Table of Contents

Class NCA<T>

Namespace
AiDotNet.Preprocessing.DimensionalityReduction
Assembly
AiDotNet.dll

Neighborhood Components Analysis (NCA) for supervised dimensionality reduction.

public class NCA<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
TransformerBase<T, Matrix<T>, Matrix<T>>
NCA<T>
Implements
IDataTransformer<T, Matrix<T>, Matrix<T>>
Inherited Members

Remarks

NCA is a supervised dimensionality reduction algorithm that learns a linear transformation to maximize the expected leave-one-out classification accuracy in the transformed space. It uses stochastic neighbor assignment for soft nearest-neighbor classification.

The algorithm: 1. Define soft neighbor probabilities using softmax over distances 2. Compute expected leave-one-out classification accuracy 3. Optimize transformation matrix using gradient descent 4. Project data using learned transformation

For Beginners: NCA learns a space where k-NN works well: - Points with same label are pulled closer together - Points with different labels are pushed apart - The learned transformation is linear (a matrix) - Can be used for feature extraction before classification

Use cases:

  • Preprocessing for k-NN classifiers
  • Metric learning for distance-based methods
  • Visualization with class structure preserved
  • Feature extraction for classification tasks

Constructors

NCA(int, int, double, double, int?, int[]?)

Creates a new instance of NCA<T>.

public NCA(int nComponents = 2, int maxIter = 100, double learningRate = 0.01, double tol = 1E-05, int? randomState = null, int[]? columnIndices = null)

Parameters

nComponents int

Target dimensionality. Defaults to 2.

maxIter int

Maximum number of optimization iterations. Defaults to 100.

learningRate double

Learning rate for gradient descent. Defaults to 0.01.

tol double

Tolerance for convergence. Defaults to 1e-5.

randomState int?

Random seed for reproducibility.

columnIndices int[]

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

Properties

NComponents

Gets the number of components (dimensions).

public int NComponents { get; }

Property Value

int

SupportsInverseTransform

Gets whether this transformer supports inverse transformation.

public override bool SupportsInverseTransform { get; }

Property Value

bool

TransformationMatrix

Gets the learned transformation matrix.

public double[,]? TransformationMatrix { get; }

Property Value

double[,]

Methods

FitCore(Matrix<T>)

Fits NCA (without labels - uses unsupervised initialization).

protected override void FitCore(Matrix<T> data)

Parameters

data Matrix<T>

Remarks

This method provides a fallback when no labels are available. For best results, use the Fit(data, labels) overload with class labels.

FitTransformSupervised(Matrix<T>, int[])

Fits NCA using the provided data and labels, then transforms the data.

public Matrix<T> FitTransformSupervised(Matrix<T> data, int[] labels)

Parameters

data Matrix<T>

The input data matrix.

labels int[]

The class labels for each sample.

Returns

Matrix<T>

The transformed data projected onto the learned space.

GetFeatureNamesOut(string[]?)

Gets the output feature names after transformation.

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

Parameters

inputFeatureNames string[]

Returns

string[]

InverseTransformCore(Matrix<T>)

Inverse transformation is not supported.

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

Parameters

data Matrix<T>

Returns

Matrix<T>

TransformCore(Matrix<T>)

Transforms data using the learned transformation matrix.

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

Parameters

data Matrix<T>

Returns

Matrix<T>
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