Cross correlation matrix

The cross correlation matrix (often called ccmatrix in Dynamo jargon) of a set of N particles is an N X N matrix. Each entry (i,j) represents the similarity of particles i and j in the data set.

Definition of similarity

This similarity of particles i and j measured in terms of the normalized cross correlation of the the two aligned particles, filtered to their common fourier components, and restricted to a region in direct space (indicated by a classification mask). The pseudo code will run as:

1. Input
particles pi and pj
alignment parameters Ai and Aj
2. read particles i and j -> pi, pj
3. align particles i, and j -> Aipi, Ajpj
4. compute missing wedges for particles i and j -> Wi, Wj
5. rotate missing wedges -> RiWi, RjWj
6. compute Fourier coefficients common to bCoth rotated missing wedges
Cij = intersection(RiWi, RjWj)
7. filter pi with Cij
pi = F-1[ F(pi).* Cij ]
8. compare the filtered particles inside the classification mask.
ccmatrix(i,j)<- normalized cross correlation

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Input for ccmatrix construction

The minimal input is a set of particles (formatted as a data folder) and their alignment parameters (formatted as a table). You also may want to specify a classification mask and optatively additional mathematical operations on the particles (as bandpassing or symmetrization).

Computation of a ccmatrix

Dynamo typically implements the computation of a ccmatrix in independent blocks that can be handled separately by different cores.

Application of a ccmatrix

A ccmatrix is most commonly used in the context of PCA classification