PCA Dimensionality Reduction Algorithm Based on Ordered Pair of Normalized Real Numbers

This paper presents a PCA (Principal Component Analysis) data dimensionality reduction algorithm based on OPNs (Ordered Pair of Normalized Real Numbers), referred to as OPNs-PCA. This algorithm aims to improve the dimensionality reduction performance of data. Especially, it shows significant advantages in removing feature redundancy and noise, providing a clearer and more effective data basis for subsequent machine learning or data mining tasks. The algorithm proposed in this paper introduces the concept of OPNs into the PCA algorithm and performs PCA dimensionality reduction operations under the framework of OPNs. Through the characteristic of OPNs' operation in processing feature relationships in non-real number spaces, it can effectively reduce data noise, enhance the processing ability of nonlinear data, and improve the performance of subsequent classification algorithms. We have conducted detailed experimental verification on multiple public data sets. The results show that unlike classic PCA, LLE, KPCA, SPCA and other algorithms that require more principal components to retain sufficient information, OPNs-PCA can achieve a similar or even better level of information retention with fewer principal components, and has a significant improvement in the processing ability of nonlinear data.