Metric Learning-Based Multi-Instance Multi-Label Classification With Label Correlation

In multi-instance multi-label learning (MIML) problems, predicting the labels of unseen bags becomes difficult when the labels of their instances are not provided directly. Therefore, it is necessary to exploit the label correlations to enhance the accuracy of the MIML classification. This paper presents the metric learning-based MIML-<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>NN (MI(ML)<inline-formula> <tex-math notation="LaTeX">$^{\mathrm{ 2}}k$ </tex-math></inline-formula>NN) method, which is composed of three parts. First, the label Laplacian matrix can be learned to obtain the label correlations by minimizing the label manifold regularizer. Then, based on label correlations, a novel objective function for the MIML is proposed where Mahalanobis distances between positively correlated labels and bags are minimized. Moreover, this objective function can be optimized by employing the Rayleigh-Ritz theorem and gradient descent (GD) alternately. Finally, the average Hausdorff distances of bag-bag pairs and bag-label pairs are calculated to construct the MIML-<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>NN classifier. Multiple classification experiments on three image and text benchmarks show the practicability and validity of our proposed method by comparing with the baseline methods.