Deep Diffusion Maps
Sergio Garc\'ia-Heredia, \'Angela Fern\'andez, Carlos M. Ala\'iz

TL;DR
This paper introduces a deep learning-based approach to approximate Diffusion Maps embeddings, enabling scalable, out-of-sample dimensionality reduction without spectral decomposition, thus addressing key limitations of traditional manifold learning methods.
Contribution
The authors reformulate Diffusion Maps as an unconstrained minimization problem and train neural networks to compute embeddings efficiently, including for data outside the training set.
Findings
Outperforms traditional Diffusion Maps on various datasets
Reduces computational complexity and memory usage
Enables out-of-sample embedding without spectral decomposition
Abstract
One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in general, improve the efficiency of storing and processing large data sets. One of the best-known nonlinear dimensionality reduction methods is Diffusion Maps. However, despite their virtues, both Diffusion Maps and many other manifold learning methods based on the spectral decomposition of kernel matrices have drawbacks such as the inability to apply them to data outside the initial set, their computational complexity, and high memory costs for large data sets. In this work, we propose to alleviate these problems by resorting to deep learning. Specifically, a new formulation of Diffusion Maps embedding is offered as a solution to a certain unconstrained…
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Taxonomy
TopicsFace and Expression Recognition · Stochastic Gradient Optimization Techniques · Neural Networks and Applications
MethodsDiffusion
