# 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: ``` ```

```Input particles pi and pj alignment parameters Ai and Aj classification mask m read particles i and j -> pi, pj align particles i, and j -> Aipi, Ajpj compute missing wedges for particles i and j -> Wi, Wj rotate missing wedges -> RiWi, RjWj compute Fourier coefficients common to bCoth rotated missing wedges Cij = intersection(RiWi, RjWj) filter pi with Cij pi = F-1[ F(pi).* Cij ] 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