TY - GEN
T1 - Sparse multi-label bilinear embedding on stiefel manifolds
AU - LIU, Yang
AU - Dong, Guohua
AU - Gu, Zhonglei
N1 - Funding Information:
Acknowledgment. This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 61503317, in part by the General Research Fund (GRF) from the Research Grant Council (RGC) of Hong Kong SAR under Project HKBU12202417, and in part by the SZSTI Grant with the Project Code JCYJ20170307161544087.
PY - 2018
Y1 - 2018
N2 - Dimensionality reduction plays an important role in various machine learning tasks. In this paper, we propose a novel method dubbed Sparse Multi-label bILinear Embedding (SMILE) on Stiefel manifolds for supervised dimensionality reduction on multi-label data. Unlike the traditional multi-label dimensionality reduction algorithms that work on the vectorized data, the proposed SMILE directly takes the second-order tensor data as the input, and thus characterizes the spatial structure of the tensor data in an efficient way. Differentiating from the existing tensor-based dimensionality reduction methods that perform the eigen-decomposition in each iteration, SMILE utilizes a gradient ascent strategy to optimize the objective function in each iteration, and thus is more efficient. Moreover, we introduce column-orthonormal constraints to transformation matrices to eliminate the redundancy between the projection directions of the learned subspace and add an $$L:1$$ -norm regularization term to the objective function to enhance the interpretability of the learned subspace. Experiments on a standard image dataset validate the effectiveness of the proposed method.
AB - Dimensionality reduction plays an important role in various machine learning tasks. In this paper, we propose a novel method dubbed Sparse Multi-label bILinear Embedding (SMILE) on Stiefel manifolds for supervised dimensionality reduction on multi-label data. Unlike the traditional multi-label dimensionality reduction algorithms that work on the vectorized data, the proposed SMILE directly takes the second-order tensor data as the input, and thus characterizes the spatial structure of the tensor data in an efficient way. Differentiating from the existing tensor-based dimensionality reduction methods that perform the eigen-decomposition in each iteration, SMILE utilizes a gradient ascent strategy to optimize the objective function in each iteration, and thus is more efficient. Moreover, we introduce column-orthonormal constraints to transformation matrices to eliminate the redundancy between the projection directions of the learned subspace and add an $$L:1$$ -norm regularization term to the objective function to enhance the interpretability of the learned subspace. Experiments on a standard image dataset validate the effectiveness of the proposed method.
KW - Column-orthonormal constraints
KW - Dimensionality reduction
KW - norm regularization
KW - Second-order tensor
KW - Sparse multi-label bilinear embedding
KW - Stiefel manifolds
UR - http://www.scopus.com/inward/record.url?scp=85055870636&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-01851-1_20
DO - 10.1007/978-3-030-01851-1_20
M3 - Conference contribution
AN - SCOPUS:85055870636
SN - 9783030018504
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 203
EP - 213
BT - Foundations of Intelligent Systems - 24th International Symposium, ISMIS 2018, Proceedings
A2 - Japkowicz, Nathalie
A2 - Papadopoulos, George A.
A2 - Ceci, Michelangelo
A2 - Ras, Zbigniew W.
A2 - Liu, Jiming
PB - Springer Verlag
T2 - 24th International Symposium on Methodologies for Intelligent Systems, ISMIS 2018
Y2 - 29 October 2018 through 31 October 2018
ER -