PLLay: Efficient Topological Layer based on Persistence Landscapes
This work addresses the challenge of integrating topological data analysis into neural networks for researchers in machine learning and computational topology, though it is incremental as it builds on existing persistence landscape methods.
The authors tackled the problem of incorporating topological features into deep learning models by proposing PLLay, a differentiable topological layer based on persistence landscapes, which improved classification performance on various datasets.
We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show differentiability with respect to layer inputs, for a general persistent homology with arbitrary filtration. Thus, our proposed layer can be placed anywhere in the network and feed critical information on the topological features of input data into subsequent layers to improve the learnability of the networks toward a given task. A task-optimal structure of PLLay is learned during training via backpropagation, without requiring any input featurization or data preprocessing. We provide a novel adaptation for the DTM function-based filtration, and show that the proposed layer is robust against noise and outliers through a stability analysis. We demonstrate the effectiveness of our approach by classification experiments on various datasets.