Manifold-based synthetic oversampling with manifold conformance estimation

Classification domains such as those in medicine, national security and the environment regularly suffer from a lack of training instances for the class of interest. In many cases, classification models induced under these conditions have poor predictive performance on the important minority class. Synthetic oversampling can be applied to mitigate the impact of imbalance by generating additional training instances. In this field, the majority of research has focused on refining the SMOTE algorithm. We note, however, that the generative bias of SMOTE is not appropriate for the large class of learning problems that conform to the manifold property. These are high-dimensional problems, such as image and spectral classification, with implicit feature spaces that are lower-dimensional than their physical data spaces. We show that ignoring this can lead to instances being generated in erroneous regions of the data space. We propose a general framework for manifold-based synthetic oversampling that helps users to select a domain-appropriate manifold learning method, such as PCA or autoencoder, and apply it to model and generate additional training samples. We evaluate data generation on theoretical distributions and image classification tasks that are standard in the manifold learning literature, and empirically show its positive impact on the classification of high-dimensional image and gamma-ray spectra tasks, along with 16 UCI datasets.