Multi-instance Metric Learning

Multi-instance learning, like other machine learning and data mining tasks, requires distance metrics. Although metric learning methods have been studied for many years, metric learners for multi-instance learning remain almost untouched. In this paper, we propose a framework called Multi-Instance MEtric Learning (MIMEL) to learn an appropriate distance under the multi-instance setting. The distance metric between two bags is defined using the Mahalanobis distance function. The problem is formulated by minimizing the KL divergence between two multivariate Gaussians under the constraints of maximizing the between-class bag distance and minimizing the within-class bag distance. To exploit the mechanism of how instances determine bag labels in multi-instance learning, we design a nonparametric density-estimation-based weighting scheme to assign higher "weights" to the instances that are more likely to be positive in positive bags. The weighting scheme itself has a small workload, which adds little extra computing costs to the proposed framework. Moreover, to further boost the classification accuracy, a kernel version of MIMEL is presented. We evaluate MIMEL, using not only several typical multi-instance tasks, but also two activity recognition datasets. The experimental results demonstrate that MIMEL achieves better classification accuracy than many state-of-the-art distance based algorithms or kernel methods for multi-instance learning.