Topology Estimation of Simulated 4D Image Data by Combining Downscaling and Convolutional Neural Networks

Four-dimensional image-type data can quickly become prohibitively large, and it may not be feasible to directly apply methods, such as persistent homology or convolutional neural networks, to determine the topological characteristics of these data because they can encounter complexity issues. This study aims to determine the Betti numbers of large four-dimensional image-type data. The experiments use synthetic data, and demonstrate that it is possible to circumvent these issues by applying downscaling methods to the data prior to training a convolutional neural network, even when persistent homology software indicates that downscaling can significantly alter the homology of the training data. When provided with downscaled test data, the neural network can estimate the Betti numbers of the original samples with reasonable accuracy.