A nonlinear multi-label learning model based on Tanh mapping

Abstract

The relationship between features and labels plays an important role in multi-label learning. The purpose of multi-label learning is to learn a mapping from the feature space to the label space. Many of the existing methods decompose the observed label matrix into the product of a low-rank latent label matrix and a projection matrix, and construct a linear mapping between the feature space and low-rank latent label space. However, in practice, the relationship between two high-dimensional spaces is often nonlinear. Consequently, these linear models may not sufficiently capture the data distribution and the true dependencies between features and labels. Herein, a novel classification model for multi-label learning is proposed, which considers nonlinear mapping from the feature space to the latent label space. Because of correlation between labels, the label matrix is usually of a low rank. To explore the low-rank structure, a latent label matrix is obtained using the decomposition of the original label matrix. To characterize the nonlinear relationship between features and latent labels, the tanh function is employed to learn a nonlinear classifier. The tanh function describes the distribution of labels by constraining the domain of the latent label space to the interval [−1,1]. In addition, the Frobenius norm regularization constraint is imposed on the variables in the model for optimization. The experimental results demonstrate that the proposed method is robust and comparable to state-of-the-art multi-label learning methods.