Rotationally Invariant Image Representation for Viewing Direction Classification in Cryo-EM

We introduce a new rotationally invariant viewing angle classification method for identifying, among a large number of Cryo-EM projection images, similar views without prior knowledge of the molecule. Our rotationally invariant features are based on the bispectrum. Each image is denoised and compressed using steerable principal component analysis (PCA) such that rotating an image is equivalent to phase shifting the expansion coefficients. Thus we are able to extend the theory of bispectrum of 1D periodic signals to 2D images. The randomized PCA algorithm is then used to efficiently reduce the dimensionality of the bispectrum coefficients, enabling fast computation of the similarity between any pair of images. The nearest neighbors provide an initial classification of similar viewing angles. In this way, rotational alignment is only performed for images with their nearest neighbors. The initial nearest neighbor classification and alignment are further improved by a new classification method called vector diffusion maps. Our pipeline for viewing angle classification and alignment is experimentally shown to be faster and more accurate than reference-free alignment with rotationally invariant K-means clustering, MSA/MRA 2D classification, and their modern approximations

The role of Eigen-matrix translation in classification of biological datasets

Driven by the challenge of integrating large amount of experimental data obtained from biological research, computational biology and bioinformatics are growing rapidly. Machine learning methods, especially kernel methods with Support Vector Machines (SVMs) are very popular tools. In the perspective of kernel matrix, a technique namely Eigen-matrix translation has been introduced for protein data classification. The Eigen-matrix translation strategy owns a lot of nice properties while the nature of which needs further exploration. We propose that its importance lies in the dimension reduction of predictor attributes within the data set. This can therefore serve as a novel perspective for future research in dimension reduction problems. © 2012 IEEE.published_or_final_versio

Hierarchical Graphical Models for Multigroup Shape Analysis using Expectation Maximization with Sampling in Kendall's Shape Space

This paper proposes a novel framework for multi-group shape analysis relying on a hierarchical graphical statistical model on shapes within a population.The framework represents individual shapes as point setsmodulo translation, rotation, and scale, following the notion in Kendall shape space.While individual shapes are derived from their group shape model, each group shape model is derived from a single population shape model. The hierarchical model follows the natural organization of population data and the top level in the hierarchy provides a common frame of reference for multigroup shape analysis, e.g. classification and hypothesis testing. Unlike typical shape-modeling approaches, the proposed model is a generative model that defines a joint distribution of object-boundary data and the shape-model variables. Furthermore, it naturally enforces optimal correspondences during the process of model fitting and thereby subsumes the so-called correspondence problem. The proposed inference scheme employs an expectation maximization (EM) algorithm that treats the individual and group shape variables as hidden random variables and integrates them out before estimating the parameters (population mean and variance and the group variances). The underpinning of the EM algorithm is the sampling of pointsets, in Kendall shape space, from their posterior distribution, for which we exploit a highly-efficient scheme based on Hamiltonian Monte Carlo simulation. Experiments in this paper use the fitted hierarchical model to perform (1) hypothesis testing for comparison between pairs of groups using permutation testing and (2) classification for image retrieval. The paper validates the proposed framework on simulated data and demonstrates results on real data.Comment: 9 pages, 7 figures, International Conference on Machine Learning 201

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Graph Convolutional Networks (GCNs) for Molecular Property Prediction in Drug Development

Molecular property prediction is key to drug development. The rising of deep learning techniques provides new possibilities to learn the molecular properties directly from chemical data. In particular, graph convolutional networks have been introduced into the field and made significant enhancements compared to traditional methods. The first part of this paper serves as a study to explore and evaluate this emerging method while the second part demonstrates that graph convolution networks can be further improved by incorporating attention mechanism, another influential deep learning idea.No embargoAcademic Major: Computer and Information Scienc