A Local Similarity-Preserving Framework for Nonlinear Dimensionality Reduction with Neural Networks

TL;DR

This paper introduces Vec2vec, a neural network-based local nonlinear dimensionality reduction method that efficiently preserves data similarity structures, outperforming many existing techniques in high-dimensional data analysis.

Contribution

The paper presents a novel neural network framework, Vec2vec, for local nonlinear dimensionality reduction that reduces computational complexity and improves performance over traditional eigen-based methods.

Findings

Vec2vec is more efficient than several state-of-the-art methods.

It outperforms classical methods in data classification and clustering.

It is competitive with the recent UMAP technique.

Abstract

Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are global and local dimensionality reduction methods to alleviate the problem. Most of existing methods for local dimensionality reduction obtain an embedding with the eigenvalue or singular value decomposition, where the computational complexities are very high for a large amount of data. Here we propose a novel local nonlinear approach named Vec2vec for general purpose dimensionality reduction, which generalizes recent advancements in embedding representation learning of words to dimensionality reduction of matrices. It obtains the nonlinear embedding using a neural network with only one hidden layer to reduce the computational complexity. To train the neural network, we build the neighborhood similarity graph of a matrix and define the context of data points by exploiting the random walk properties. Experiments demenstrate that Vec2vec is more efficient than several state-of-the-art local dimensionality reduction methods in a large number of high-dimensional data. Extensive experiments of data classification and clustering on eight real datasets show that Vec2vec is better than several classical dimensionality reduction methods in the statistical hypothesis test, and it is competitive with recently developed state-of-the-art UMAP.