  In single-particle cryo-electron microscopy (cryo-EM), K-means clustering
algorithm is widely used in unsupervised 2D classification of projection images
of biological macromolecules. 3D ab initio reconstruction requires accurate
unsupervised classification in order to separate molecular projections of
distinct orientations. Due to background noise in single-particle images and
uncertainty of molecular orientations, traditional K-means clustering algorithm
may classify images into wrong classes and produce classes with a large
variation in membership. Overcoming these limitations requires further
development on clustering algorithms for cryo-EM data analysis. We propose a
novel unsupervised data clustering method building upon the traditional K-means
algorithm. By introducing an adaptive constraint term in the objective
function, our algorithm not only avoids a large variation in class sizes but
also produces more accurate data clustering. Applications of this approach to
both simulated and experimental cryo-EM data demonstrate that our algorithm is
a significantly improved alterative to the traditional K-means algorithm in
single-particle cryo-EM analysis.
