Rank-κ 2-D multinomial logistic regression for matrix data classification

Kun Song, Feiping Nie, Junwei Han, Xuelong Li

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)3524-3537
Number of pages14
JournalIEEE Transactions on Neural Networks and Learning Systems
Volume29
Issue number8
DOIs
StatePublished - Aug 2018

Keywords

  • 2-D logistic regression (2DLR)
  • matrix analysis
  • matrix data classification
  • multinomial logistic regression

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