VoronoiIterationT Class 
Namespace: Accord.MachineLearning
The VoronoiIterationT type exposes the following members.
Name  Description  

VoronoiIterationT 
Initializes a new instance of VoronoiIteration algorithm

Name  Description  

Clusters 
Gets the clusters found by kMedoids.
(Inherited from KMedoidsT.)  
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.
(Inherited from KMedoidsT.)  
Dimension 
Gets the dimensionality of the data space.
(Inherited from KMedoidsT.)  
Distance 
Gets or sets the distance function used
as a distance metric between data points.
(Inherited from KMedoidsT.)  
Error 
Gets the cluster distortion error (the average distance
between data points and the cluster centroids) after the
last call to this class' Compute methods.
(Inherited from KMedoidsT.)  
Initialization 
Gets or sets the strategy used to initialize the
centroids of the clustering algorithm. Default is
PamBuild.
(Inherited from KMedoidsT.)  
Iterations 
Gets the number of iterations performed in the
last call to this class' Compute methods.
(Inherited from KMedoidsT.)  
K 
Gets the number of clusters.
(Inherited from KMedoidsT.)  
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.
(Inherited from KMedoidsT.)  
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.
(Inherited from KMedoidsT.) 
Name  Description  

Compute 
Implementation of the Voronoi Iteration algorithm.
(Overrides KMedoidsTCompute(T, Int32, Int32).)  
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.
(Inherited from KMedoidsT.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
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.) 
From Wikipedia:
The kmedoids algorithm is a clustering algorithm related to the kmeans algorithm and the medoidshift algorithm. Both the kmeans and kmedoids algorithms are partitional (breaking the dataset up into groups) and both attempt to minimize the distance between points labeled to be in a cluster and a point designated as the center of that cluster. In contrast to the kmeans algorithm, kmedoids chooses datapoints as centers (medoids or exemplars) and works with a generalization of the Manhattan Norm to define distance between datapoints instead of L2. This method was proposed in 1987[1] for the work with L1 norm and other distances.
Voronoi iteration algorithm (or Lloyd algorithm) is one of possible implementations of the kmedoids clustering. It was suggested in the [2] and [3].
[1] Kaufman, L. and Rousseeuw, P.J. (1987), Clustering by means of Medoids, in Statistical Data Analysis Based on the L1–Norm and Related Methods, edited by Y. Dodge, NorthHolland, 405–416. [2] T. Hastie, R. Tibshirani, and J.Friedman.The Elements of Statistical Learning, Springer (2001), 468–469. [3] H.S.Park , C.H.Jun, A simple and fast algorithm for Kmedoids clustering, Expert Systems with Applications, 36, (2) (2009), 3336–3341.
Accord.Math.Random.Generator.Seed = 0; // Declare some observations int[][] observations = new int[][] { new[] { 2, 6 }, // a new[] { 3, 4 }, // a new[] { 3, 8 }, // a new[] { 4, 7 }, // a new[] { 6, 2 }, // b new[] { 6, 4 }, // b new[] { 7, 3 }, // b new[] { 7, 4 }, // b new[] { 8, 5 }, // b new[] { 7, 6 } // b }; // Create a new 2Medoids algorithm. var kmedoidsVi = new VoronoiIteration<int>(2, new Manhattan()); kmedoidsVi.MaxIterations = 100; // Set initial medoids kmedoidsVi.Clusters.Centroids[0] = observations[1]; kmedoidsVi.Clusters.Centroids[1] = observations[7]; // Compute and retrieve the data centroids var clusters = kmedoidsVi.Learn(observations); // Use the centroids to parition all the data int[] labels = clusters.Decide(observations);