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 p_i and p_j

   alignment parameters A_i and A_j

   classification mask m

2. read particles i and j -> p_i, p_j
3. align particles i, and j -> A_ip_i, A_jp_j
4. compute missing wedges for particles i and j -> W_i, W_j
5. rotate missing wedges -> R_iW_i, R_jW_j
6. compute Fourier coefficients common to bCoth rotated missing wedges

   C_ij = intersection(R_iW_i, R_jW_j)

7. filter p_i with C_ij

   p_i = F^-1[ F(p_i).* C_ij ]

8. compare the filtered particles inside the classification mask.

   ccmatrix(i,j)<- normalized cross correlation

&ptilde;

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