On the Complexity of One-class SVM for Multiple Instance Learning
  In traditional multiple instance learning (MIL), both positive and negative bags are required to learn a prediction function. However, a high human cost is needed to know the label of each bag---positive or negative. Only positive bags contain our focus (positive instances) while negative bags consist of noise or background (negative instances). So we do not expect to spend too much to label the negative bags. Contrary to our expectation, nearly all existing MIL methods require enough negative bags besides positive ones. In this paper we propose an algorithm called "Positive Multiple Instance" (PMI), which learns a classifier given only a set of positive bags. So the annotation of negative bags becomes unnecessary in our method. PMI is constructed based on the assumption that the unknown positive instances in positive bags be similar each other and constitute one compact cluster in feature space and the negative instances locate outside this cluster. The experimental results demonstrate that PMI achieves the performances close to or a little worse than those of the traditional MIL algorithms on benchmark and real data sets. However, the number of training bags in PMI is reduced significantly compared with traditional MIL algorithms. 
Zhen Hu, Zhuyin Xue
cs.LG