Principal Components Analysis Transform

The PCA transform algorithm transforms the data set to principal components.

Details

Given a transformation matrix T
computed by PCA (eigenvectors in row-major order) and data set X
as input, the PCA Transform algorithm transforms input data set X
of size $LaTex Math image.$ to the data set Y
of size $LaTex Math image.$ , $LaTex Math image.$ .

Batch Processing

Algorithm Input

The PCA Transform 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	Use when the input data is a normalized or non-normalized data set. Pointer to the $LaTex Math image.$ numeric table that contains the input data set. This input can be an object of any class derived from NumericTable .
eigenvectors	Principal components computed using the PCA algorithm. Pointer to the $LaTex Math image.$ numeric table $LaTex Math image.$ . You can define it as an object of any class derived from NumericTable , except for PackedSymmetricMatrix , PackedTriangularMatrix , and CSRNumericTable .
dataForTransform	Optional. Pointer to the key value-data collection containing the following data for PCA. The collection contains the following key-value pairs: mean means variance variances eigenvalue eigenvalues If you do not provide the collection, the library will not apply the corresponding centering, normalization or whitening operation. If one of the numeric tables in collection is NULL , the corresponding operation will not be applied: centering for means, normalization for variances, whitening for eigenvalues. If mean or variance tables exist, it should be a pointer to the $LaTex Math image.$ numeric table. If eigenvalue table is not NULL , it is the pointer to ( $LaTex Math image.$ ) numeric table, where the number of the columns is greater than or equal to nComponents .

Algorithm Parameters

The PCA Transform algorithm has the following parameters:

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 .
nComponents	defaultDense	0	The number of principal components $LaTex Math image.$ . If zero, the algorithm will compute the result for $LaTex Math image.$ .

Algorithm Output

The PCA Transform algorithm calculates the results described below. Pass the

Result ID

as a parameter to the methods that access the results of your algorithm.

Result ID	Result
transformedData	Pointer to the $LaTex Math image.$ numeric table that contains data projected to the proncipal components basis. By default, this result is an 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 .