Author(s)

Marin van Heel^1,2,3, Rodrigo V. Portugal³, Michael Schatz⁴

¹Institute of Biology Leiden, Leiden University, NeCEN, Leiden, The Netherlands.
²Sir Ernst Chain Building, Imperial College London, London, UK.
³Brazilian Nanotechnology National Laboratory, CNPEM, Campinas, Brazil.
⁴Image Science Software GmbH, Berlin, Germany.

Biology is a challenging and complicated mess. Understanding this challenging complexity is the realm of the biological sciences: Trying to make sense of the massive, messy data in terms of discovering patterns and revealing its underlying general rules. Among the most powerful mathematical tools for organizing and helping to structure complex, heterogeneous and noisy data are the tools provided by multivariate statistical analysis (MSA) approaches. These eigenvector/eigenvalue data-compression approaches were first introduced to electron microscopy (EM) in 1980 to help sort out different views of macromolecules in a micrograph. After 35 years of continuous use and developments, new MSA applications are still being proposed regularly. The speed of computing has increased dramatically in the decades since their first use in electron microscopy. However, we have also seen a possibly even more rapid increase in the size and complexity of the EM data sets to be studied. MSA computations had thus become a very serious bottleneck limiting its general use. The parallelization of our programs—speeding up the process by orders of magnitude—has opened whole new avenues of research. The speed of the automatic classification in the compressed eigenvector space had also become a bottleneck which needed to be removed. In this paper we explain the basic principles of multivariate statistical eigenvector-eigenvalue data compression; we provide practical tips and application examples for those working in structural biology, and we provide the more experienced researcher in this and other fields with the formulas associated with these powerful MSA approaches.

Single Particle Cryo-EM, Multivariate Statistical Analysis, Unsupervised Classification, Modulation Distance, Manifold Separation

Heel, M. , Portugal, R. and Schatz, M. (2016) Multivariate Statistical Analysis of Large Datasets: Single Particle Electron Microscopy. Open Journal of Statistics, 6, 701-739. doi: 10.4236/ojs.2016.64059.