Dimensionality Reduction of Spectral Reflectance by Dividing the Error Space of Principal Component Analysis

Abstract

A method based on the error space division of principal component analysis (PCA) is proposed to improve both the spectral and colorimetric reconstruction accuracy in spectral dimensionality reduction. Founded on the error source analysis of PCA from a geometric point of view, an objective function minimizing the within-cluster spectral reconstruction error is established to divide the error space of PCA. PCA is implemented again to each divided cluster to reduce the dimensionality of spectral reflectance. The proposed method, error-space-divided PCA (ESDPCA), is tested using four different spectral datasets. The root mean squared error (RMSE) and CIEDE2000 colour difference are adopted as the spectral and colorimetric evaluation metric respectively. Statistical results indicate that ESDPCA can outperform PCA by at least one principal component (PC) in colorimetric accuracy, while it can outperform PCA by at least two or three PCs in spectral accuracy. Comparisons with other three representative methods (i.e., LabPQR, LabRGB, and XYZLMS) show that ESDPCA outperforms them both in spectral and colorimetric accuracy significantly. In addition, the proposed method is robust for spectral datasets and compatible with few other methods involving PCA. Moreover, the computation complexity of ESPCA has the same order of magnitude as that of PCA.