Class PCA<T>

Namespace

AiDotNet.Preprocessing.DimensionalityReduction

Assembly

AiDotNet.dll

Principal Component Analysis for dimensionality reduction.

public class PCA<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>>

PCA<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

PCA finds the directions of maximum variance in the data and projects the data onto these principal components. This reduces dimensionality while preserving as much variance as possible.

PCA is useful for: - Reducing the number of features while retaining most information - Removing multicollinearity between features - Visualizing high-dimensional data - Noise reduction

For Beginners: PCA transforms your features into new features called "principal components" that are: - Uncorrelated with each other - Ordered by importance (how much variance they explain) - Linear combinations of your original features

Example: 100 features might be reduced to 10 principal components that capture 95% of the information in your data.

Constructors

PCA(int?, double?, bool, int[]?)

Creates a new instance of PCA<T>.

public PCA(int? nComponents = null, double? varianceRatio = null, bool whiten = false, int[]? columnIndices = null)

Parameters

nComponents int?

Number of components to keep. If null, keeps all.

varianceRatio double?

Keep enough components to explain this variance ratio (0-1). Overrides nComponents if set.

whiten bool

If true, scale components to unit variance. Defaults to false.

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[]

ExplainedVarianceRatio

Gets the explained variance ratio for each component.

public double[]? ExplainedVarianceRatio { get; }

Property Value

double[]

Mean

Gets the mean of each feature.

public double[]? Mean { get; }

Property Value

double[]

NComponents

Gets the number of components to keep.

public int? NComponents { get; }

Property Value

int?

NComponentsOut

Gets the number of components after fitting.

public int NComponentsOut { 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

VarianceRatio

Gets the target variance ratio to retain.

public double? VarianceRatio { get; }

Property Value

double?

Whiten

Gets whether whitening is applied.

public bool Whiten { get; }

Property Value

bool

Methods

FitCore(Matrix<T>)

Fits PCA by computing principal components.

protected override void FitCore(Matrix<T> data)

Parameters

data Matrix<T>

The training data matrix.

GetFeatureNamesOut(string[]?)

Gets the output feature names after transformation.

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

Parameters

inputFeatureNames string[]

Returns

string[]

InverseTransformCore(Matrix<T>)

Transforms data back to original space.

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

Parameters

data Matrix<T>

The transformed data.

Returns

Matrix<T>

Data in original feature space.

TransformCore(Matrix<T>)

Transforms the data by projecting onto principal components.

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

Parameters

data Matrix<T>

The data to transform.

Returns

Matrix<T>

The transformed data.