/// <summary>
/// Compare the exact coarseness with an estimate for all numbers of bits.
///
/// This takes an assemblage of many clusters and finds the most concentrated
/// cluster according to a single bit Hilbert curve.
/// Then it composes a GridCoarseness for the points in that cluster.
/// </summary>
/// <param name="numPoints">Number of points</param>
/// <param name="dimensions">Number of dimensions</param>
/// <param name="clusterCount">Number of clusters</param>
/// <param name="maxCoordinate">Larges value any cooedinate of any dimension can hold</param>
/// <param name="maxStdDeviation">Maximum standard deviation among coordinate values relative to the center of each Gaussian cluster generated.</param>
/// <param name="minStdDeviation">Maximum standard deviation among coordinate values relative to the center of each Gaussian cluster generated.</param>
/// <returns>The GridCoarseness.</returns>
GridCoarseness MakeTestGrid(int numPoints, int dimensions, int clusterCount, int maxCoordinate, int minStdDeviation = 10, int maxStdDeviation = 30)
{
var avgClusterSize = numPoints / clusterCount;
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = avgClusterSize - 100,
MaxClusterSize = avgClusterSize + 100,
MaxDistanceStdDev = maxStdDeviation,
MinDistanceStdDev = minStdDeviation
};
var clusters = data.MakeClusters();
var points = clusters.Points().ToList();
PointBalancer balancer = null;
var bitsRequired = (maxCoordinate + 1).SmallestPowerOfTwo();
var lowresSort = HilbertSort.SortWithTies(points, 1, ref balancer);
var largestBucket = lowresSort.OrderByDescending(bucket => bucket.Length).FirstOrDefault();
var bucketSize = largestBucket.Length;
var grid = new GridCoarseness(largestBucket, bitsRequired);
return(grid);
}
public void DensityCompared()
{
var bitsPerDimension = 10;
var data = new GaussianClustering
{
ClusterCount = 50,
Dimensions = 100,
MaxCoordinate = (1 << bitsPerDimension) - 1,
MinClusterSize = 100,
MaxClusterSize = 500
};
var expectedClusters = data.MakeClusters();
var hIndex = new HilbertIndex(expectedClusters, bitsPerDimension);
var cc = new ClusterCounter {
NoiseSkipBy = 10, OutlierSize = 5, ReducedNoiseSkipBy = 1
};
var count = cc.Count(hIndex.SortedPoints);
var neighborhoodDistance = count.MaximumSquareDistance * 2 / 5;
var numPoints = hIndex.SortedPoints.Count;
var windowRadius = (int)Math.Sqrt(numPoints / 2);
var dMeter = new DensityMeter(hIndex, neighborhoodDistance, windowRadius);
Console.WriteLine($"Window Radius = {windowRadius}. {hIndex.SortedPoints.Count} points");
Console.Write("Exact,Estimated");
for (var i = 0; i < numPoints; i++)
{
var p = hIndex.SortedPoints[i];
var exact = dMeter.ExactNeighbors(p);
var estimate = dMeter.EstimatedDensity(p, windowRadius);
Console.Write($"{exact},{estimate}");
}
}
private void OptimalIndexTestCase(
int hilbertTries, int minClusterSize, int maxClusterSize, int dimensions, int clusterCount, int acceptableClusterCount,
int bitsPerDimension, int outlierSize, int noiseSkipBy)
{
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = 1000,
MinClusterSize = minClusterSize,
MaxClusterSize = maxClusterSize
};
var clusters = data.MakeClusters();
var points = clusters.Points().Select(p => HilbertPoint.CastOrConvert(p, bitsPerDimension, true)).ToList();
var results = OptimalIndex.Search(
points,
outlierSize,
noiseSkipBy,
hilbertTries, // maxTrials
4 // maxIterationsWithoutImprovement
);
var message = $"Estimated cluster count = {results.EstimatedClusterCount}, actual = {clusterCount}, acceptable = {acceptableClusterCount}";
Console.WriteLine(message);
Assert.LessOrEqual(results.EstimatedClusterCount, acceptableClusterCount, $"HilbertIndex fragmented by more than 50%: {message}");
}
/// <summary>
/// For random clustered data, discover how unique shortened versions of the Hilbert index are.
/// </summary>
/// <param name="numPoints">Number of points.</param>
/// <param name="dimensions">Dimensions per point.</param>
/// <param name="clusterCount">Number of clusters.</param>
/// <param name="smallBucketSize">Count of items that constitutes a small bucket.</param>
/// <param name="maxCoordinate">Highest permitted coordinate value.</param>
public void ClusteredUniquenessByBits(int numPoints, int dimensions, int clusterCount, int smallBucketSize, int maxCoordinate)
{
var clusterSizeVariation = 100;
var minClusterSize = (numPoints / clusterCount) - clusterSizeVariation;
var maxClusterSize = (numPoints / clusterCount) + clusterSizeVariation;
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = minClusterSize,
MaxClusterSize = maxClusterSize
};
var clusters = data.MakeClusters();
var points = clusters.Points().ToList();
PointBalancer balancer = null;
var bitsRequired = (maxCoordinate + 1).SmallestPowerOfTwo();
for (var iBits = 1; iBits <= bitsRequired; iBits++)
{
var maxBucketSize = MaxBucketSizePerBits(points, iBits, smallBucketSize, ref balancer, out int pointsInSmallBuckets);
var pctInSmallBuckets = 100.0 * pointsInSmallBuckets / points.Count;
Console.WriteLine($"Bits: {iBits} Max Bucket: {maxBucketSize} # in Small Buckets: {pointsInSmallBuckets} - {pctInSmallBuckets} %");
}
}
/// <summary>
/// Create test data in known clusters, perform unattended clustering, time the process.
/// Make no attempt to verify the correctness of the result.
/// The timing does not include the creation of the test data, just the clustering.
/// </summary>
/// <param name="numPoints">Number of points to cluster.</param>
/// <param name="clusterCount">Cluster count.</param>
/// <param name="dimensions">Dimensions per point.</param>
/// <param name="clusterSizeVariation">Cluster size variation.
/// The average number of points per cluster is numPoints/clusterCount.
/// The actual size of a given cluster will be permitted to vary by as much as ± clusterSizeVariation.
/// </param>
/// <param name="maxCoordinate">All points will have coordinate values in the range 0 to maxCoordinate.</param>
/// <returns>Time in seconds and an Boolean which is false if the clustering did not produce perfect results.</returns>
private Tuple <double, bool> ClassifyPerformance(int numPoints, int clusterCount, int dimensions,
int clusterSizeVariation = 0, int maxCoordinate = 1000)
{
var minClusterSize = (numPoints / clusterCount) - clusterSizeVariation;
var maxClusterSize = (numPoints / clusterCount) + clusterSizeVariation;
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = minClusterSize,
MaxClusterSize = maxClusterSize
};
var expectedClusters = data.MakeClusters();
var timer = new Stopwatch();
timer.Start();
var classifier = new HilbertClassifier(expectedClusters.Points(), 10);
classifier.IndexConfig.UseSample = true;
var actualClusters = classifier.Classify();
timer.Stop();
var success = expectedClusters.IsSimilarTo(actualClusters);
if (!success)
{
Console.WriteLine($"Clustering was not perfect. # of Clusters actual/expected: {actualClusters.NumPartitions}/{expectedClusters.NumPartitions}");
}
var seconds = timer.ElapsedMilliseconds / 1000.0;
return(new Tuple <double, bool>(seconds, success));
}
public void ClusterWithoutFiles()
{
var bitsPerDimension = 10;
var data = new GaussianClustering
{
ClusterCount = 20,
Dimensions = 50,
MaxCoordinate = (1 << bitsPerDimension) - 1,
MinClusterSize = 200,
MaxClusterSize = 600
};
var expectedClassification = data.MakeClusters();
var config = new SlashConfig()
{
AcceptableBCubed = 0.98
};
config.Index.BitsPerDimension = bitsPerDimension;
config.UseNoFiles();
var command = new SlashCommand(SlashCommand.CommandType.Cluster, config)
{
InputFile = null,
OutputFile = null
};
command.Configuration.DensityClassifier.SkipDensityClassification = true;
// Need to put this here, because the command initializes the logger differently.
Logger.SetupForTests(null);
command.LoadData(expectedClassification);
command.Execute();
Assert.IsTrue(command.IsClassificationAcceptable, $"The BCubed value of {command.MeasuredChange.BCubed} was not good enough.");
}
/// <summary>
/// For the same test data, create a single HilbertIndex many times and average the execution time across all indices.
///
/// The goal is to identify how the time depends on number of points N, number of dimensions D, and bits per coordinate B.
/// (It should be insensitive to cluster count K.)
/// </summary>
/// <param name="N">Number of points to index.</param>
/// <param name="K">Number of clusters of points to create.</param>
/// <param name="D">Number dimensions.</param>
/// <param name="B">Number bits.</param>
/// <param name="repeats">Number of times to repeat.</param>
/// <returns>Average number of seconds to create the index, averaged over several tries.
/// The time excludes the time to create the test data.
/// </returns>
private double SingleIndexCreationPerformanceCase(int N, int K, int D, int B, int repeats)
{
var data = new GaussianClustering
{
ClusterCount = K,
Dimensions = D,
MaxCoordinate = (1 << B) - 1,
MinClusterSize = N / K,
MaxClusterSize = N / K
};
var clusters = data.MakeClusters();
var timer = new Stopwatch();
var totalTimeMilliseconds = 0L;
for (var i = 0; i < repeats; i++)
{
timer.Reset();
timer.Start();
var hIndex = new HilbertIndex(clusters, B);
Assert.AreEqual(N, hIndex.Count, "Index has wrong number of points");
timer.Stop();
totalTimeMilliseconds += timer.ElapsedMilliseconds;
}
return((double)totalTimeMilliseconds / (1000.0 * repeats));
}
public void Classify_DensitySpread()
{
var clusterCount = 50;
var dimensions = 100;
var maxCoordinate = 1000;
var acceptableBCubed = 0.99;
var clusterSizes = new int[50];
foreach (var i in Enumerable.Range(0, 50))
{
clusterSizes[i] = 100 + (100 * i);
}
var minClusterSize = clusterSizes.Min();
var maxClusterSize = clusterSizes.Max();
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = minClusterSize,
MaxClusterSize = maxClusterSize,
ClusterSizes = clusterSizes
};
ClusterCore(data, acceptableBCubed);
}
/// <summary>
/// A test case for PolyChromaticClosestPoint.FindPairByCentroids where clusters conform to a Gaussian distribution.
/// </summary>
/// <param name="nPoints">Number of points in each cluster.</param>
/// <param name="dimensions">Number of Dimensions in each point.</param>
/// <param name="numClusters">Number of clusters to create.</param>
public void FindPairByCentroidsTestCase(int nPoints, int dimensions, int numClusters)
{
var successes = 0;
var worstRatio = 1.0;
var color1 = "0";
var data = new GaussianClustering
{
ClusterCount = numClusters,
Dimensions = dimensions,
MaxCoordinate = 1000,
MinClusterSize = nPoints,
MaxClusterSize = nPoints
};
var clusters = data.MakeClusters();
PolyChromaticClosestPoint <string> pccp;
pccp = new PolyChromaticClosestPoint <string>(clusters);
for (var iColor2 = 1; iColor2 < numClusters; iColor2++)
{
var color2 = iColor2.ToString();
var exact = pccp.FindPairExhaustively(color1, color2);
var approximate = pccp.FindPairByCentroids(color1, color2);
var expectedDistance = exact.SquareDistance;
var actualDistance = approximate.SquareDistance;
if (actualDistance <= expectedDistance)
{
successes++;
}
else
{
worstRatio = Math.Max(worstRatio, actualDistance / (double)expectedDistance);
}
if (exact.SquareDistance >= approximate.SquareDistance)
{
Console.WriteLine("FindPairByCentroids CORRECT. Exact {0}. Approx {1}", exact, approximate);
}
else
{
Console.WriteLine("FindPairByCentroids INCORRECT. Exact {0}. Approx {1}. Too high by {2:N3}%",
exact, approximate, 100.0 * (approximate.SquareDistance / (double)exact.SquareDistance - 1.0));
}
}
Assert.AreEqual(numClusters - 1, successes,
string.Format("Did not succeed every time. Failed {0} of {1} times. Worst distance ratio is {2:N4}. {3} points of {4} dimensions.",
numClusters - successes - 1,
numClusters - 1,
worstRatio,
nPoints,
dimensions
)
);
}
public void AllColorPairsClosestClusterTest(int nPoints, int dimensions, int numClusters, int numCurvesToTry)
{
var rankHistogram = new int[numClusters + 1]; // We will skip the first element so as to have a one-based array.
var data = new GaussianClustering
{
ClusterCount = numClusters,
Dimensions = dimensions,
MaxCoordinate = 1000,
MinClusterSize = nPoints,
MaxClusterSize = nPoints
};
var worstDistanceRatio = 1.0;
var ratioSum = 0.0;
var ratioCount = 0;
var clusters = data.MakeClusters();
var bitsPerDimension = (1 + data.MaxCoordinate).SmallestPowerOfTwo();
var results = OptimalIndex
.Search(
clusters.Points().Select(up => HilbertPoint.CastOrConvert(up, bitsPerDimension, true)).ToList(),
5 /*outlier size */, 10 /* NoiseSkipBy */, 1 /* ReducedNoiseSkipBy */, numCurvesToTry
);
var pccp1 = new PolyChromaticClosestPoint <string>(clusters, results.Index);
var allColorPairs = pccp1.FindAllClustersApproximately();
foreach (var color1 in clusters.ClassLabels())
{
var exact = pccp1.FindClusterExhaustively(color1).Swap(color1);
var color1Pairs = allColorPairs
.Where(cp => cp.Color1.Equals(color1) || cp.Color2.Equals(color1))
.Select(cp => cp.Swap(color1))
.ToList();
var approximateColor2Distance = color1Pairs.First(cp => cp.Color2.Equals(exact.Color2)).SquareDistance;
var approximateRank = color1Pairs.Count(cp => cp.SquareDistance < approximateColor2Distance) + 1;
rankHistogram[approximateRank]++;
#pragma warning disable RECS0018 // Comparison of floating point numbers with equality operator
var ratio = exact.SquareDistance == 0.0 ? 0 : approximateColor2Distance / (double)exact.SquareDistance;
#pragma warning restore RECS0018 // Comparison of floating point numbers with equality operator
ratioSum += ratio;
ratioCount++;
worstDistanceRatio = Math.Max(worstDistanceRatio, ratio);
}
Debug.WriteLine(string.Format("Worst distance overage = {0:N3}%", (worstDistanceRatio - 1.0) * 100.0));
Debug.WriteLine(string.Format("Average distance overage = {0:N3}%", ((ratioSum / ratioCount) - 1.0) * 100.0));
for (var iRank = 1; iRank <= numClusters; iRank++)
{
if (rankHistogram[iRank] > 0 || iRank < 4)
{
Debug.WriteLine(string.Format("For {0} Clusters the closest cluster found was Ranked #{1}.", rankHistogram[iRank], iRank));
}
}
// Accept a win, place or show: the true closest cluster shows up as no worse than the 3rd ranked cluster according to the approximate measure.
Assert.IsTrue(rankHistogram[1] + rankHistogram[2] + rankHistogram[3] == numClusters,
string.Format("Found the closest cluster for {0} colors", rankHistogram[1])
);
}
/// <summary>
/// Create test data in known clusters, perform unattended clustering, and compare the results to the known clusters.
/// The test passes if the BCubed value is high enough.
/// </summary>
/// <param name="numPoints">Number of points to cluster.</param>
/// <param name="clusterCount">Cluster count.</param>
/// <param name="dimensions">Dimensions per point.</param>
/// <param name="clusterSizeVariation">Cluster size variation.
/// The average number of points per cluster is numPoints/clusterCount.
/// The actual size of a given cluster will be permitted to vary by as much as ± clusterSizeVariation.
/// </param>
/// <param name="maxCoordinate">All points will have coordinate values in the range 0 to maxCoordinate.</param>
/// <param name="acceptableBCubed">The comparison of the actual and expected clusters must yield a BCubed value
/// that is this high or higher. A value of 1.0 means a perfect clustering, with no points out of place.</param>
private void ClassifyCase(int numPoints, int clusterCount, int dimensions,
int clusterSizeVariation = 0, int maxCoordinate = 1000, double acceptableBCubed = 0.99)
{
var minClusterSize = (numPoints / clusterCount) - clusterSizeVariation;
var maxClusterSize = (numPoints / clusterCount) + clusterSizeVariation;
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = minClusterSize,
MaxClusterSize = maxClusterSize
};
ClusterCore(data, acceptableBCubed);
}
private void ClusterCore(GaussianClustering data, double acceptableBCubed)
{
var expectedClusters = data.MakeClusters();
var classifier = new HilbertClassifier(expectedClusters.Points(), 10);
classifier.IndexConfig.UseSample = true;
var actualClusters = classifier.Classify();
var comparison = expectedClusters.Compare(actualClusters);
var message = $" Comparison of clusters: {comparison}.\n Clusters expected/actual: {expectedClusters.NumPartitions}/{actualClusters.NumPartitions}.";
Console.WriteLine(message);
Console.WriteLine($" Large clusters: {actualClusters.NumLargePartitions(classifier.OutlierSize)}");
Assert.GreaterOrEqual(comparison.BCubed, acceptableBCubed, $"Clustering was not good enough. BCubed = {comparison.BCubed}");
}
private Dictionary <string, CorrelationStats> DensityCorrelationCases(int[] varyWindowRadius, int[] varyNumPoints, int dimensions, int clusterCount, int repeats = 1)
{
var stats = new Dictionary <string, CorrelationStats>();
for (var iRepeat = 0; iRepeat < repeats; iRepeat++)
{
foreach (var numPoints in varyNumPoints)
{
var bitsPerDimension = 10;
var clusterSize = numPoints / clusterCount;
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = (1 << bitsPerDimension) - 1,
MinClusterSize = clusterSize,
MaxClusterSize = clusterSize
};
var expectedClusters = data.MakeClusters();
var hIndex = new HilbertIndex(expectedClusters, bitsPerDimension);
var cc = new ClusterCounter {
NoiseSkipBy = 10, OutlierSize = 5, ReducedNoiseSkipBy = 1
};
var count = cc.Count(hIndex.SortedPoints);
var neighborhoodDistance = count.MaximumSquareDistance * 2 / 5;
var dMeter = new DensityMeter(hIndex, neighborhoodDistance, varyWindowRadius[0]);
// It is more efficient to process windowRadius in descending order,
// because the DistanceMemo can reuse more work that way. Once a larger window has been processed,
// it includes all shorter windows as well.
foreach (var windowRadius in varyWindowRadius.OrderByDescending(r => r))
{
var label = MakeLabel(numPoints, windowRadius, dimensions, clusterCount);
CorrelationStats corStats;
if (!stats.TryGetValue(label, out corStats))
{
corStats = new CorrelationStats(label);
stats[label] = corStats;
}
corStats.Add(DensityCorrelationCase(dMeter, windowRadius));
Console.Write(corStats);
}
}
}
return(stats);
}
private Classification <UnsignedPoint, string> TestData(int[] clusterSizes, int dimensions, int maxCoordinate)
{
var clusterCount = clusterSizes.Length;
var minClusterSize = clusterSizes.Min();
var maxClusterSize = clusterSizes.Max();
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = minClusterSize,
MaxClusterSize = maxClusterSize,
ClusterSizes = clusterSizes
};
return(data.MakeClusters());
}
/// <summary>
/// Create test data in known chained clusters, perform unattended clustering, and compare the results to the known clusters.
/// The test passes if the BCubed value is high enough.
/// </summary>
/// <param name="numPoints">Number of points to cluster.</param>
/// <param name="clusterCount">Cluster count.</param>
/// <param name="chainLength">Number of segments in each chain.</param>
/// <param name="dimensions">Dimensions per point.</param>
/// <param name="clusterSizeVariation">Cluster size variation.
/// The average number of points per cluster is numPoints/clusterCount.
/// The actual size of a given cluster will be permitted to vary by as much as ± clusterSizeVariation.
/// </param>
/// <param name="maxCoordinate">All points will have coordinate values in the range 0 to maxCoordinate.</param>
/// <param name="acceptableBCubed">The comparison of the actual and expected clusters must yield a BCubed value
/// that is this high or higher. A value of 1.0 means a perfect clustering, with no points out of place.</param>
private void ClassifyChainCase(int numPoints, int clusterCount, int chainLength, int dimensions,
int clusterSizeVariation = 0, int maxCoordinate = 1000, double acceptableBCubed = 0.99)
{
var minClusterSize = (numPoints / clusterCount) - clusterSizeVariation;
var maxClusterSize = (numPoints / clusterCount) + clusterSizeVariation;
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = minClusterSize,
MaxClusterSize = maxClusterSize,
MaxDistanceStdDev = 300,
MinDistanceStdDev = 150
};
ClusterChainCore(data, acceptableBCubed, chainLength);
}
UnsignedPoint[] TestData(int numPoints, int dimensions, int clusterCount, int maxCoordinate, int minStdDeviation, int maxStdDeviation, out int bitsPerDimension)
{
var avgClusterSize = numPoints / clusterCount;
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = avgClusterSize - 100,
MaxClusterSize = avgClusterSize + 100,
MaxDistanceStdDev = maxStdDeviation,
MinDistanceStdDev = minStdDeviation
};
var clusters = data.MakeClusters();
var points = clusters.Points().ToArray();
bitsPerDimension = (maxCoordinate + 1).SmallestPowerOfTwo();
return(points);
}
public void DensityCorrelation()
{
var bitsPerDimension = 10;
var data = new GaussianClustering
{
ClusterCount = 50,
Dimensions = 100,
MaxCoordinate = (1 << bitsPerDimension) - 1,
MinClusterSize = 100,
MaxClusterSize = 500
};
var expectedClusters = data.MakeClusters();
var hIndex = new HilbertIndex(expectedClusters, bitsPerDimension);
var cc = new ClusterCounter {
NoiseSkipBy = 10, OutlierSize = 5, ReducedNoiseSkipBy = 1
};
var count = cc.Count(hIndex.SortedPoints);
// Choice of neighborhoodDistance is crucial.
// - If it is too large, then a huge number of neighbors will be caught up in the dragnet, and estimating
// that value with a window into the Hilbert curve will yield poor results. Why? If there are 200 neighbors
// and your window size is 100 then many points will have their neighbor count saturate near 100 and
// no meaningful variation in density will be found.
// - If it is too small, then too few neighbors (or none!) will be found, and we get no meaningful density.
// - We know that almost every point has two neighbors within MaximumSquareDistance, so we should
// make it smaller than MaximumSquareDistance.
var neighborhoodDistance = count.MaximumSquareDistance * 2 / 5;
var numPoints = hIndex.SortedPoints.Count;
var windowRadius = (int)Math.Sqrt(numPoints / 2);
var dMeter = new DensityMeter(hIndex, neighborhoodDistance, windowRadius);
Func <HilbertPoint, long> exactMetric = p => (long)dMeter.ExactNeighbors(p);
Func <HilbertPoint, long> estimatedMetric = p => (long)dMeter.EstimatedDensity(p, windowRadius);
var correlator = new KendallTauCorrelation <HilbertPoint, long>(exactMetric, estimatedMetric);
var correlation = correlator.TauB(hIndex.SortedPoints.Take(1000));
Console.WriteLine($"Correlation between exact and estimated density is: {correlation}");
Assert.GreaterOrEqual(correlation, 0.90, $"Correlation {correlation} is not high enough");
}
private void ClusterChainCore(GaussianClustering data, double acceptableBCubed, int chainLength)
{
var expectedClusters = data.MakeChains(chainLength);
var classifier = new HilbertClassifier(expectedClusters.Points(), 10);
classifier.IndexConfig.UseSample = true;
var actualClusters = classifier.Classify();
var comparison = expectedClusters.Compare(actualClusters);
var message = $" Comparison of clusters: {comparison}.\n Clusters expected/actual: {expectedClusters.NumPartitions}/{actualClusters.NumPartitions}.";
Logger.Info(message);
var message2 = $" Large clusters: {actualClusters.NumLargePartitions(classifier.OutlierSize)}";
Logger.Info(message2);
var pointsInOutliers = actualClusters.LabelToPoints.Values
.Select(values => values.Count())
.Where(count => count < classifier.OutlierSize)
.Sum();
var message3 = $" Points in Outliers/Total Point: {pointsInOutliers} / {actualClusters.NumPoints}";
Logger.Info(message3);
Assert.GreaterOrEqual(comparison.BCubed, acceptableBCubed, $"Clustering was not good enough. BCubed = {comparison.BCubed}");
}
/// <summary>
/// UnsignedPoint.SquareDistanceCompare has an optimization. This tests how often this optimization
/// can be exploited in a realistic test. The comparison will be against an estimated characteristic distance
/// between points. This distance is assumed to be close enough to trigger two points to be merged into a single cluster.
/// </summary>
private double SquareDistanceCompareOptimizableCase(int totalComparisons, bool useExtendedOptimization = false)
{
// 1. Make test data.
var bitsPerDimension = 10;
var data = new GaussianClustering
{
ClusterCount = 100,
Dimensions = 100,
MaxCoordinate = (1 << bitsPerDimension) - 1,
MinClusterSize = 50,
MaxClusterSize = 150
};
var clusters = data.MakeClusters();
// 2. Create HilbertIndex for points.
var hIndex = new HilbertIndex(clusters, bitsPerDimension);
// 3. Deduce the characteristic distance.
var counter = new ClusterCounter
{
OutlierSize = 5,
NoiseSkipBy = 10
};
var count = counter.Count(hIndex.SortedPoints);
var mergeDistance = count.MaximumSquareDistance;
var longDistance = 5 * mergeDistance;
// 4. Select random pairs of points and see how many distance comparisons can exploit the optimization.
var rng = new FastRandom();
var points = clusters.Points().ToList();
var ableToUseOptimizationsAtShortDistance = 0;
var ableToUseOptimizationsAtLongDistance = 0;
for (var i = 0; i < totalComparisons; i++)
{
var p1 = points[rng.Next(points.Count)];
var p2 = points[rng.Next(points.Count)];
if (useExtendedOptimization)
{
if (IsExtendedDistanceOptimizationUsable(p1, p2, mergeDistance, bitsPerDimension))
{
ableToUseOptimizationsAtShortDistance++;
}
if (IsExtendedDistanceOptimizationUsable(p1, p2, longDistance, bitsPerDimension))
{
ableToUseOptimizationsAtLongDistance++;
}
}
else
{
if (IsDistanceOptimizationUsable(p1, p2, mergeDistance))
{
ableToUseOptimizationsAtShortDistance++;
}
if (IsDistanceOptimizationUsable(p1, p2, longDistance))
{
ableToUseOptimizationsAtLongDistance++;
}
}
}
var percentOptimizable = 100.0 * ableToUseOptimizationsAtShortDistance / totalComparisons;
var percentOptimizableLongDistance = 100.0 * ableToUseOptimizationsAtLongDistance / totalComparisons;
var message = $"Comparisons were {percentOptimizable} % Optimizable at short distance, {percentOptimizableLongDistance} % at long distance";
Console.WriteLine(message);
return(percentOptimizable);
}
public void LowresVersusHiresCase(int numPoints, int dimensions, int clusterCount, int lowresBits)
{
var maxCoordinate = 1000;
var clusterSizeVariation = 100;
var minClusterSize = (numPoints / clusterCount) - clusterSizeVariation;
var maxClusterSize = (numPoints / clusterCount) + clusterSizeVariation;
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = minClusterSize,
MaxClusterSize = maxClusterSize
};
var clusters = data.MakeClusters();
var points = clusters.Points().ToList();
PointBalancer balancer = null;
var hiresSort = HilbertSort.BalancedSort(points, ref balancer);
var lowresSort = HilbertSort.SortWithTies(points, lowresBits, ref balancer);
var lowresPositions = new Dictionary <UnsignedPoint, int>();
var hiresPosition = new Dictionary <UnsignedPoint, int>();
foreach (var p in hiresSort.Select((p, i) => { hiresPosition[p] = i; return(p); }))
{
;
}
foreach (var ties in lowresSort.Select((p, i) => new { Points = p, Position = i }))
{
foreach (var point in ties.Points)
{
lowresPositions[point] = ties.Position;
}
}
// Compare the positions of many pairs of points in the two orderings to see that
// they are either in the same relative order
// or tied for position in the lowres ordering.
var actualNumPoints = points.Count;
var largestBucket = lowresSort.Select(bucket => bucket.Length).Max();
var caseDescription = $"N = {actualNumPoints} D = {dimensions} K = {clusterCount} B = {lowresBits}";
Console.WriteLine(caseDescription);
Console.WriteLine($"Lowres buckets = {lowresSort.Count} Largest bucket = {largestBucket}");
int outOfPlaceCount = 0;
for (var i = 0; i < actualNumPoints - 1; i++)
{
var p1 = points[i];
for (var j = i + 1; j < actualNumPoints; j++)
{
var p2 = points[j];
var lowresPosition1 = lowresPositions[p1];
var lowresPosition2 = lowresPositions[p2];
var hiresPosition1 = hiresPosition[p1];
var hiresPosition2 = hiresPosition[p2];
if (lowresPosition1 != lowresPosition2)
{
if (lowresPosition1 < lowresPosition2 != hiresPosition1 < hiresPosition2)
{
outOfPlaceCount++;
}
}
}
}
var msg = $"Out of place count = {outOfPlaceCount}";
Console.WriteLine(msg);
Assert.AreEqual(0, outOfPlaceCount, msg);
}
public void DistanceDistribution()
{
/*
* Percentile,By Index,By Random
* -----------------------------
* 0%,111.35,146.55
* 1%,142.06,255.96
* 2%,147.21,2163.43
* 3%,151.2,2214.15
* 4%,154.06,2245.2
* 5%,156.24,2271.37
* 6%,158.38,2292.29
* 7%,160.42,2313.55
* 8%,162.29,2327.14
* 9%,164.07,2345.25
* 10%,165.41,2359.95
* 11%,166.72,2372.83
* 12%,167.99,2386.15
* 13%,169.29,2398.47
* 14%,170.43,2410.01
* 15%,171.53,2422.34
* 16%,172.48,2432.43
* 17%,173.58,2443.08
* 18%,174.73,2454.27
* 19%,175.56,2463.71
* 20%,176.35,2472.97
* 21%,177.35,2483.24
* 22%,178.3,2491.9
* 23%,179.1,2501.44
* 24%,179.82,2510.26
* 25%,180.64,2517.73
* 26%,181.55,2524.97
* 27%,182.33,2531.58
* 28%,182.98,2538.08
* 29%,183.67,2543.83
* 30%,184.33,2550.93
* 31%,185.09,2556.59
* 32%,185.7,2563.37
* 33%,186.41,2570.29
* 34%,187.09,2577.29
* 35%,187.7,2583.56
* 36%,188.43,2589.95
* 37%,189.07,2596.13
* 38%,189.71,2602.24
* 39%,190.46,2608.28
* 40%,191.08,2615.25
* 41%,191.79,2620.81
* 42%,192.46,2626.02
* 43%,193.09,2632.7
* 44%,193.71,2638.18
* 45%,194.31,2643.35
* 46%,194.98,2648.69
* 47%,195.65,2655.47
* 48%,196.3,2660.26
* 49%,196.96,2666.37
* 50%,197.66,2670.94
* 51%,198.34,2677.09
* 52%,199.07,2681.9
* 53%,199.72,2687.11
* 54%,200.3,2692.42
* 55%,201.06,2697.92
* 56%,201.71,2703.76
* 57%,202.4,2710.17
* 58%,203.16,2715.06
* 59%,203.82,2720.25
* 60%,204.51,2725.99
* 61%,205.32,2731.6
* 62%,206.08,2736.59
* 63%,206.79,2741.72
* 64%,207.58,2746.59
* 65%,208.29,2754.03
* 66%,209.07,2760.81
* 67%,209.8,2766.65
* 68%,210.68,2771.98
* 69%,211.71,2778.27
* 70%,212.38,2784.23
* 71%,213.19,2790.71
* 72%,213.92,2796.42
* 73%,214.82,2802.84
* 74%,215.68,2809.36
* 75%,216.54,2814.55
* 76%,217.48,2821.32
* 77%,218.43,2827.56
* 78%,219.35,2833.35
* 79%,220.28,2840.72
* 80%,221.33,2848.87
* 81%,222.31,2856.89
* 82%,223.42,2864
* 83%,224.46,2872.51
* 84%,225.83,2881.09
* 85%,227.06,2891.57
* 86%,228.27,2900.46
* 87%,229.63,2910.46
* 88%,231.55,2919.5
* 89%,233.59,2933.76
* 90%,235.6,2944.88
* 91%,237.25,2959.45
* 92%,239.83,2976.08
* 93%,241.88,2990.4
* 94%,244.97,3010.08
* 95%,248.23,3029.15
* 96%,252.34,3052.37
* 97%,260.68,3074.84
* 98%,282.76,3112.43 *** Note the jump from 282 to 2550, which shows that the characteristic distance is about 282.
* 99%,2550.87,3170.93
* 100%,3114.89,3412.57
*/
var data = new GaussianClustering
{
ClusterCount = 100,
Dimensions = 50,
MaxCoordinate = 1000,
MinClusterSize = 50,
MaxClusterSize = 150
};
var clusters = data.MakeClusters();
var bitsPerDimension = 10;
var points = clusters.Points().Select(p => HilbertPoint.CastOrConvert(p, bitsPerDimension, true)).ToList();
var results = OptimalIndex.Search(
points,
5, // outlierSize
10, // noiseSkipBy
1000, // maxTrials
4 // maxIterationsWithoutImprovement
);
var pointsFromIndex = results.Index.SortedPoints;
var distancesRandom = new List <long>();
var distancesHilbert = new List <long>();
var n = pointsFromIndex.Count;
var rng = new FastRandom();
for (var i = 0; i < n - 1; i++)
{
var p1 = pointsFromIndex[i];
var p2 = pointsFromIndex[i + 1];
distancesHilbert.Add(p1.Measure(p2));
var p3 = pointsFromIndex[rng.Next(n)];
var p4 = pointsFromIndex[rng.Next(n)];
distancesRandom.Add(p3.Measure(p4));
}
distancesHilbert.Sort();
distancesRandom.Sort();
Console.WriteLine("Percentile,By Index,By Random");
for (var percentile = 0; percentile <= 100; percentile++)
{
var i = Math.Min(n - 2, (n - 1) * percentile / 100);
var distHilbert = Math.Round(Math.Sqrt(distancesHilbert[i]), 2);
var distRandom = Math.Round(Math.Sqrt(distancesRandom[i]), 2);
Console.Write($"{percentile}%,{distHilbert},{distRandom}");
}
}
/// <summary>
/// A test case for PolyChromaticClosestPoint.FindPairApproximately where clusters conform to a Gaussian distribution.
/// </summary>
/// <param name="nPoints">Number of points in each cluster.</param>
/// <param name="dimensions">Number of Dimensions in each point.</param>
/// <param name="numClusters">Number of clusters to create.</param>
/// <param name="hilbertsToTry">Number of randomly generated Hilbert curves to try.</param>
public void GaussianPolyChromaticPairTestCase(int nPoints, int dimensions, int numClusters, int hilbertsToTry = 1)
{
var successes = 0;
var worstRatio = 1.0;
var color1 = "0";
var data = new GaussianClustering
{
ClusterCount = numClusters,
Dimensions = dimensions,
MaxCoordinate = 1000,
MinClusterSize = nPoints,
MaxClusterSize = nPoints
};
var clusters = data.MakeClusters();
PolyChromaticClosestPoint <string> pccp;
if (hilbertsToTry <= 1)
{
pccp = new PolyChromaticClosestPoint <string>(clusters);
}
else
{
var bitsPerDimension = (1 + data.MaxCoordinate).SmallestPowerOfTwo();
var results = OptimalIndex.Search(
clusters.Points().Select(up => HilbertPoint.CastOrConvert(up, bitsPerDimension, true)).ToList(),
5 /*outlier size */, 10 /* NoiseSkipBy */, 1 /* ReducedNoiseSkipBy */, hilbertsToTry
);
pccp = new PolyChromaticClosestPoint <string>(clusters, results.Index);
}
for (var iColor2 = 1; iColor2 < numClusters; iColor2++)
{
var color2 = iColor2.ToString();
var exact = pccp.FindPairExhaustively(color1, color2);
var approximate = pccp.FindPairApproximately(color1, color2);
var expectedDistance = exact.SquareDistance;
var actualDistance = approximate.SquareDistance;
if (actualDistance <= expectedDistance)
{
successes++;
}
else
{
worstRatio = Math.Max(worstRatio, actualDistance / (double)expectedDistance);
}
if (exact.SquareDistance >= approximate.SquareDistance)
{
Console.WriteLine("FindPairApproximately CORRECT. Exact {0}. Approx {1}", exact, approximate);
}
else
{
Console.WriteLine("FindPairApproximately INCORRECT. Exact {0}. Approx {1}. Too high by {2:N3}%",
exact, approximate, 100.0 * (approximate.SquareDistance / (double)exact.SquareDistance - 1.0));
}
}
Assert.AreEqual(numClusters - 1, successes,
string.Format("Did not succeed every time. Failed {0} of {1} times. Worst distance ratio is {2:N4}. {3} points of {4} dimensions.",
numClusters - successes - 1,
numClusters - 1,
worstRatio,
nPoints,
dimensions
)
);
}
public void ClosestClusterTest(int nPoints, int dimensions, int numClusters, int numCurvesToTry, int numCurvesToKeep)
{
var correctColorCount = 0;
var correctDistanceCount = 0;
var data = new GaussianClustering
{
ClusterCount = numClusters,
Dimensions = dimensions,
MaxCoordinate = 1000,
MinClusterSize = nPoints,
MaxClusterSize = nPoints
};
var closestExact = new PolyChromaticClosestPoint <string> .ClosestPair();
var closestApproximate = new PolyChromaticClosestPoint <string> .ClosestPair();
var clusters = data.MakeClusters();
var pccps = new List <PolyChromaticClosestPoint <string> >();
var bitsPerDimension = (1 + data.MaxCoordinate).SmallestPowerOfTwo();
var bestIndices = OptimalIndex.SearchMany(
clusters.Points().Select(up => HilbertPoint.CastOrConvert(up, bitsPerDimension, true)).ToList(),
numCurvesToKeep,
5 /*outlier size */, 10 /* NoiseSkipBy */, 1 /* ReducedNoiseSkipBy */, numCurvesToTry
);
//var pointLists = bestIndices.Select(result => result.Index.SortedPoints).ToList();
//foreach (var pList in pointLists)
// pccps.Add(new PolyChromaticClosestPoint<string>(clusters, pList));
var indices = bestIndices.Select(result => result.Index).ToList();
foreach (var index in indices)
{
pccps.Add(new PolyChromaticClosestPoint <string>(clusters, index));
}
var pccp1 = pccps[0];
foreach (var color in pccp1.Clusters.ClassLabels())
{
var exact = pccp1.FindClusterExhaustively(color);
var approximate = pccps.Select(pccp => pccp.FindClusterApproximately(color)).OrderBy(cp => cp).First();
if (exact.SquareDistance >= approximate.SquareDistance)
{
correctDistanceCount++;
}
if (exact.Color2.Equals(approximate.Color2))
{
correctColorCount++;
}
if (exact.SquareDistance < closestExact.SquareDistance)
{
closestExact = exact;
}
if (approximate.SquareDistance < closestApproximate.SquareDistance)
{
closestApproximate = approximate;
}
var ratio = approximate.SquareDistance / (double)exact.SquareDistance;
Console.WriteLine(string.Format("Exact {0} vs Approx. {1}. Over by {2:N3}%", exact, approximate, (ratio - 1.0) * 100.0));
}
if (closestExact.SquareDistance >= closestApproximate.SquareDistance)
{
Console.WriteLine("DID FIND the closest pair of points overall. Exact {0}. Approx {1}", closestExact, closestApproximate);
}
else
{
Console.WriteLine("DID NOT FIND the closest pair of points overall. Exact {0}. Approx {1}", closestExact, closestApproximate);
}
Assert.IsTrue(correctColorCount == numClusters && correctDistanceCount == numClusters,
string.Format("Of {0} clusters, only {1} searches found the closest cluster and {2} found the shortest distance.",
numClusters,
correctColorCount,
correctDistanceCount
)
);
}
/// <summary>
/// Perform a classification of two clusters that are near enough to each other to partially overlap, causing problems.
///
/// From this we can deduce which of six cases obtain (the SplitQuality).
/// </summary>
/// <returns>A Tuple with these parts:
/// 1) comparison of actual to expected (with its BCubed),
/// 2) the expected number of clusters
/// 3) the actual number of clusters
/// 4) a qualitative assessment of the results.
/// </returns>
/// <param name="numPoints">Number of points.</param>
/// <param name="dimensions">Number of Dimensions.</param>
/// <param name="overlapPercent">Overlap percent.</param>
/// <param name="clusterSizeVariation">Cluster size variation.</param>
/// <param name="maxCoordinate">Max value of any coordinate.</param>
/// <param name="acceptablePrecision">Acceptable precision</param>
/// <param name="useDensityClassifier">If set to <c>true</c> use density classifier.</param>
private Tuple <ClusterMetric <UnsignedPoint, string>, int, int, SplitQuality> ClassifyTwoClustersHelper(int numPoints, int dimensions, double overlapPercent,
int clusterSizeVariation = 0, int maxCoordinate = 1000, double acceptablePrecision = 0.98, bool useDensityClassifier = true)
{
Logger.SetupForTests();
var bitsPerDimension = maxCoordinate.SmallestPowerOfTwo();
var clusterCount = 2;
var minClusterSize = (numPoints / clusterCount) - clusterSizeVariation;
var maxClusterSize = (numPoints / clusterCount) + clusterSizeVariation;
var outlierSize = 5;
var radiusShrinkage = 0.6; // 0.7 merges too many that belong apart!
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = maxCoordinate,
MinClusterSize = minClusterSize,
MaxClusterSize = maxClusterSize
};
var expectedClusters = data.TwoClusters(overlapPercent);
Classification <UnsignedPoint, string> actualClusters;
if (useDensityClassifier)
{
var hIndex = new HilbertIndex(expectedClusters, bitsPerDimension);
var cc = new ClusterCounter {
NoiseSkipBy = 10, OutlierSize = outlierSize, ReducedNoiseSkipBy = 1
};
var count = cc.Count(hIndex.SortedPoints);
var unmergeableSize = expectedClusters.NumPoints / 6;
var densityClassifier = new DensityClassifier(hIndex, count.MaximumSquareDistance, unmergeableSize)
{
MergeableShrinkage = radiusShrinkage
};
actualClusters = densityClassifier.Classify();
}
else
{
var classifier = new HilbertClassifier(expectedClusters.Points(), 10)
{
OutlierSize = outlierSize
};
//classifier.IndexConfig.NoiseSkipBy = 0;
classifier.IndexConfig.UseSample = false;
actualClusters = classifier.Classify();
}
var comparison = expectedClusters.Compare(actualClusters);
SplitQuality qualitativeResult = SplitQuality.Unsplit;
if (comparison.BCubed >= 1.0)
{
qualitativeResult = SplitQuality.PerfectSplit;
}
else if (actualClusters.NumPartitions == 1)
{
qualitativeResult = SplitQuality.Unsplit;
}
else if (actualClusters.NumPartitions > expectedClusters.NumPartitions && comparison.Precision >= 1.0)
{
qualitativeResult = SplitQuality.GoodOverSplit;
}
else if (actualClusters.NumPartitions > expectedClusters.NumPartitions && comparison.Precision >= acceptablePrecision)
{
qualitativeResult = SplitQuality.FairOverSplit;
}
else if (actualClusters.NumPartitions == expectedClusters.NumPartitions && comparison.Precision >= acceptablePrecision)
{
qualitativeResult = SplitQuality.GoodSplit;
}
else if (actualClusters.NumPartitions > expectedClusters.NumPartitions && comparison.Precision < 1.0)
{
qualitativeResult = SplitQuality.BadOverSplit;
}
else // Assume correct number of clusters.
{
qualitativeResult = SplitQuality.BadSplit;
}
Logger.Info($" Quality: {qualitativeResult} Comparison: {comparison}");
return(new Tuple <ClusterMetric <UnsignedPoint, string>, int, int, SplitQuality>(
comparison,
expectedClusters.NumPartitions,
actualClusters.NumPartitions,
qualitativeResult
));
}
public void ClosestOfFiftyClusters()
{
int hilbertTries = 1000;
var correctColorCount = 0;
var correctCrosscheckCount = 0;
var correctDistanceCount = 0;
var nPoints = 100;
var dimensions = 100;
var clusterCount = 50;
var data = new GaussianClustering
{
ClusterCount = clusterCount,
Dimensions = dimensions,
MaxCoordinate = 1000,
MinClusterSize = nPoints,
MaxClusterSize = nPoints
};
var closestExact = new PolyChromaticClosestPoint <string> .ClosestPair();
var closestApproximate = new PolyChromaticClosestPoint <string> .ClosestPair();
var bitsPerDimension = (1 + data.MaxCoordinate).SmallestPowerOfTwo();
var clusters = data.MakeClusters();
Assert.AreEqual(clusterCount, clusters.NumPartitions, "Test data are grouped into fewer clusters than requested.");
PolyChromaticClosestPoint <string> pccp;
if (hilbertTries <= 1)
{
pccp = new PolyChromaticClosestPoint <string>(clusters);
}
else
{
var reducedNoiseSkipBy = 1;
var results = OptimalIndex.Search(
clusters.Points().Select(up => HilbertPoint.CastOrConvert(up, bitsPerDimension, true)).ToList(),
5 /*outlier size */, 10 /* NoiseSkipBy */, reducedNoiseSkipBy, hilbertTries
);
pccp = new PolyChromaticClosestPoint <string>(clusters, results.Index);
}
foreach (var color in pccp.Clusters.ClassLabels())
{
var exact = pccp.FindClusterExhaustively(color);
var approximate = pccp.FindClusterApproximately(color);
var crosscheck = pccp.FindClusterIteratively(color);
if (exact.SquareDistance >= approximate.SquareDistance)
{
correctDistanceCount++;
}
if (exact.Color2.Equals(approximate.Color2))
{
correctColorCount++;
}
if (exact.Color2.Equals(crosscheck.Color2))
{
correctCrosscheckCount++;
}
if (exact.SquareDistance < closestExact.SquareDistance)
{
closestExact = exact;
}
if (approximate.SquareDistance < closestApproximate.SquareDistance)
{
closestApproximate = approximate;
}
var ratio = approximate.SquareDistance / (double)exact.SquareDistance;
Console.WriteLine(string.Format("Exact {0} vs Approx. {1} vs Cross {2}. Over by {3:N3}%", exact, approximate, crosscheck, (ratio - 1.0) * 100.0));
}
if (closestExact.SquareDistance >= closestApproximate.SquareDistance)
{
Console.WriteLine("DID FIND the closest pair of points overall. Exact {0}. Approx {1}", closestExact, closestApproximate);
}
else
{
Console.WriteLine("DID NOT FIND the closest pair of points overall. Exact {0}. Approx {1}", closestExact, closestApproximate);
}
Assert.IsTrue(correctColorCount == clusterCount && correctDistanceCount == clusterCount,
string.Format("Of {0} clusters, only {1} searches found the closest cluster and {2} found the shortest distance. Crosscheck = {3}",
clusterCount,
correctColorCount,
correctDistanceCount,
correctCrosscheckCount
)
);
}
public double SquareDistanceCompareValidationCase(int numTriangulationPoints)
{
var correctResult = 0;
var wrongResult = 0;
var totalComparisons = 10000;
var extraShortTrianagulatable = 0;
var extraShortNotTrianagulatable = 0;
var shortTrianagulatable = 0;
var shortNotTrianagulatable = 0;
var longTrianagulatable = 0;
var longNotTrianagulatable = 0;
// 1. Make test data.
var bitsPerDimension = 10;
var data = new GaussianClustering
{
ClusterCount = 100,
Dimensions = 100,
MaxCoordinate = (1 << bitsPerDimension) - 1,
MinClusterSize = 50,
MaxClusterSize = 150
};
var clusters = data.MakeClusters();
// 2. Create HilbertIndex for points.
var hIndex = new HilbertIndex(clusters, bitsPerDimension);
hIndex.SetTriangulation(numTriangulationPoints);
// 3. Deduce the characteristic distance.
var counter = new ClusterCounter
{
OutlierSize = 5,
NoiseSkipBy = 10
};
var count = counter.Count(hIndex.SortedPoints);
var mergeDistance = count.MaximumSquareDistance;
var longDistance = 5 * mergeDistance;
// 4. Select random pairs of the HilbertPoints points and see how many distance comparisons yield the correct result.
var rng = new FastRandom();
var points = hIndex.SortedPoints.ToList();
for (var i = 0; i < totalComparisons; i++)
{
var p1 = points[rng.Next(points.Count)];
var p2 = points[rng.Next(points.Count)];
var d = p1.Measure(p2);
if (d.CompareTo(mergeDistance) == p1.SquareDistanceCompare(p2, mergeDistance))
{
correctResult++;
}
else
{
wrongResult++;
}
if (d.CompareTo(longDistance) == p1.SquareDistanceCompare(p2, longDistance))
{
correctResult++;
}
else
{
wrongResult++;
}
if (p1.Triangulatable(p2, mergeDistance / 2))
{
extraShortTrianagulatable++;
}
else
{
extraShortNotTrianagulatable++;
}
if (p1.Triangulatable(p2, mergeDistance))
{
shortTrianagulatable++;
}
else
{
shortNotTrianagulatable++;
}
if (p1.Triangulatable(p2, longDistance))
{
longTrianagulatable++;
}
else
{
longNotTrianagulatable++;
}
}
var extraShortPct = 100.0 * extraShortTrianagulatable / (extraShortTrianagulatable + extraShortNotTrianagulatable);
var shortPct = 100.0 * shortTrianagulatable / (shortTrianagulatable + shortNotTrianagulatable);
var longPct = 100.0 * longTrianagulatable / (longTrianagulatable + longNotTrianagulatable);
Console.WriteLine($"Triangulatable? \n XS: {extraShortPct} % \n Short: {shortPct} % Yes {shortTrianagulatable}, No {shortNotTrianagulatable}\n Long: {longPct} % Yes {longTrianagulatable}, No {longNotTrianagulatable}");
Assert.AreEqual(wrongResult, 0, $"{correctResult} correct, {wrongResult} wrong");
return(shortPct);
}