A multi-manifold learning based instance weighting and under-sampling for imbalanced data classification problems

Under-sampling is a technique to overcome imbalanced class problem, however, selecting the instances to be dropped and measuring their informativeness is an important concern. This paper tries to bring up a new point of view in this regard and exploit the structure of data to decide on the importance of the data points. For this purpose, a multi-manifold learning approach is proposed. Manifolds represent the underlying structures of data and can help extract the latent space for data distribution. However, there is no evidence that we can rely on a single manifold to extract the local neighborhood of the dataset. Therefore, this paper proposes an ensemble of manifold learning approaches and evaluates each manifold based on an information loss-based heuristic. Having computed the optimality score of each manifold, the centrality and marginality degrees of samples are computed on the manifolds and weighted by the corresponding score. A gradual elimination approach is proposed, which tries to balance the classes while avoiding a drop in the F measure on the validation dataset. The proposed method is evaluated on 22 imbalanced datasets from the KEEL and UCI repositories with different classification measures. The results of the experiments demonstrate that the proposed approach is more effective than other similar approaches and is far better than the previous approaches, especially when the imbalance ratio is very high.