# 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 $$n \times p$$ to the data set $$Y$$ of size $$n \times p_r$$, $$pr \leq p$$.

## 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 $$n \times p$$ 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 $$p_r \times p$$ numeric table $$(p_r \leq p)$$. 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

Note

• 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 $$1 \times p$$ numeric table.

• If eigenvalue table is not NULL, it is the pointer to ($$1 \times \text{nColumns}$$) 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 $$(p_r \leq p)$$. If zero, the algorithm will compute the result for $$\text{nComponents} = p_r$$.

### 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 $$n \times p_r$$ numeric table that contains data projected to the principal components basis.

Note

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.

## Examples¶

Batch Processing:

Note

There is no support for Java on GPU.

Batch Processing:

Batch Processing:

Batch Processing: