Principal Loading Analysis

TL;DR

Principal Loading Analysis (PLA) is a new dimension reduction technique that simplifies data by removing variables that minimally affect the covariance structure, with theoretical bounds for sample noise.

Contribution

The paper introduces PLA as a novel dimension reduction method and provides an algorithm and noise bounds for practical implementation.

Findings

PLA effectively reduces dimensions by discarding minimally impactful variables.

The method includes an algorithm for practical application.

Bounds for noise in sample-based PLA are established.

Abstract

This paper proposes a tool for dimension reduction where the dimension of the original space is reduced: a Principal Loading Analysis (PLA). PLA is a tool to reduce dimensions by discarding variables. The intuition is that variables are dropped which distort the covariance matrix only by a little. Our method is introduced and an algorithm for conducting PLA is provided. Further, we give bounds for the noise arising in the sample case.