Remote sensing data are often adversely affected by noises due to atmospheric water absorption, transmission errors, sensor sensitivity, and saturation. Therefore, the performance of the classical principal component analysis (PCA) is negatively affected when dealing with such noisy data. To overcome this problem, a robust deflated PCA via multiple instance factorings (RDPCA-MIF) for dimension reduction in remote sensing images is proposed. In contrast to the traditional PCA, a penalty is imposed on the instance space through instance factoring technique to suppress the effect of noise in pursuing projections. To achieve this, we use two strategies, total distance, and cosine similarity metrics. Both strategies discriminate between noise and authentic data points by iteratively learning the relationship between instances and projections. Moreover, a deflation strategy that enables multiple relationships learning between instances and projections is applied to thoroughly evaluate the importance of instances in relation to all projections. Extensive experimental evaluations of the proposed RDPCA-MIF on Salinas-A dataset and shallow and deep features from the NWPU-RESISC45 remote sensing dataset prove its superiority over six comparative methods in dimension reduction and classification tasks.