# Nonlinear Dimensionality Reduction via Path-Based Isometric Mapping

Source: [Nonlinear Dimensionality Reduction via Path-Based Isometric Mapping](<https://www.sota2.com/research/paper/68fa614f1e209131ce9f3a9c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T19:56:35.880Z

Authors: Amir Najafi, Amir Joudaki, Emad Fatemizadeh

Published: 2013-12-03T12:56:46.000Z

## Abstract

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which render them inapplicable to large-scale datasets. To leverage such cases we propose a new method called "Path-Based Isomap". Similar to Isomap, we exploit geodesic paths to find the low-dimensional embedding. However, instead of preserving pairwise geodesic distances, the low-dimensional embedding is computed via a path-mapping algorithm. Due to the much fewer number of paths compared to number of data points, a significant improvement in time and memory complexity without any decline in performance is achieved. The method demonstrates state-of-the-art performance on well-known synthetic and real-world datasets, as well as in the presence of noise.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1312.0803>)

[PDF](<https://arxiv.org/pdf/1312.0803.pdf>)