Landmark Diffusion Maps (L-dMaps): Accelerated manifold learning out-of-sample extension

06/28/2017
by   Andrew W. Long, et al.
0

Diffusion maps are a nonlinear manifold learning technique based on harmonic analysis of a diffusion process over the data. Out-of-sample extensions with computational complexity O(N), where N is the number of points comprising the manifold, frustrate applications to online learning applications requiring rapid embedding of high-dimensional data streams. We propose landmark diffusion maps (L-dMaps) to reduce the complexity to O(M), where M ≪ N is the number of landmark points selected using pruned spanning trees or k-medoids. Offering (N/M) speedups in out-of-sample extension, L-dMaps enables the application of diffusion maps to high-volume and/or high-velocity streaming data. We illustrate our approach on three datasets: the Swiss roll, molecular simulations of a C_24H_50 polymer chain, and biomolecular simulations of alanine dipeptide. We demonstrate up to 50-fold speedups in out-of-sample extension for the molecular systems with less than 4 manifold reconstruction fidelity relative to calculations over the full dataset.

READ FULL TEXT
research
06/25/2015

Diffusion Nets

Non-linear manifold learning enables high-dimensional data analysis, but...
research
01/27/2023

From partial data to out-of-sample parameter and observation estimation with Diffusion Maps and Geometric Harmonics

A data-driven framework is presented, that enables the prediction of qua...
research
01/03/2020

Scalability and robustness of spectral embedding: landmark diffusion is all you need

While spectral embedding is a widely applied dimension reduction techniq...
research
02/23/2018

Diffusion Maps meet Nyström

Diffusion maps are an emerging data-driven technique for non-linear dime...
research
07/21/2021

Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models

In this work we introduce a manifold learning-based method for uncertain...
research
03/06/2022

Diffusion Maps : Using the Semigroup Property for Parameter Tuning

Diffusion maps (DM) constitute a classic dimension reduction technique, ...
research
09/28/2021

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

In this paper, a novel surrogate model based on the Grassmannian diffusi...

Please sign up or login with your details

Forgot password? Click here to reset