Novel dimensionality reduction approach for unsupervised learning on small datasets

Abstract We focus on an image classification task in which only several unlabeled images per class are available for learning and low computational complexity is required. We recall the state-of-the-art methods that are used to solve the task: autoencoder-based approaches and manifold-decomposition-based approaches. Next, we introduce our proposed method, which is based on a combination of the F-transform and (kernel) principal component analysis. F-transform significantly reduces the computation time of PCA and increases the robustness of PCA to translation, while PCA proposes more descriptive features. This combination performs 3D reduction: the F-transform reduces dimensionality over a single 2D image, while PCA reduces dimensionality through the whole set of processed images. Based on the benchmark results, our method may outperform deep-learning-based methods in limited settings. For completeness, we also address other image resampling algorithms that can be used instead of the F-transform, and we find that the F-transform is the most suitable.