Principal component analysis

In general, a Principal Component Analysis (PCA) aims at analyzing a data set and discovering a set of coordinates that capture the most representative features of said data. Often the term PCA classification is loosely used. PCA is not a classification method: classification itself is performed on the features extracted through PCA.

In Dynamo, the PCA is the process of finding a reduced set of "eigenvolumes" that allow to approximatively represent each particle in our data set as a combination of these eigenvolumes. Which this representation, a generic particle can be represented by the contributions of each "eigenvolume" to the particle, i.e., by a set of "eigencomponents", normally in a number no much higher than 20.

Once the particles are represent by small sets of scalars, they can be classified with standard methods like k-means.

Operative steps

PCA classifications are most easily handled through classification projects. These projects can be controled through GUIs or the command line

In whichever way you control the classification project, operatively a PCA based classification will require the completion of these steps:

Selecting the input

a data folder, a table, a mask

Computing a cross-correlation matrix

Computing the eigenvalues, eigenvolumes and eigencomponents

Using the eigencomponents to create a classification.

Input

PCA is computed on a set of aligned particles. Thus, you need a data folder and a table that describes the alignment. In the most common case, you want to focus the classification in a region of the box, so that you need a classification mask.

Additionally, there are some fine tuning parameters that can be passed: particles can be symmetrized, resized or bandpassed.

Computation of cross-correlation matrix

Main article: Cross correlation matrix

All the aligned particles are compared to each other through cross correlation. This produces an NxN matrix for a set of N matrix. This is typically the most time consuming part of the PCA workflow.

Computation of PCA

Eigenvalues

The cross-correlation matrix is diagonalized, producing a set eigenvalues which should decay to zero (the slower the decay, the more eigenvolumes will be relevant). This computation occurs very fast.

Eigenvolumes

To each eigenvalue an eigenvector is attached. Eigenvectors are called eigenvolumes in this context. Note that they will be only defined inside the classification mask attached to the classification.

Eigencomponents

Main article: Eigentable

Also a time consuming step (although much less intensive than the computation of the ccmatrix). Each particle is compared to each eigenvolume.

GUIs for PCA classification

There are two GUIs available to cover the pipeline through a classification project:

dynamo_ccmatrix_project_manager

for setting up the project and computing the ccmatrix

dynamo_ccmatrix_analysis

to use a previously computed ccmatrix. Computes a PCA on it, and allows running different classification experiments on the result of the PCA.

In the general case, you will use dynamo_ccmatrix_project_manager to set up a project for ccmatrix computation very quickly, put the project to run, go for coffee, lunch or sleep (depending on the number or particles), and then go back to office to use the result of the prokject (a ccmatrix to define a PCA interacting with the dynamo_ccmatrix_analysis GUI.

dynamo_ccmatrix_project_manager

It is a rather general tool to define ccmatrix projects in different situations (from scratch, deriving them from other projects..).

Creating a project from scratch

We will work with the Derived ccmatrix project panel. This panel contains the settings for the project to be created in a session of dynamo_ccmatrix_project_manager (the source project panel is used when you want to apply PCA on the results of an alignment project).

Enter the name of the project in the project field, and fill the fields for data, table and mask.

Optatively, additional numerical parameters can be chosen in the Actions panel: symmetrization, bandpassing or resizing (to increase speed).

Preparing a project for execution

We are back into the Derived ccmatrix project panel. Here, you have to decide in which environment to execute the project: Matlab or standalone, and in which case how many cores to use. GPU computations are not available for classification projects. For big matrices (i.e. big data sets), you'll need to tune the batch parameter, which controls how many particles are kept in memory in any given time.

dynamo_ccmatrix_analysis

This GUI can be invoked directly from dynamo_ccmatrix_project_manager, or opened directly on an existing project.

Computing a PCA

You need to check if an Xmatrix is available. If not, just ask Dynamo to compute one.

PCA classification through the command line

This is explained in the tutorial below: XX

Tutorials

There are some pdf tutorials available inside the Dynamo distribution:

• General introduction to PCA based classification. XX
• Command line classification. XX

GPU in PCA

GPU computing can not be used for PCA computations. The kind of computations carried during PCA are not "GPU friendly": in order to create the cross correlation matrix, individual particles are accessed in the disk, rotated just once, and filtered with the missing wedge of a different particle in order to compute the similarity measurement between the two particles. This means that once a particle has been transfer to memory, the number of actions operated on the same particle is rather reduced. This is not a favorable scenario for the GPU.