PI-Net: A Deep Learning Approach to Extract Topological Persistence Images

Topological features such as persistence diagrams and their functional approximations like persistence images (PIs) have been showing substantial promise for machine learning and computer vision applications. Key bottlenecks to their large scale adoption are computational expenditure and difficulty in incorporating them in a differentiable architecture. We take an important step in this paper to mitigate these bottlenecks by proposing a novel one-step approach to generate PIs directly from the input data. We propose a simple convolutional neural network architecture called PI-Net that allows us to learn mappings between the input data and PIs. We design two separate architectures, one designed to take in multi-variate time series signals as input and another that accepts multi-channel images as input. We call these networks Signal PI-Net and Image PI-Net respectively. To the best of our knowledge, we are the first to propose the use of deep learning for computing topological features directly from data. We explore the use of the proposed method on two applications: human activity recognition using accelerometer sensor data and image classification. We demonstrate the ease of fusing PIs in supervised deep learning architectures and speed up of several orders of magnitude for extracting PIs from data. Our code is available at https://github.com/anirudhsom/PI-Net.