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

Area of Science:

• Computational topology
• Machine learning
• Computer vision

Background:

• Topological features like persistence diagrams and persistence images (PIs) offer robust data representations against real-world variations.
• However, computational cost and integration into differentiable architectures hinder their widespread adoption.

Purpose of the Study:

• To address the bottlenecks in generating persistence images (PIs).
• To propose a novel, one-step deep learning approach for direct PI generation from input data.

Main Methods:

• Developed two convolutional neural network architectures, Signal PI-Net and Image PI-Net, for generating PIs from time-series and image data, respectively.
• Proposed a novel one-step approach for direct PI generation using deep learning.

Main Results:

• Demonstrated the efficacy of PI-Nets in human activity recognition and image classification tasks.
• Achieved significant speedups (orders of magnitude) in PI extraction compared to traditional methods.
• Showcased the seamless integration of PIs within supervised deep learning frameworks.

Conclusions:

• PI-Nets offer a computationally efficient and easily integrable method for topological feature extraction.
• This deep learning approach facilitates the broader application of topological data analysis in machine learning and computer vision.