PI-Net

PI-Net generates persistence images from raw multi-variate time series and multi-channel images to extract topological features for integration into supervised deep learning models.

Key Features:

• One-step PI generation: Generates persistence images directly from raw inputs without intermediate topological computations, reducing computational overhead.
• Dual CNN architectures: Comprises two convolutional neural network architectures—Signal PI-Net for multivariate time series and Image PI-Net for multi-channel images.
• Differentiable integration: Produces representations that facilitate integration into differentiable architectures for supervised learning.
• Robustness to nuisance variables: Leverages topological representations to provide robustness against viewpoint changes and illumination variations.
• Deep learning–based topological computation: Uses convolutional neural networks to compute topological features directly from input data.
• Computational efficiency: Accelerates persistence image computation by several orders of magnitude compared to traditional multi-step pipelines.

Scientific Applications:

• Human Activity Recognition: Applied to human activity recognition using tri-axial accelerometer sensor data with persistence images integrated into supervised deep learning architectures.
• Image Classification: Applied to image classification where Image PI-Net extracts topological features from multi-channel images, including experiments using CIFAR10, contributing to improved classification performance.

Methodology:

Convolutional neural networks are trained on specific datasets (e.g., CIFAR10 for Image PI-Net) to map raw inputs directly to persistence images, eliminating intermediate topological computations and accelerating feature extraction by several orders of magnitude.