Metric learning for multi-instance classification with collapsed bags

As a kind of popular problem in machine learning, multi-instance task has been researched by means of many classical methods, such as kNN, SVM, etc. For kNN classification, its performance on traditional task can be boosted by metric learning, which seeks for a data-dependent metric to make similar examples closer and separate dissimilar examples by a margin. It is a challenge to define distance between bags in multi-instance problem, let alone learning appropriate metric for the problem. In this paper, we propose a new approach for multi-instance classification, with the idea of metric learning embedded. A new kind of distance is used to measure the similarity between bags. To weaken redundant information from bags and reduce computation complexity, k-means method is implemented to get collapsed bags by replacing each instance with its corresponding cluster centroid. The aim of metric learning is to expand inter-class bag distance and shrink intra-class bag distance, leading to the construction of an optimization problem with maximal relative distance. Kernel function can be introduced into the model to extract nonlinear information from the inputs. Gradient descent is utilized to solve the problem effectively. Numerical experiments on both artificial datasets and benchmark datasets demonstrated that the method can obtain competitive performance comparative to kNN and the state-of-the-art method in multi-instance classification.