How Principal Component Analysis works in ML pipelines part4(Machine Learning)

Abstract: Principal component analysis (PCA) plays an important role in the analysis of cryo-EM images for various tasks such as classification, denoising, compression, and ab-initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-electron microscopy projection images that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier-Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For N images of size L L, our method has time complexity O(NL3 L4) and space complexity O(NL2 L3). In contrast to previous work, these complexities are independent of the number of different contrast transfer functions of the images.