MIL-SKDE: Multiple-instance learning with supervised kernel density estimation

Multiple-instance learning (MIL) is a variation on supervised learning. Instead of receiving a set of labeled instances, the learner receives a set of bags that are labeled. Each bag contains many instances. The aim of MIL is to classify new bags or instances. In this work, we propose a novel algorithm, MIL-SKDE (multiple-instance learning with supervised kernel density estimation), which addresses MIL problem through an extended framework of KDE (kernel density estimation)+mean shift. Since the KDE+mean shift framework is an unsupervised learning method, we extend KDE to its supervised version, called supervised KDE (SKDE), by considering class labels of samples. To seek the modes (local maxima) of SKDE, we also extend mean shift to a supervised version by taking into account sample labels. SKDE is an alternative of the well-known diverse density estimation (DDE) whose modes are called concepts. Comparing to DDE, SKDE is more convenient to learn multi-modal concepts and robust to labeling noise (mistakenly labeled bags). Finally, each bag is mapped into a concept space where the multi-class SVM classifiers are learned. Experimental results demonstrate that our approach outperforms the state-of-the-art MIL approaches.