ClustersExplain Method

public static IndexCollection Explain(
	DoubleMatrix data,
	IndexPartition<double> partition,
	int numberOfExplanatoryFeatures
)

using System;

namespace Novacta.Analytics.CodeExamples
{
    public class ClustersExplainExample0  
    {
        public void Main()
        {
            // Set the number of items and features under study.
            const int numberOfItems = 12;
            int numberOfFeatures = 7;

            // Define a partition that must be explained.
            // Three parts (clusters) are included,
            // containing, respectively, items 0 to 3,
            // 5 to 8, and 9 to 11.
            var partition = IndexPartition.Create(
                new double[numberOfItems]
                    { 0 ,0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2 });

            // Create a matrix that will represent
            // an artificial data set,
            // having 12 items (rows) and 7 features (columns).
            // This will store the observations which
            // explanation will be based on.
            var data = DoubleMatrix.Dense(
                numberOfRows: numberOfItems,
                numberOfColumns: numberOfFeatures);

            // The first 5 features are built to be almost
            // surely non informative, since they result
            // as samples drawn from a same distribution.
            var g = new GaussianDistribution(mu: 0, sigma: .01);
            for (int j = 0; j < 5; j++)
            {
                data[":", j] = g.Sample(sampleSize: numberOfItems);
            }

            // Features 5 to 6 are instead built to be informative,
            // since they are sampled from different distributions
            // while filling rows whose indexes are in different parts
            // of the partition to be explained.
            var partIdentifiers = partition.Identifiers;
            double mu = 1.0;
            for (int i = 0; i < partIdentifiers.Count; i++)
            {
                var part = partition[partIdentifiers[i]];
                int partSize = part.Count;
                g.Mu = mu;
                data[part, 5] = g.Sample(sampleSize: partSize);
                mu += 2.0;
                g.Mu = mu;
                data[part, 6] = g.Sample(sampleSize: partSize);
                mu += 2.0;
            }

            Console.WriteLine("The data set:");
            Console.WriteLine(data);

            // Define how many features must be selected
            // for explanation.
            int numberOfExplanatoryFeatures = 2;

            // Select the best features.
            IndexCollection optimalExplanatoryFeatureIndexes =
                Clusters.Explain(
                    data,
                    partition,
                    numberOfExplanatoryFeatures);

            // Show the results.
            Console.WriteLine();
            Console.WriteLine(
                "The {0} features best explaining the given partition have column indexes:",
                numberOfExplanatoryFeatures);
            Console.WriteLine(optimalExplanatoryFeatureIndexes);

            Console.WriteLine();
            Console.WriteLine("The Davies-Bouldin Index for the selected features:");
            var dbi = IndexPartition.DaviesBouldinIndex(
                data[":", optimalExplanatoryFeatureIndexes],
                partition);
            Console.WriteLine(dbi);
        }
    }
}

// Executing method Main() produces the following output:
// 
// The data set:
// 0.00443412894    0.00269053161    0.00413587909    -0.00765022956   -0.0051623096    1.00663787       3.01053155       
// -0.0020667716    0.0208840726     -0.00323082939   -0.00939014629   0.00144991289    0.999318094      3.01264231       
// 0.0115714824     0.00980880506    0.0049017337     0.0032788575     0.0157818958     0.990821676      3.01207396       
// -0.0156854206    -0.00757566325   -0.00972832587   -0.00217925896   0.0107421303     0.992541729      2.99695621       
// 0.00220674309    -0.00321077807   -0.00611898588   0.00720305795    0.0128767272     4.99440474       6.99892958       
// -0.00637438186   0.0050524291     -0.00409270388   0.00210944391    -0.0152463979    4.9974367        6.99460151       
// -0.00662648189   -0.0149292848    0.00236975764    0.0103282088     -0.0108846478    4.99249371       6.98860335       
// -0.0219354055    0.0122820889     0.0109569101     -0.0108910035    0.00275269082    5.02268395       6.99732006       
// -0.00172760644   0.000890969086   -0.0121749938    -0.0060896535    -0.0125774475    9.00956698       10.9938497       
// 0.0157657881     0.0084084921     0.00295384059    -0.00358519595   0.00447359708    8.98856241       11.0013196       
// 0.0129253424     -0.000948574239  0.00235032211    -0.0135124599    -0.0233090879    9.00738398       10.9891406       
// -0.0084813634    -0.00459883432   -0.0148632861    0.0223964957     -0.00259506386   9.00721897       11.005672        
// 
// 
// 
// The 2 features best explaining the given partition have column indexes:
// 5, 6
// 
// The Davies-Bouldin Index for the selected features:
// 0.003700083159450854