# 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:

## Contents

# 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;

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:

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

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

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

### 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.

### Series of histograms

## Eigenvolumes

eigSet=wb.getEigenvolume(1:30);

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

mbvol.groups.montage(eigSet);

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));

## Correlation of tilts

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

wb.show.correlationEigenvectorTilt(1:10)

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

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 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

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

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.

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.

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

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

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

# 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()