# Incremental Principal Component Analysis Exact implementation and continuity corrections

## TL;DR

This paper presents an exact incremental PCA algorithm that updates transformation coefficients in real-time without storing all data, ensuring continuity of principal components during online analysis.

## Contribution

It introduces a formally equivalent incremental PCA method with continuity corrections, enabling real-time data analysis without batch processing.

## Key findings

- The incremental PCA produces identical results to batch PCA.
- The method maintains PC continuity during online updates.
- Applications demonstrate real-time data analysis benefits.

## Abstract

This paper describes some applications of an incremental implementation of the principal component analysis (PCA). The algorithm updates the transformation coefficients matrix on-line for each new sample, without the need to keep all the samples in memory. The algorithm is formally equivalent to the usual batch version, in the sense that given a sample set the transformation coefficients at the end of the process are the same. The implications of applying the PCA in real time are discussed with the help of data analysis examples. In particular we focus on the problem of the continuity of the PCs during an on-line analysis.