Some Multilinear Variants of Principal Component Analysis: Examples in Grayscale Image Recognition and Reconstruction

Principal component analysis (PCA) has long been used in computer vision applications such as face recognition. Here, we present an overview of some variants of PCA, including 2D PCA (2DPCA), bidirectional 2DPCA (B2DPCA), and coupled subspace analysis (CSA). Unlike conventional PCA, the variants 2DPCA, B2DPCA, and CSA preserve the original image structure, often providing better recognition and reconstruction results than those obtained with PCA. This article considers the background for these techniques and steps involved in applying these methods, including typical preprocessing of sample images, algorithm description, and classification. These variants of PCA have been successfully used in a number of different areas such as identification of wood species, biometrics (not limited to face recognition), medical imaging, and image compression, to name a few examples; we briefly mention some of these to provide an idea of the scope of applications. We address some advantages and disadvantages of these variants in relation to PCA. Utilizing the Modified National Institute of Standards and Technology (MNIST) digits and Fashion-MNIST image sets, we demonstrate application of CSA for image recognition and reconstruction compared to PCA. Finally, we mention how these PCA variants fit into a more general framework using tensors.