Walkthrough on PCA through the command line

PCA computations through the command line are governed through PCA workflow objects. We describe here how to create and handle them:

Creation of a synthetic data set

dtutorial ttest128 -M 64 -N 64 -linear_tags 1 -tight 1

This generates a set of 128 particles where 64 are slightly closer than the other 64. The particle subtomogram are randomly oriented, but the alignment parameters are known.

Creation of a workflow

Input elements

The input of a PCA workflow are:

• a set of particles (called data container in this article)
• a table that expreses the alignment
• a mask that indicates the area of each alignment particle that will be taken into account during the classification procedure.

Data

dataFolder = 'ttest128/data';

Table

tableFile  = 'ttest128/real.tbl';

Mask

We create a cylindrical mask with the dimensions of the particles (40 pixels) mask = dcylinder([20,20],40);

Syntax

We decide a name for the workflow itself, for instance

name = 'classtest128';

Now we are ready to create the workflow:

 wb = dpkpca.new(name,'t',tableFile,'d',dataFolder,'m',mask);

This creates an workflow object (arbitrarily called wb in the workspace during the current session). It also creates a folder called classtest128.PCA where results will be stored as they are produced.

Mathematical parameters

The main parameters that can be chosen in this area are:

• bandpass
• symmetry
• binning level (to accelerate the computations)

Computational parameters

The main burden of the PCA computation is the creation of the cross correlation matrix.

Computing device

PCA computations can be run on GPUs of on CPUs, in both cases in parallel.

Size of parallel blocks

The

Running

In this workflow we run the steps one by one to discuss them. In real workflows, you can use the run methods to just launch all steps sequentially.

Prealigning

wb.steps.items.prealign.compute(); 

Correlation matrix

All pairs of correlations are computed in blocks, as described above

wb.steps.items.ccmatrix.compute(); 

Eigentable

The correlation matrix is diagonalised. The eigenvectors are used to expressed as the particles as combinations of weights.

wb.steps.items.eigentable.compute(); 

These weights are ordered in descending order relative to their impact on the variance of the set, ideally a particle should be represented by its few components on this basis. The weights are stored in a regula Dynamo table. First eigencomponent of a particle goes into column 41.

Eigenvolumes

The eigenvectors are expressed as three=dimensional volumes.

wb.steps.items.eigenvolumes.compute(); 

TSNE reduction

TSNE remaps the particles into 2D maps which can be visualised and operated interactively.

wb.steps.items.tsene.compute(); 

Visualization

Computed elements have been stored in the workflow folder. Some of them () can be directly access through workflow tools.

Correlation matrix

m=wb.getCCMatrix();

figure;dshow(cmm);h=gca();h.YDir = 'reverse';

Eigencomponents

Series of plots

To check all the eigencomponents, it is a good idea to do some scripting. The script below uses a handy Dynamo trick to create several plots in the same figure.

 gui = mbgraph.montage();
for i=1:10
    plot(m(:,i),'.','Parent',gui.gca);
    % gui.gca captures the
      gui.step;
end
gui.first();
gui.shg(); 

Eigenvolumes

eigSet=wb.getEigenvolume(1:30);

mbvol.groups.montage(eigSet); 

mbvol.groups.montage(dynamo_normalize_roi(eigSet)); 

Correlation of tilts

It is a good idea to check if some eigenvolumes correlate strongly with the tilt.

wb.show.correlationEigenvectorTilt(1:10) 

In this plot, each point represents a particle in your data set. We see that in this particular experiment, eigencomponent 3 seems to have been "corrupted by the missing wedge"