JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1158 10.6339/24-JDS1158 Statistical Data Science SPA: Signflip Parallel Analysis to Optimize the Number of Principal Components in Two-dimensional PCA https://orcid.org/0000-0002-8222-810X LiZhaoyuanlizhaoyuan@cuhk.edu.cn1 KuangYiling2 The Chinese University of Hong Kong, Shenzhen, China The Chinese University of Hong Kong, China Corresponding author. Email: lizhaoyuan@cuhk.edu.cn. 20242211202400118 Supplementary Material

The supplementary material contains a zipped folder, which contains codes and three data sets for reproducing all results. Please go to https://figshare.com/s/824176b60a12b8ee0535.

237202420102024 2024 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2024 Open access article under the CC BY license.

Yang et al. (2004) developed the two-dimensional principal component analysis (2DPCA) for image representation and recognition, widely used in different fields, including face recognition, biometrics recognition, cancer diagnosis, tumor classification, and others. 2DPCA has been proven to perform better and computationally more efficiently than traditional principal component analysis (PCA). However, some theoretical properties of 2DPCA are still unknown, including determining the number of principal components (PCs) in the training set, which is the critical step in applying 2DPCA. Without rigorous criteria for determining the number of PCs hampers the generalization of the application of 2DPCA. Given this issue, we propose a new method based on parallel analysis to determine the number of PCs in 2DPCA with statistical justification. Several image classification experiments demonstrate that the proposed method compares favourably to other state-of-the-art approaches regarding recognition accuracy and storage requirement, with a low computational cost.

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