Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

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

Linear Discriminant Analysis (LDA).

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

[SerializableAttribute]
public class LinearDiscriminantAnalysis : BaseDiscriminantAnalysis, 
	IDiscriminantAnalysis, IMultivariateAnalysis, IAnalysis, IProjectionAnalysis, ISupervisedLearning<LinearDiscriminantAnalysisPipeline, double[], int>

<SerializableAttribute>
Public Class LinearDiscriminantAnalysis
	Inherits BaseDiscriminantAnalysis
	Implements IDiscriminantAnalysis, IMultivariateAnalysis, IAnalysis, IProjectionAnalysis, 
	ISupervisedLearning(Of LinearDiscriminantAnalysisPipeline, Double(), Integer)

The LinearDiscriminantAnalysis type exposes the following members.

Transform 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 Linear 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.

Linear Discriminant Analysis (LDA) is a method of finding such a linear combination of variables which best separates two or more classes.

In itself LDA is not a classification algorithm, although it makes use of class labels. However, the LDA result is mostly used as part of a linear classifier. The other alternative use is making a dimension reduction before using nonlinear classification algorithms.

It should be noted that several similar techniques (differing in requirements to the sample) go together under the general name of Linear Discriminant Analysis. Described below is one of these techniques with only two requirements:

1. The sample size shall exceed the number of variables, and
2. Classes may overlap, but their centers shall be distant from each other.

Moreover, LDA requires the following assumptions to be true:

• Independent subjects.
• Normality: the variance-covariance matrix of the predictors is the same in all groups.

If the latter assumption is violated, it is common to use quadratic discriminant analysis in the same manner as linear discriminant analysis instead.

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

References:

• R. Gutierrez-Osuna, Linear Discriminant Analysis. Available on: http://research.cs.tamu.edu/prism/lectures/pr/pr_l10.pdf

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 lda = new LinearDiscriminantAnalysis();


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


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


int[] results = classifier.Decide(inputs);

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4