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 regular 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

Predefined exploring tools

You can use a general browser for Dynamo tables:

wb.exploreGUI;

general tool for exploring tables

Advanced users: This is just a wrapper to the function dpktbl.gui applied on the eigentable produced by the workflow.

For instance, you can check how two eigencomponents relate to each other:

scatter tab tuned to show co-behaviour of first two eigencomponents

Pressing the [Scatter 2D] button will create this interactive plot

scatterplot eigencomponents

Where each point represents a different particle. Right-click on it to create a "lasso", a tool to hand-draw sets of particles.

right click to get the options to manually select particles through a lasso tool

lasso particles

Right clicking on the "lassoed" particles give you the option of saving the information on the selected set of particles.

right click on the lasso to get options on that subset of particles

Custom approach

You can use your own methods to visualize the eigencomponents. They can be accessed through:

m = w.getEigencomponents();

will produce a matrix m where each column represents an eigenvector and each row a particle. Thus, to see how a particular eigencomponent distributes among the particles, you can just write:

plot(m(:,i),'.'); 

first eigencomponent of each particle

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(); 

this will produce ten plots (as i=1:10) collected in a single GUI. Each plot is called a "frame", and you can view them sequentially or in sets, just play with the layout given by the rows and columns, and use the [Refresh] icon on the top left of the GUI.

sliding montage on the distribution of several eigencomponent

Series of histograms

sliding montage of sets of eigencomponent

Eigenvolumes

eigSet=wb.getEigenvolume(1:30);

This creates a cell array (arbitrarily called eigSet). We can visualise it through:

mbvol.groups.montage(eigSet); 

eigenvolumes

This plot is showing the true relative intensity of the eigenvolumes. In order to compare them, we can show the normalised eigenvolumes instead:

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

eigenvolumes after nomrmalization

Correlation of tilts

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

wb.show.correlationEigenvectorTilt(1:10) 

correlation of eigencomponens with tilt

Remember that each particle is accessible through right clicking on it.

right click on each point to access the particle

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"

TSNE reduction

We create on the fly the TSNE reduction for eigencomponents:

wb.show.tsne([1,2,4,5]);

will produce the graphics:

tsne clustering

TSNE has created a bidimensional proximity map for the 4-dimensional distribution induced by the 4 selected eigenvectors. Note that you can enter a cell array of several sets of indices. You could then navigate through different indices to check the shape of the TSNE reduction for different selections of eigenvolumes:

# wb.show.tsne({[1,2,4,5] , [1:6]});

Automated clustering

Right clicking on a plot you get an option to automatically segment it using the dbscan method

right click on the axes for an automated clustering

This functionality is intended to let you get a feeling of the results you would get if you would use dbscan in an algorithm.

automated clustering

The results are reasonable, but inferior to what human inspection would yield.

Manual clustering

We first right click on the axis to get a lasso tool.

right click on the axes to select a set of particles

Remember that you will have a different plot (depending on the random seed used in TSNE). However, you will probably have at least a well defined cluster.

use the lasso tool to select a group

lassoed particles can be averaged together

average of particles inside lasso

a second lasso can be created

After delimiting the second subset, we can create the class averages corresponding to this manual selection.

average all manually selected clusters

On opening, dmapview will show all slices of a single volume:

dmapview on opening

Use the "simultaneous view" icon in the toolbar to show the two volumes together.

showing several volumes in dmapview

correspondig slices of

you can select a single slice for depiction

use keys 1 and 2 to set anchors

right click one anchor to show an intensity profile

intensity profile

Manipulation of PCA workflows

Reading workflows

The workflow object can be recreated by reading the workflow folder.

wb2 = dread('classtest128');

It however needs to be unfolded before using:

wb2.unfold();

Workflow GUIs

Execution of a PCA workflow can be controlled graphically through:

wb.workflowGUI()