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This paper describes a fast and accurate method for obtaining steerable principal components from a large dataset of images, assuming the images are well localized in space and frequency. The obtained steerable principal components are optimal for expanding the images in the dataset and all of their rotations. The method relies upon first expanding the images using a series of two-dimensional Prolate Spheroidal Wave Functions (PSWFs), where the expansion coefficients are evaluated using a specially designed numerical integration scheme. Then, the expansion coefficients are used to construct a rotationally-invariant covariance matrix which admits a block-diagonal structure, and the eigen-decomposition of its blocks provides us with the desired steerable principal components. The proposed method is shown to be faster then existing methods, while providing appropriate error bounds which guarantee its accuracy.
Cryo-electron microscopy nowadays often requires the analysis of hundreds of thousands of 2D images as large as a few hundred pixels in each direction. Here we introduce an algorithm that efficiently and accurately performs principal component analys
Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear, ``branched, ``disconnected, ``bended, ``curved, ``heterogeneous, or, more general, ``complex. In these ca
The two-dimensional principal component analysis (2DPCA) has become one of the most powerful tools of artificial intelligent algorithms. In this paper, we review 2DPCA and its variations, and propose a general ridge regression model to extract featur
In this paper we argue that (lexical) meaning in science can be represented in a 13 dimension Meaning Space. This space is constructed using principal component analysis (singular decomposition) on the matrix of word category relative information gai
Recent works show that deep neural networks trained on image classification dataset bias towards textures. Those models are easily fooled by applying small high-frequency perturbations to clean images. In this paper, we learn robust image classificat