The Linear Geometry Structure of Label Matrix for Multi-label Learning.

Multi-label learning annotates a data point with the relevant labels. Under the low-rank assumption, many approaches embed the label space into the low-dimension space to capture the label correlation. However these approaches usually have weak prediction performance because the low-rank assumption is usually violated in real-world applications. In this paper, we observe the fact that the linear representation of row and column vectors of label matrix does not depend on the rank structure and it can capture the linear geometry structure of label matrix (LGSLM). Inspired by the fact, we propose the LGSLM classifier to improve the prediction performance. More specifically, after rearranging the columns of a label matrix in decreasing order according to the number of positive labels, we capture the linear representation of the row vectors of the compact region in the label matrix. Moreover, we also capture the linear and sparse representation of column vectors using the \\(L_1\\)-norm. The experimental results for five real-world datasets show the superior performance of our approach compared with state-of-the-art methods.