PLLay: Efficient Topological Layer based on Persistence Landscapes
arXiv:2002.02778
Abstract
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.
29 pages, 7 figures
References in corpus (10)
- Statistical topological data analysis using persistence landscapes
- A persistence landscapes toolbox for topological statistics
- The persistence landscape and some of its properties
- Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
- Finding cosmic voids and filament loops using topological data analysis
- On Characterizing the Capacity of Neural Networks using Algebraic Topology
- Topological Data Analysis for Arrhythmia Detection through Modular Neural Networks
- A Topology Layer for Machine Learning
- Connectivity-Optimized Representation Learning via Persistent Homology
- Applying Topological Persistence in Convolutional Neural Network for Music Audio Signals