Distributed Processing

Note

Distributed processing mode for Principal Component Analysis is not available on GPU.

This mode assumes that data set is split in nblocks blocks across computation nodes.

PCA computation in the distributed processing mode follows the general schema described in Algorithms.

Algorithm Parameters

The PCA algorithm in the distributed processing mode has the following parameters, depending on the computation method parameter method:

Parameter

Method

Default Value

Description

computeStep

defaultDense or svdDense

Not applicable

The parameter required to initialize the algorithm. Can be:

  • step1Local - the first step, performed on local nodes

  • step2Master - the second step, performed on a master node

algorithmFPType

defaultDense or svdDense

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

method

Not applicable

defaultDense

Available computation methods for PCA computation:

  • defaultDense - the correlation method

  • svdDense - the SVD method

covariance

defaultDense

SharedPtr<covariance::Distributed <computeStep, algorithmFPType, covariance::defaultDense> >

The correlation and variance-covariance matrices algorithm to be used for PCA computations with the correlation method. For details, see Correlation and Variance-covariance Matrices. Distributed Processing.

Use the following two-step schema:

Step 1 - on Local Nodes

In this step, the PCA algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input ID

Input

data

Pointer to the \(n_i \times p\) numeric table that represents the Lmath:i-th data block on the local node. The input can be an object of any class derived from NumericTable.

In this step, PCA calculates the results described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Result ID

Result

nObservationsCorrelation

Pointer to the \(1 \times 1\) numeric table with the number of observations processed so far on the local node.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define it as an object of any class derived from NumericTable except CSRNumericTable.

crossProductCorrelation

Pointer to the \(p \times p\) numeric table with the cross-product matrix computed so far on the local node.

Note

By default, this table is an object of the HomogenNumericTable class, but you can define it as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

sumCorrelation

Pointer to the \(1 \times p\) numeric table with partial sums computed so far on the local node.

Note

By default, this table is an object of the HomogenNumericTable class, but you can define it as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

In this step, the PCA algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input ID

Input

data

Pointer to the \(n_i \times p\) numeric table that represents the Lmath:i-th data block on the local node. The input can be an object of any class derived from NumericTable.

In this step, PCA calculates the results described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Result ID

Result

nObservationsCorrelation

Pointer to the \(1 \times 1\) numeric table with the number of observations processed so far on the local node.

Note

By default, this result is an object of the HomogenNumericTable class, but you can define it as an object of any class derived from NumericTable except CSRNumericTable.

sumSVD

Pointer to the \(1 \times p\) numeric table with partial sums computed so far on the local node.

Note

By default, this table is an object of the HomogenNumericTable class, but you can define it as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

sumSquaresSVD

Pointer to the \(1 \times p\) numeric table with partial sums of squares computed so far on the local node.

Note

By default, this table is an object of the HomogenNumericTable class, but you can define it as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

auxiliaryDataSVD

A collection of numeric tables each with the partial result to transmit to the master node for Step 2.

Note

The collection can contain objects of any class derived from NumericTable except the PackedSymmetricMatrix and PackedTriangularMatrix.

Step 2 - on Master Node

In this step, the PCA algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input ID

Input

partialResults

A collection that contains results computed in Step 1 on local nodes (nObservationsCorrelation, crossProductCorrelation, and sumCorrelation).

Note

The collection can contain objects of any class derived from NumericTable except the PackedSymmetricMatrix and PackedTriangularMatrix.

In this step, PCA calculates the results described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Result ID

Result

eigenvalues

Pointer to the \(1 \times p\) numeric table that contains eigenvalues in the descending order.

eigenvectors

Pointer to the \(p \times p\) numeric table that contains eigenvectors in the row-major order.

Note

By default, these results are object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

In this step, the PCA algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Input ID

Input

partialResults

A collection that contains results computed in Step 1 on local nodes (nObservationsSVD, sumSVD, sumSquaresSVD, and auxiliaryDataSVD).

Note

The collection can contain objects of any class derived from NumericTable except the PackedSymmetricMatrix and PackedTriangularMatrix.

In this step, PCA calculates the results described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Result ID

Result

eigenvalues

Pointer to the \(1 \times p\) numeric table that contains eigenvalues in the descending order.

eigenvectors

Pointer to the \(p \times p\) numeric table that contains eigenvectors in the row-major order.

Note

By default, these results are object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.