Dimension reduction in representation of the data

TL;DR

This paper introduces a novel algorithm for dimension reduction that identifies low-dimensional structures within high-dimensional data, focusing on neighborhoods with maximal point concentration, distinct from PCA.

Contribution

The paper presents a new dimension reduction algorithm that differs from PCA, capable of finding low-dimensional manifolds in high-dimensional data.

Findings

Successfully identifies low-dimensional structures in high-dimensional data

Effective in locating neighborhoods with maximum point density

Offers an alternative to PCA for manifold detection

Abstract

Suppose the data consist of a set $S$ of points $x_j$, $1\leq j \leq J$, distributed in a bounded domain $D\subset R^N$, where $N$ is a large number. An algorithm is given for finding the sets $L_k$ of dimension $k\ll N$, $k=1,2,...K$, in a neighborhood of which maximal amount of points $x_j\in S$ lie. The algorithm is different from PCA (principal component analysis)