KMeans Class 
Namespace: Accord.MachineLearning
[SerializableAttribute] public class KMeans : ParallelLearningBase, IUnsupervisedLearning<KMeansClusterCollection, double[], int>, IClusteringAlgorithm<double[], double>, IClusteringAlgorithm<double[]>, IUnsupervisedLearning<IClusterCollection<double[]>, double[], int>
The KMeans type exposes the following members.
Name  Description  

KMeans(Int32) 
Initializes a new instance of the KMeans algorithm
 
KMeans(Int32, IDistanceDouble) 
Initializes a new instance of the KMeans algorithm
 
KMeans(Int32, FuncDouble, Double, Double)  Obsolete.
Initializes a new instance of KMeans algorithm

Name  Description  

Centroids 
Gets or sets the cluster centroids.
 
Clusters 
Gets the clusters found by Kmeans.
 
ComputeCovariances 
Gets or sets whether covariance matrices for the clusters should
be computed at the end of an iteration. Default is true.
 
ComputeError 
Gets or sets whether the clustering distortion error (the
average distance between all data points and the cluster
centroids) should be computed at the end of the algorithm.
The result will be stored in Error. Default is true.
 
Dimension 
Gets the dimensionality of the data space.
 
Distance 
Gets or sets the distance function used
as a distance metric between data points.
 
Error 
Gets the cluster distortion error after the
last call to this class' Compute methods.
 
Iterations 
Gets the number of iterations performed in the
last call to this class' Compute methods.
 
K 
Gets the number of clusters.
 
MaxIterations 
Gets or sets the maximum number of iterations to
be performed by the method. If set to zero, no
iteration limit will be imposed. Default is 0.
 
ParallelOptions 
Gets or sets the parallelization options for this algorithm.
(Inherited from ParallelLearningBase.)  
Token 
Gets or sets a cancellation token that can be used
to cancel the algorithm while it is running.
(Inherited from ParallelLearningBase.)  
Tolerance 
Gets or sets the relative convergence threshold
for stopping the algorithm. Default is 1e5.
 
UseSeeding 
Gets or sets the strategy used to initialize the
centroids of the clustering algorithm. Default is
KMeansPlusPlus.

Name  Description  

Compute(Double)  Obsolete.
Divides the input data into K clusters.
 
Compute(Double, Double)  Obsolete.
Divides the input data into K clusters.
 
Compute(Double, Double)  Obsolete.
Divides the input data into K clusters.
 
ComputeInformation(Double) 
Computes the information about each cluster (covariance, proportions and error).
 
ComputeInformation(Double, Int32) 
Computes the information about each cluster (covariance, proportions and error).
 
converged 
Determines if the algorithm has converged by comparing the
centroids between two consecutive iterations.
 
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
Learn 
Learns a model that can map the given inputs to the desired outputs.
 
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
Randomize 
Randomizes the clusters inside a dataset.
 
ToString  Returns a string that represents the current object. (Inherited from Object.) 
Name  Description  

HasMethod 
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)  
IsEqual 
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.)  
To(Type)  Overloaded.
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.
(Defined by ExtensionMethods.)  
ToT  Overloaded.
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.
(Defined by ExtensionMethods.) 
In statistics and machine learning, kmeans clustering is a method of cluster analysis which aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean.
It is similar to the expectationmaximization algorithm for mixtures of Gaussians in that they both attempt to find the centers of natural clusters in the data as well as in the iterative refinement approach employed by both algorithms.
The algorithm is composed of the following steps:
This particular implementation uses the squared Euclidean distance as a similarity measure in order to form clusters.
References:
How to perform clustering with KMeans.
Accord.Math.Random.Generator.Seed = 0; // Declare some observations double[][] observations = { new double[] { 5, 2, 1 }, new double[] { 5, 5, 6 }, new double[] { 2, 1, 1 }, new double[] { 1, 1, 2 }, new double[] { 1, 2, 2 }, new double[] { 3, 1, 2 }, new double[] { 11, 5, 4 }, new double[] { 15, 5, 6 }, new double[] { 10, 5, 6 }, }; // Create a new KMeans algorithm KMeans kmeans = new KMeans(k: 3); // Compute and retrieve the data centroids var clusters = kmeans.Learn(observations); // Use the centroids to parition all the data int[] labels = clusters.Decide(observations);
How to perform clustering with KMeans applying different weights to different columns (dimensions) in the data.
Accord.Math.Random.Generator.Seed = 0; // A common desire when doing clustering is to attempt to find how to // weight the different components / columns of a dataset, giving them // different importances depending on the end goal of the clustering task. // Declare some observations double[][] observations = { new double[] { 5, 2, 1 }, new double[] { 5, 5, 6 }, new double[] { 2, 1, 1 }, new double[] { 1, 1, 2 }, new double[] { 1, 2, 2 }, new double[] { 3, 1, 2 }, new double[] { 11, 5, 4 }, new double[] { 15, 5, 6 }, new double[] { 10, 5, 6 }, }; // Create a new KMeans algorithm KMeans kmeans = new KMeans(k: 3) { // For example, let's say we would like to consider the importance of // the first column as 0.1, the second column as 0.7 and the third 0.9 Distance = new WeightedSquareEuclidean(new double[] { 0.1, 0.7, 1.1 }) }; // Compute and retrieve the data centroids var clusters = kmeans.Learn(observations); // Use the centroids to parition all the data int[] labels = clusters.Decide(observations);
How to perform clustering with KMeans with mixed discrete, continuous and categorical data.
Accord.Math.Random.Generator.Seed = 0; // Declare some mixed discrete and continuous observations double[][] observations = { // (categorical) (discrete) (continuous) new double[] { 1, 1, 2.2 }, new double[] { 1, 6, 5.5 }, new double[] { 2, 1, 1.1 }, new double[] { 2, 2, 1.2 }, new double[] { 2, 2, 2.6 }, new double[] { 3, 2, 1.4 }, new double[] { 3, 4, 5.2 }, new double[] { 1, 6, 5.1 }, new double[] { 1, 6, 5.9 }, }; // Create a new codification algorithm to convert // the mixed variables above into all continuous: var codification = new Codification<double>() { CodificationVariable.Categorical, CodificationVariable.Discrete, CodificationVariable.Continuous }; // Learn the codification from observations var model = codification.Learn(observations); // Transform the mixed observations into only continuous: double[][] newObservations = model.ToDouble().Transform(observations); // (newObservations will be equivalent to) double[][] expected = { // (one hot) (discrete) (continuous) new double[] { 1, 0, 0, 1, 2.2 }, new double[] { 1, 0, 0, 6, 5.5 }, new double[] { 0, 1, 0, 1, 1.1 }, new double[] { 0, 1, 0, 2, 1.2 }, new double[] { 0, 1, 0, 2, 2.6 }, new double[] { 0, 0, 1, 2, 1.4 }, new double[] { 0, 0, 1, 4, 5.2 }, new double[] { 1, 0, 0, 6, 5.1 }, new double[] { 1, 0, 0, 6, 5.9 }, }; // Create a new KMeans algorithm KMeans kmeans = new KMeans(k: 3); // Compute and retrieve the data centroids var clusters = kmeans.Learn(observations); // Use the centroids to parition all the data int[] labels = clusters.Decide(observations);
The following example demonstrates how to use the KMeans algorithm for color clustering. It is the same code which can be found in the color clustering sample application.
// Load a test image (shown in a picture box below) var sampleImages = new TestImages(path: basePath); Bitmap image = sampleImages.GetImage("airplane.png"); // ImageBox.Show("Original", image).Hold(); // Create converters to convert between Bitmap images and double[] arrays var imageToArray = new ImageToArray(min: 1, max: +1); var arrayToImage = new ArrayToImage(image.Width, image.Height, min: 1, max: +1); // Transform the image into an array of pixel values double[][] pixels; imageToArray.Convert(image, out pixels); // Create a KMeans algorithm using given k and a // square Euclidean distance as distance metric. KMeans kmeans = new KMeans(k: 5) { Distance = new SquareEuclidean(), // We will compute the KMeans algorithm until cluster centroids // change less than 0.5 between two iterations of the algorithm Tolerance = 0.05 }; // Learn the clusters from the data var clusters = kmeans.Learn(pixels); // Use clusters to decide class labels int[] labels = clusters.Decide(pixels); // Replace every pixel with its corresponding centroid double[][] replaced = pixels.Apply((x, i) => clusters.Centroids[labels[i]]); // Retrieve the resulting image (shown in a picture box) Bitmap result; arrayToImage.Convert(replaced, out result); // ImageBox.Show("kMeans clustering", result).Hold();
The original image is shown below:
The resulting image will be: