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Showing content from http://accord-framework.net/docs/html/T_Accord_Statistics_Analysis_KernelDiscriminantAnalysis.htm below:

Kernel (Fisher) Discriminant Analysis.

Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0

[SerializableAttribute]
public class KernelDiscriminantAnalysis : BaseDiscriminantAnalysis, 
	ISupervisedLearning<KernelDiscriminantAnalysisPipeline, double[], int>

<SerializableAttribute>
Public Class KernelDiscriminantAnalysis
	Inherits BaseDiscriminantAnalysis
	Implements ISupervisedLearning(Of KernelDiscriminantAnalysisPipeline, Double(), Integer)

The KernelDiscriminantAnalysis type exposes the following members.

Classifies a new instance into one of the available classes.

Classifies new instances into one of the available classes.

Classifies a new instance into one of the available classes.

Computes the Multi-Class Kernel Discriminant Analysis algorithm.

Creates additional information about principal components.

Gets the output of the discriminant function for a given class.

Determines whether the specified object is equal to the current object.

Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.

Serves as the default hash function.

Returns the minimum number of discriminant space dimensions (discriminant factors) required to represent a given percentile of the data.

Gets the Type of the current instance.

Obsolete.

Initializes common properties.

Learns a model that can map the given inputs to the given outputs.

Creates a shallow copy of the current Object.

Returns a string that represents the current object.

Obsolete.

Applies the transformation to an input, producing an associated output.

Applies the transformation to an input, producing an associated output.

Obsolete.

Obsolete.

Obsolete.

Applies the transformation to an input, producing an associated output.

Checks whether an object implements a method with the given name.

Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.

Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.

Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.

Kernel (Fisher) discriminant analysis (kernel FDA) is a non-linear generalization of linear discriminant analysis (LDA) using techniques of kernel methods. Using a kernel, the originally linear operations of LDA are done in a reproducing kernel Hilbert space with a non-linear mapping.

The algorithm used is a multi-class generalization of the original algorithm by Mika et al. in Fisher discriminant analysis with kernels (1999).

This class can also be bound to standard controls such as the DataGridView by setting their DataSource property to the analysis' Discriminants property.

References:

• Mika et al, Fisher discriminant analysis with kernels (1999). Available on http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.9904

double[][] inputs = 
{
    
    new double[] {  4,  1 }, 
    new double[] {  2,  4 },
    new double[] {  2,  3 },
    new double[] {  3,  6 },
    new double[] {  4,  4 },

    
    new double[] {  9, 10 },
    new double[] {  6,  8 },
    new double[] {  9,  5 },
    new double[] {  8,  7 },
    new double[] { 10,  8 }
};

int[] output = 
{
    0, 0, 0, 0, 0, 
    1, 1, 1, 1, 1  
};



var kda = new KernelDiscriminantAnalysis()
{
    Kernel = new Linear() 
};


var classifier = kda.Learn(inputs, output); 


double[][] projection = kda.Transform(inputs);


int[] results = kda.Classify(inputs);

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