TY - JOUR
T1 - Rank-κ 2-D multinomial logistic regression for matrix data classification
AU - Song, Kun
AU - Nie, Feiping
AU - Han, Junwei
AU - Li, Xuelong
N1 - Publisher Copyright:
© 2012 IEEE.
PY - 2018/8
Y1 - 2018/8
N2 - The amount of matrix data has increased rapidly nowadays. How to classify matrix data efficiently is an important issue. In this paper, by discovering the shortages of 2-D linear discriminant analysis and 2-D logistic regression, a novel 2-D framework named rank- κ 2-D multinomial logistic regression (2DMLR-RK) is proposed. The 2DMLR-RK is designed for a multiclass matrix classification problem. In the proposed framework, each category is modeled by a left projection matrix and a right projection matrix with rank κ. The left projection matrices capture the row information of matrix data, and the right projection matrices acquire the column information. We identify the parameter κ plays the role of balancing the capacity of learning and generalization of the 2DMLR-RK. In addition, we develop an effective framework for solving the proposed nonconvex optimization problem. The convergence, initialization, and computational complexity are discussed. Extensive experiments on various types of data sets are conducted. Comparing with 1-D methods, 2DMLR-RK not only achieves a better classification accuracy, but also costs less computation time. Comparing with other state-of-the-art 2-D methods, the 2DMLR-RK achieves a better performance for matrix data classification.
AB - The amount of matrix data has increased rapidly nowadays. How to classify matrix data efficiently is an important issue. In this paper, by discovering the shortages of 2-D linear discriminant analysis and 2-D logistic regression, a novel 2-D framework named rank- κ 2-D multinomial logistic regression (2DMLR-RK) is proposed. The 2DMLR-RK is designed for a multiclass matrix classification problem. In the proposed framework, each category is modeled by a left projection matrix and a right projection matrix with rank κ. The left projection matrices capture the row information of matrix data, and the right projection matrices acquire the column information. We identify the parameter κ plays the role of balancing the capacity of learning and generalization of the 2DMLR-RK. In addition, we develop an effective framework for solving the proposed nonconvex optimization problem. The convergence, initialization, and computational complexity are discussed. Extensive experiments on various types of data sets are conducted. Comparing with 1-D methods, 2DMLR-RK not only achieves a better classification accuracy, but also costs less computation time. Comparing with other state-of-the-art 2-D methods, the 2DMLR-RK achieves a better performance for matrix data classification.
KW - 2-D logistic regression (2DLR)
KW - matrix analysis
KW - matrix data classification
KW - multinomial logistic regression
UR - http://www.scopus.com/inward/record.url?scp=85028448036&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2017.2731999
DO - 10.1109/TNNLS.2017.2731999
M3 - 文章
C2 - 28816682
AN - SCOPUS:85028448036
SN - 2162-237X
VL - 29
SP - 3524
EP - 3537
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 8
ER -