462360
M3 - Article
C2 - 27046494
AN - SCOPUS:84962090301
VL - 38
SP - 504
EP - 517
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
SN - 0162-8828
IS - 3
M1 - 7172559
ER -