The similarities and differences between PLS2 and PCA

Based on the principle of Principal component analysis (PCA), we present an unsupervised dimensionality reduction method called PLS2-B which using X instead of Y in the regression of Partial least squares (PLS). we proved that the number of PLS2-B latent variables is equal to the components of PLS2-B and is equal to the principal components of PCA, PLS2-B and PCA will be completely equivalent, and analyzed the different eigenvalues distribution of these two methods. In addition, under the cumulative contribution rate conditions, the results of PLS2-B method will be better in two datasets.