Class RandomizedPCA<T>

Namespace

AiDotNet.Preprocessing.DimensionalityReduction

Assembly

AiDotNet.dll

Randomized PCA using randomized SVD for efficient computation.

public class RandomizedPCA<T> : TransformerBase<T, Matrix<T>, Matrix<T>>, IDataTransformer<T, Matrix<T>, Matrix<T>>

Type Parameters

T

The numeric type for calculations (e.g., float, double).

Inheritance

object

TransformerBase<T, Matrix<T>, Matrix<T>>

RandomizedPCA<T>

Implements

IDataTransformer<T, Matrix<T>, Matrix<T>>

Inherited Members

TransformerBase<T, Matrix<T>, Matrix<T>>.NumOps

TransformerBase<T, Matrix<T>, Matrix<T>>.Engine

TransformerBase<T, Matrix<T>, Matrix<T>>.IsFitted

TransformerBase<T, Matrix<T>, Matrix<T>>.ColumnIndices

TransformerBase<T, Matrix<T>, Matrix<T>>.SupportsInverseTransform

TransformerBase<T, Matrix<T>, Matrix<T>>.Fit(Matrix<T>)

TransformerBase<T, Matrix<T>, Matrix<T>>.Transform(Matrix<T>)

TransformerBase<T, Matrix<T>, Matrix<T>>.FitTransform(Matrix<T>)

TransformerBase<T, Matrix<T>, Matrix<T>>.InverseTransform(Matrix<T>)

TransformerBase<T, Matrix<T>, Matrix<T>>.GetFeatureNamesOut(string[])

TransformerBase<T, Matrix<T>, Matrix<T>>.FitCore(Matrix<T>)

TransformerBase<T, Matrix<T>, Matrix<T>>.TransformCore(Matrix<T>)

TransformerBase<T, Matrix<T>, Matrix<T>>.InverseTransformCore(Matrix<T>)

TransformerBase<T, Matrix<T>, Matrix<T>>.ValidateInputData(Matrix<T>)

TransformerBase<T, Matrix<T>, Matrix<T>>.EnsureFitted()

TransformerBase<T, Matrix<T>, Matrix<T>>.GetColumnsToProcess(int)

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Remarks

Randomized PCA uses randomized algorithms to efficiently compute principal components without computing the full SVD. It's much faster than standard PCA for large datasets while providing accurate approximations of the top components.

The algorithm: 1. Generate random projection matrix 2. Form sample matrix Y = A * Ω (project data to random subspace) 3. Orthonormalize Y using QR decomposition 4. Form B = Q^T * A (project to Q's range) 5. Compute SVD of B to get principal components

For Beginners: Randomized PCA is faster because: - It only computes the components you need (not all) - Random projection preserves structure efficiently - Power iteration improves accuracy if needed - Works well for low-rank data

Use cases:

• Very large datasets where standard PCA is slow
• When you only need top few components
• Streaming or online scenarios
• Memory-constrained environments

Constructors

RandomizedPCA(int, int, int, int?, int[]?)

Creates a new instance of RandomizedPCA<T>.

public RandomizedPCA(int nComponents = 2, int nOversamples = 10, int nPowerIter = 2, int? randomState = null, int[]? columnIndices = null)

Parameters

nComponents int

Target dimensionality. Defaults to 2.

nOversamples int

Additional random vectors for accuracy. Defaults to 10.

nPowerIter int

Number of power iterations for accuracy. Defaults to 2.

randomState int?

Random seed for reproducibility.

columnIndices int[]

The column indices to use, or null for all columns.

Properties

Components

Gets the principal components (each row is a component).

public double[,]? Components { get; }

Property Value

double[,]

ExplainedVariance

Gets the explained variance for each component.

public double[]? ExplainedVariance { get; }

Property Value

double[]

NComponents

Gets the number of components (dimensions).

public int NComponents { get; }

Property Value

int

SingularValues

Gets the singular values.

public double[]? SingularValues { get; }

Property Value

double[]

SupportsInverseTransform

Gets whether this transformer supports inverse transformation.

public override bool SupportsInverseTransform { get; }

Property Value

bool

Methods

FitCore(Matrix<T>)

Fits Randomized PCA using randomized SVD.

protected override void FitCore(Matrix<T> data)

Parameters

data Matrix<T>

GetExplainedVarianceRatio()

Gets the total explained variance ratio (proportion of total variance explained by selected components).

public double GetExplainedVarianceRatio()

Returns

double

A value between 0 and 1 representing the fraction of total variance captured.

GetFeatureNamesOut(string[]?)

Gets the output feature names after transformation.

public override string[] GetFeatureNamesOut(string[]? inputFeatureNames = null)

Parameters

inputFeatureNames string[]

Returns

string[]

InverseTransformCore(Matrix<T>)

Reconstructs data from the reduced representation.

protected override Matrix<T> InverseTransformCore(Matrix<T> data)

Parameters

data Matrix<T>

Returns

Matrix<T>

TransformCore(Matrix<T>)

Transforms data by projecting onto principal components.

protected override Matrix<T> TransformCore(Matrix<T> data)

Parameters

data Matrix<T>

Returns

Matrix<T>