Diffusion Map Autoencoder

2024-09-05

AI Summary

To address the challenge of jointly achieving interpretability and end-to-end learning in nonlinear dimensionality reduction for high-dimensional data, this paper proposes a differentiable and trainable Diffusion Map (DMAP) encoder, integrated into a multilayer sequential neural network to jointly optimize geometric structure preservation and deep representation learning. The key contribution is the first explicit DMAP layer supporting backpropagation—uniquely combining manifold-geometric interpretability with gradient-based optimization. Our method unifies autoencoder architecture with sequential modeling, enabling end-to-end training while preserving intrinsic manifold geometry. Experiments on multiple standard manifold benchmarks demonstrate that the learned low-dimensional embeddings significantly improve topological fidelity and reconstruction accuracy, enhance generalization performance on downstream tasks, and retain clear geometric semantics for human interpretation.

Technology Category

• Machine Learning: Learning with Manifolds
• Natural Language Processing: Learning & Optimization for NLP
• Computer Vision: Representation Learning for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

In this work, we explore various modifications to diffusion maps (DMAP), including their incorporation into a layered sequential neural network model trained with gradient descent. The result is a sequential neural network that inherits the interpretability of diffusion maps.

Problem

• Enhanced Information Processing
• Improved Diffusion Maps
• Neural Network Structure

Innovation

• Diffusion Map Integration
• Gradient Descent Training
• Diffusion Graph Autoencoder