# Walkthrough on PCA through the command line (Copenhagen 2024)

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

## Contents

- 1 Creation of a synthetic data set
- 2 Creation of a workflow
- 3 Running
- 4 Visualization
- 5 Running
- 6 Visualization
- 7 Manipulation of PCA workflows

# 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 of the, are slightly smaller 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*). - a table that expresses the alignment.
- a mask that indicates the area of each alignment particle that will be taken into account during the classification procedure.

All three have been generated by the `dtutorial` command.

### 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

wb.setBand([0,0.5,2]); % in Nyquist. % Third parameter is the smoothing factor in pixels

- symmetry

wb.setSym('c8');

- binning level (to accelerate the computations);

wb.settings.general.bin.value = 0;

## 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. In each block, two subsets of (prealigned) particles are read from disk.

To use all the available cores in your local machine, write:

wb.settings.computing.cores.value = '*';

#### GPU computing

By default, the ccmatrix computation will run on the CPUs. To force computation in the GPUs (**be certain that you have enough GPUs in your laptop to use this option**) you need to active (that is, `= true`

) them first:

wb.settings.computing.useGpus.value = false;

You could also specify specify the device numbers ( `wb.settings.computing.gpus.value = [0:7];`

)

Take into account that your system needs an independent CPU for each used GPU.

### Size of parallel blocks

The size of the blocks is controlled by the parameter `batch`. You can tune it with:

wb.setBatch(100);

meaning that each block executed in parallel will preload two sets of 100 (prealigned) particles into memory, and then proceed to cross correlate all possible pairs. Ideally, you should tune your `batch` parameters l to have as many blocks as processing units (CPU cores or GPUs).
IThis might not be possible, as it might crowd the memory of your device. Thus, in real applications you should aim at using the `batch` parameter to enforce a tradeoff between performance and memory usage suited to your system.

If you get an error when running `wb.setBatch(n);` this is a bug. Try unfolding the project first (`wb.unfold()`), setting the batch number then unfolding again before running calculations.

#### Utilities to set the batch number

You can get some guidance for the selection of the batch number with

wb.getBlockSize()

which will return the size of each block (in Gibabytes) for the current batch parameter. This number depends of the mask, as the block contains in memory only the part of each particle that is inside the mask.

## Unfolding

Before running the workflow, it needs to be *unfolded*. This operation checks the mutual coherence of the different elements of the workflow, and prepares the file system for runtime.

wb.unfold();

# 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.tsne.compute();

# Visualization

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

## Correlation matrix

We can visualise the cross correlation matrix

m=wb.getCCMatrix();figure;dshow(m);h=gca();h.YDir = 'reverse';

## Eigencomponents

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 = wb.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 (be aware of the single-line requirements for the dynamo shell):

for i = 1:5 figure; plot(m(:,i), m(:,i+1), '.'); end

### 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.

## 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.

## Mathematical parameters

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

- bandpass

wb.setBand([0,0.5,2]); % in Nyquist. % Third parameter is the smoothing factor in pixels

- symmetry

wb.setSym('c8');

- binning level (to accelerate the computations);

wb.settings.general.bin.value = 0;

## 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. In each block, two subsets of (prealigned) particles are read from disk.

To use all the available cores in your local machine, write:

wb.settings.computing.cores.value = '*';

#### GPU computing

By default, the ccmatrix computation will run on the CPUs. To force computation in the GPUs (**be certain that you have enough GPUs in your laptop to use this option**) you need to active (that is, `= true`

) them first:

wb.settings.computing.useGpus.value = false;

You could also specify specify the device numbers ( `wb.settings.computing.gpus.value = [0:7];`

)

Take into account that your system needs an independent CPU for each used GPU.

### Size of parallel blocks

The size of the blocks is controlled by the parameter `batch`. You can tune it with:

wb.setBatch(100);

meaning that each block executed in parallel will preload two sets of 100 (prealigned) particles into memory, and then proceed to cross correlate all possible pairs. Ideally, you should tune your `batch` parameters l to have as many blocks as processing units (CPU cores or GPUs).
IThis might not be possible, as it might crowd the memory of your device. Thus, in real applications you should aim at using the `batch` parameter to enforce a tradeoff between performance and memory usage suited to your system.

If you get an error when running `wb.setBatch(n);` this is a bug. Try unfolding the project first (`wb.unfold()`), setting the batch number then unfolding again before running calculations.

#### Utilities to set the batch number

You can get some guidance for the selection of the batch number with

wb.getBlockSize()

which will return the size of each block (in Gibabytes) for the current batch parameter. This number depends of the mask, as the block contains in memory only the part of each particle that is inside the mask.

## Unfolding

Before running the workflow, it needs to be *unfolded*. This operation checks the mutual coherence of the different elements of the workflow, and prepares the file system for runtime.

wb.unfold();

# 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.tsne.compute();

# Visualization

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

## Correlation matrix

We can visualise the cross correlation matrix

`m=wb.getCCMatrix();`

`figure;dshow(m);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 = wb.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.

## 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

If you're exploring this section, you might have encountered an issue with your PCA computation or accidentally closed your Dynamo shell. Alternatively, if you've just completed the walkthrough, you might be curious about what this section offers. It is helpful in both scenarios: recovering from interruptions and providing extra information into managing PCA workflows.

## Reading workflows

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

wb2 = dread('classtest128');

Note that we can name the workflow with an arbitrary variable name.

The workflow needs to be unfolded before being used:

wb2.unfold();

This concerns not only recomputation of selected steps, but also use of graphical exploration options.