Ellipsoidal Multiple Instance Learning
Gabriel Krummenacher, Cheng Soon Ong, Joachim M. Buhmann · 2013
We propose a large margin method for asym-metric learning with ellipsoids, called eMIL, suited to multiple instance learning (MIL). We derive the distance between ellipsoids and the hyperplane, generalising the stan-dard support vector machine. Negative bags in MIL contain only negative instances, and we treat them akin to uncertain observations in the robust optimisation framework. How-ever, our method allows positive bags to cross the margin, since it is not known which in-stances within are positive. We show that representing bags as ellipsoids under the introduced distance is the most ro-bust solution when treating a bag as a ran-dom variable with finite mean and covari-ance. Two algorithms are derived to solve the resulting non-convex optimization prob-lem: a concave-convex procedure and a quasi-Newton method. Our method achieves com-petitive results on benchmark datasets. We introduce a MIL dataset from a real world application of detecting wheel defects from multiple partial observations, and show that eMIL outperforms competing approaches. 1.