TY - GEN
T1 - Feature Extraction for Incomplete Data via Low-rank Tucker Decomposition
AU - Shi, Qiquan
AU - CHEUNG, Yiu Ming
AU - Zhao, Qibin
N1 - Funding Information:
Acknowledgment. This work is supported by the NSFC Grant: 61672444, HKBU Faculty Research Grant: FRG2/16-17/051, the SZSTI Grant: JCYJ2016053119400 6833, Hong Kong PhD Fellowship Scheme, and JSPS KAKENHI Grant: 17K00326. We thank Prof. Canyi Lu, Dr. Guoxu Zhou, Prof. Guangcan Liu, and Dr. Johann Bengua, for their helpful discussion.
PY - 2017
Y1 - 2017
N2 - Extracting features from incomplete tensors is a challenging task which is not well explored. Due to the data with missing entries, existing feature extraction methods are not applicable. Although tensor completion techniques can estimate the missing entries well, they focus on data recovery and do not consider the relationships among tensor samples for effective feature extraction. To solve this problem of feature extraction for incomplete data, we propose an unsupervised method, TDVM, which incorporates low-rank T ucker D ecomposition with feature V ariance M aximization in a unified framework. Based on Tucker decomposition, we impose nuclear norm regularization on the core tensors while minimizing reconstruction errors, and meanwhile maximize the variance of core tensors (i.e., extracted features). Here, the relationships among tensor samples are explored via variance maximization while estimating the missing entries. We thus can simultaneously obtain lower-dimensional core tensors and informative features directly from observed entries. The alternating direction method of multipliers approach is utilized to solve the optimization objective. We evaluate the features extracted from two real data with different missing entries for face recognition tasks. Experimental results illustrate the superior performance of our method with a significant improvement over the state-of-the-art methods.
AB - Extracting features from incomplete tensors is a challenging task which is not well explored. Due to the data with missing entries, existing feature extraction methods are not applicable. Although tensor completion techniques can estimate the missing entries well, they focus on data recovery and do not consider the relationships among tensor samples for effective feature extraction. To solve this problem of feature extraction for incomplete data, we propose an unsupervised method, TDVM, which incorporates low-rank T ucker D ecomposition with feature V ariance M aximization in a unified framework. Based on Tucker decomposition, we impose nuclear norm regularization on the core tensors while minimizing reconstruction errors, and meanwhile maximize the variance of core tensors (i.e., extracted features). Here, the relationships among tensor samples are explored via variance maximization while estimating the missing entries. We thus can simultaneously obtain lower-dimensional core tensors and informative features directly from observed entries. The alternating direction method of multipliers approach is utilized to solve the optimization objective. We evaluate the features extracted from two real data with different missing entries for face recognition tasks. Experimental results illustrate the superior performance of our method with a significant improvement over the state-of-the-art methods.
KW - Feature extraction
KW - Low-rank tucker decomposition
KW - Missing data
KW - Variance maximization
UR - http://www.scopus.com/inward/record.url?scp=85040258490&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-71249-9_34
DO - 10.1007/978-3-319-71249-9_34
M3 - Conference proceeding
AN - SCOPUS:85040258490
SN - 9783319712482
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 564
EP - 581
BT - Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2017, Proceedings
A2 - Ceci, Michelangelo
A2 - Dzeroski, Saso
A2 - Vens, Celine
A2 - Todorovski, Ljupco
A2 - Hollmen, Jaakko
PB - Springer Verlag
T2 - European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, ECML PKDD 2017
Y2 - 18 September 2017 through 22 September 2017
ER -