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Contents

Online Processing

Note

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

Online processing computation mode assumes that data arrives in blocks \(i = 1, 2, 3, \ldots, \mathrm{nblocks}\).

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

Algorithm Input

The PCA algorithm in the online processing mode 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.

Algorithm Input for Principal Component Analysis (Online Processing)

Input ID	Input
data	Pointer to the \(n_i \times p\) numeric table that represents the current data block. The input can be an object of any class derived from NumericTable.

Algorithm Parameters

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

Algorithm Parameters for Principal Component Analysis (Online Processing)

Parameter	Method	Default Value	Description
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
initializationProcedure	defaultDense or svdDense	Not applicable	The procedure for setting initial parameters of the algorithm in the online processing mode. By default, the algorithm with the defaultDense method initializes nObservationsCorrelation, sumCorrelation, and crossProductCorrelation with zeros. By default, the algorithm with the svdDense method initializes nObservationsSVD, sumSVD, and sumSquaresSVD with zeros.
covariance	defaultDense	SharedPtr<covariance::Online<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. Online Processing.

Partial Results

The PCA algorithm in the online processing mode calculates partial results described below. They depend on the computation method. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Correlation method (defaultDense)SVD method (svdDense)

Partial Results for Principal Component Analysis using Correlation method (Online Processing)

Result ID	Result
nObservationsCorrelation	Pointer to the \(1 \times 1\) numeric table with the number of observations processed so far. 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 partial cross-product matrix computed so far. 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. 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.

Algorithm Output

The PCA algorithm in the online processing mode 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.

Algorithm Output for Principal Component Analysis (Online Processing)

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 objects of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and CSRNumericTable.

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