/// <inheritdoc/>
/// <remarks>
/// <para>
/// This method has been overridden to support
/// the optimization of functions whose arguments
/// are continuous variables.
/// </para>
/// </remarks>
protected internal override void PartialSample(
double[] destinationArray,
Tuple <int, int> sampleSubsetRange,
RandomNumberGenerator randomNumberGenerator,
DoubleMatrix parameter,
int sampleSize)
{
// Must be Item1 included, Item2 excluded
int subSampleSize =
sampleSubsetRange.Item2 - sampleSubsetRange.Item1;
for (int j = 0; j < this.StateDimension; j++)
{
var distribution = new
GaussianDistribution(
mu: parameter[0, j],
sigma: parameter[1, j])
{
RandomNumberGenerator = randomNumberGenerator
};
distribution.Sample(
subSampleSize,
destinationArray,
j * sampleSize + sampleSubsetRange.Item1);
}
}
public static Matrix RandomOrthogonal(int size)
{
GaussianDistribution dist = new GaussianDistribution();
Matrix m = new Matrix(size, size, (i, j) => dist.Sample());
(Matrix q, Matrix r) = m.GramSchmidt();
return(q);
}
public double Evaluate(Vector input)
{
double sum = 0;
for (int i = 0; i < input.Length; ++i)
{
double xi = input[i];
sum += (i + 1) * (xi * xi * xi * xi) + noise.Sample();
}
return(sum);
}
static TestableCombinationOptimizationContext01()
{
const int numberOfItems = 12;
var target = DoubleMatrix.Dense(numberOfItems, 1,
new double[numberOfItems]
{
0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2
});
partition = IndexPartition.Create(target);
data = DoubleMatrix.Dense(numberOfItems, 7);
// features 0 to 4
var g = new GaussianDistribution(mu: 0, sigma: .1);
for (int j = 0; j < 5; j++)
{
data[":", j] = g.Sample(sampleSize: numberOfItems);
}
var partIdentifiers = partition.Identifiers;
// feature 5 to 6
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;
}
}
// Set how to sample system states
// given the specified parameter.
protected internal override void PartialSample(
double[] destinationArray,
Tuple <int, int> sampleSubsetRange,
RandomNumberGenerator randomNumberGenerator,
DoubleMatrix parameter,
int sampleSize)
{
// Must be Item1 included, Item2 excluded
int subSampleSize = sampleSubsetRange.Item2 - sampleSubsetRange.Item1;
var distribution = new GaussianDistribution(
parameter[0], parameter[1])
{
RandomNumberGenerator = randomNumberGenerator
};
distribution.Sample(
subSampleSize,
destinationArray, sampleSubsetRange.Item1);
}
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);
}
public void Main()
{
// Set the number of items and features under study.
const int numberOfItems = 12;
int numberOfFeatures = 7;
// Create a matrix that will represent
// an artificial data set,
// having 12 items (rows) and 7 features (columns).
// This will store the observations which
// partition discovery will be based on.
var data = DoubleMatrix.Dense(
numberOfRows: numberOfItems,
numberOfColumns: numberOfFeatures);
// Fill the data rows by sampling from a different
// distribution while, respectively, drawing observations
// for items 0 to 3, 4 to 7, and 8 to 11: these will be the
// three different parts expected to be included in the
// optimal partition.
double mu = 1.0;
var g = new GaussianDistribution(mu: mu, sigma: .01);
IndexCollection range = IndexCollection.Range(0, 3);
for (int j = 0; j < numberOfFeatures; j++)
{
data[range, j] = g.Sample(sampleSize: range.Count);
}
mu += 5.0;
g.Mu = mu;
range = IndexCollection.Range(4, 7);
for (int j = 0; j < numberOfFeatures; j++)
{
data[range, j] = g.Sample(sampleSize: range.Count);
}
mu += 5.0;
g.Mu = mu;
range = IndexCollection.Range(8, 11);
for (int j = 0; j < numberOfFeatures; j++)
{
data[range, j] = g.Sample(sampleSize: range.Count);
}
Console.WriteLine("The data set:");
Console.WriteLine(data);
// Define the optimization problem as
// the minimization of the Davies-Bouldin Index
// of a candidate partition.
double objectiveFunction(DoubleMatrix x)
{
// An argument x has 12 entries, each belonging
// to the set {0,...,k-1}, where k is the
// maximum number of allowed parts, so
// x[j]==i signals that, at x, item j
// has been assigned to part i.
IndexPartition <double> selected =
IndexPartition.Create(x);
var performance = IndexPartition.DaviesBouldinIndex(
data: data,
partition: selected);
return(performance);
}
var optimizationGoal = OptimizationGoal.Minimization;
// Define the maximum number of parts allowed in the
// partition to be discovered.
int maximumNumberOfParts = 3;
// Create the required context.
var context = new PartitionOptimizationContext(
objectiveFunction: objectiveFunction,
stateDimension: numberOfItems,
partitionDimension: maximumNumberOfParts,
probabilitySmoothingCoefficient: .8,
optimizationGoal: optimizationGoal,
minimumNumberOfIterations: 3,
maximumNumberOfIterations: 1000);
// Create the optimizer.
var optimizer = new SystemPerformanceOptimizer()
{
PerformanceEvaluationParallelOptions = { MaxDegreeOfParallelism = -1 },
SampleGenerationParallelOptions = { MaxDegreeOfParallelism = -1 }
};
// Set optimization parameters.
double rarity = 0.01;
int sampleSize = 2000;
// Solve the problem.
var results = optimizer.Optimize(
context,
rarity,
sampleSize);
IndexPartition <double> optimalPartition =
IndexPartition.Create(results.OptimalState);
// Show the results.
Console.WriteLine(
"The Cross-Entropy optimizer has converged: {0}.",
results.HasConverged);
Console.WriteLine();
Console.WriteLine("Initial guess parameter:");
Console.WriteLine(context.InitialParameter);
Console.WriteLine();
Console.WriteLine("The minimizer of the performance is:");
Console.WriteLine(results.OptimalState);
Console.WriteLine();
Console.WriteLine(
"The optimal partition is:");
Console.WriteLine(optimalPartition);
Console.WriteLine();
Console.WriteLine("The minimum performance is:");
Console.WriteLine(results.OptimalPerformance);
Console.WriteLine();
Console.WriteLine("The Dunn Index for the optimal partition is:");
var di = IndexPartition.DunnIndex(
data,
optimalPartition);
Console.WriteLine(di);
}
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,
// 4 to 7, and 8 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 the selection problem as
// the maximization of the Dunn Index.
double objectiveFunction(DoubleMatrix x)
{
// An argument x has entries equal to one,
// signaling that the corresponding features
// are selected at x. Otherwise, the entries
// are zero.
IndexCollection selected = x.FindNonzero();
double performance =
IndexPartition.DunnIndex(
data: data[":", selected],
partition: partition);
return(performance);
}
var optimizationGoal = OptimizationGoal.Maximization;
// Define how many features must be selected
// for explanation.
int numberOfExplanatoryFeatures = 2;
// Create the required context.
var context = new CombinationOptimizationContext(
objectiveFunction: objectiveFunction,
stateDimension: numberOfFeatures,
combinationDimension: numberOfExplanatoryFeatures,
probabilitySmoothingCoefficient: .8,
optimizationGoal: optimizationGoal,
minimumNumberOfIterations: 3,
maximumNumberOfIterations: 1000);
// Create the optimizer.
var optimizer = new SystemPerformanceOptimizer()
{
PerformanceEvaluationParallelOptions = { MaxDegreeOfParallelism = -1 },
SampleGenerationParallelOptions = { MaxDegreeOfParallelism = -1 }
};
// Set optimization parameters.
double rarity = 0.01;
int sampleSize = 1000;
// Solve the problem.
var results = optimizer.Optimize(
context,
rarity,
sampleSize);
IndexCollection optimalExplanatoryFeatureIndexes =
results.OptimalState.FindNonzero();
// Show the results.
Console.WriteLine(
"The Cross-Entropy optimizer has converged: {0}.",
results.HasConverged);
Console.WriteLine();
Console.WriteLine("Initial guess parameter:");
Console.WriteLine(context.InitialParameter);
Console.WriteLine();
Console.WriteLine("The maximizer of the performance is:");
Console.WriteLine(results.OptimalState);
Console.WriteLine();
Console.WriteLine(
"The {0} features best explaining the given partition have column indexes:",
numberOfExplanatoryFeatures);
Console.WriteLine(optimalExplanatoryFeatureIndexes);
Console.WriteLine();
Console.WriteLine("The maximum performance is:");
Console.WriteLine(results.OptimalPerformance);
Console.WriteLine();
Console.WriteLine("This is the Dunn Index for the selected features:");
var di = IndexPartition.DunnIndex(
data[":", optimalExplanatoryFeatureIndexes],
partition);
Console.WriteLine(di);
}
public void ExplainTest()
{
// data is null
{
string parameterName = "data";
ArgumentExceptionAssert.Throw(
() =>
{
Clusters.Explain(
data: null,
partition: IndexPartition.Create(
DoubleMatrix.Dense(10, 1)),
numberOfExplanatoryFeatures: 2);;
},
expectedType: typeof(ArgumentNullException),
expectedPartialMessage:
ArgumentExceptionAssert.NullPartialMessage,
expectedParameterName: parameterName);
}
// data is null
{
string parameterName = "partition";
ArgumentExceptionAssert.Throw(
() =>
{
Clusters.Explain(
data: DoubleMatrix.Dense(10, 5),
partition: null,
numberOfExplanatoryFeatures: 2);;
},
expectedType: typeof(ArgumentNullException),
expectedPartialMessage:
ArgumentExceptionAssert.NullPartialMessage,
expectedParameterName: parameterName);
}
// numberOfExplanatoryFeatures is zero
{
var STR_EXCEPT_PAR_MUST_BE_POSITIVE =
ImplementationServices.GetResourceString(
"STR_EXCEPT_PAR_MUST_BE_POSITIVE");
string parameterName = "numberOfExplanatoryFeatures";
ArgumentExceptionAssert.Throw(
() =>
{
Clusters.Explain(
data: DoubleMatrix.Dense(10, 5),
partition: IndexPartition.Create(
DoubleMatrix.Dense(10, 1)),
numberOfExplanatoryFeatures: 0);
},
expectedType: typeof(ArgumentOutOfRangeException),
expectedPartialMessage:
STR_EXCEPT_PAR_MUST_BE_POSITIVE,
expectedParameterName: parameterName);
}
// numberOfExplanatoryFeatures is negative
{
var STR_EXCEPT_PAR_MUST_BE_POSITIVE =
ImplementationServices.GetResourceString(
"STR_EXCEPT_PAR_MUST_BE_POSITIVE");
string parameterName = "numberOfExplanatoryFeatures";
ArgumentExceptionAssert.Throw(
() =>
{
Clusters.Explain(
data: DoubleMatrix.Dense(10, 5),
partition: IndexPartition.Create(
DoubleMatrix.Dense(10, 1)),
numberOfExplanatoryFeatures: -1);
},
expectedType: typeof(ArgumentOutOfRangeException),
expectedPartialMessage:
STR_EXCEPT_PAR_MUST_BE_POSITIVE,
expectedParameterName: parameterName);
}
// numberOfExplanatoryFeatures is equal to the number of columns in data
{
var STR_EXCEPT_PAR_MUST_BE_LESS_THAN_OTHER_COLUMNS =
string.Format(
ImplementationServices.GetResourceString(
"STR_EXCEPT_PAR_MUST_BE_LESS_THAN_OTHER_COLUMNS"),
"numberOfExplanatoryFeatures",
"data");
string parameterName = "numberOfExplanatoryFeatures";
ArgumentExceptionAssert.Throw(
() =>
{
Clusters.Explain(
data: DoubleMatrix.Dense(10, 5),
partition: IndexPartition.Create(
DoubleMatrix.Dense(10, 1)),
numberOfExplanatoryFeatures: 5);
},
expectedType: typeof(ArgumentException),
expectedPartialMessage:
STR_EXCEPT_PAR_MUST_BE_LESS_THAN_OTHER_COLUMNS,
expectedParameterName: parameterName);
}
// numberOfExplanatoryFeatures is greater than the number of columns in data
{
var STR_EXCEPT_PAR_MUST_BE_LESS_THAN_OTHER_COLUMNS =
string.Format(
ImplementationServices.GetResourceString(
"STR_EXCEPT_PAR_MUST_BE_LESS_THAN_OTHER_COLUMNS"),
"numberOfExplanatoryFeatures",
"data");
string parameterName = "numberOfExplanatoryFeatures";
ArgumentExceptionAssert.Throw(
() =>
{
Clusters.Explain(
data: DoubleMatrix.Dense(10, 5),
partition: IndexPartition.Create(
DoubleMatrix.Dense(10, 1)),
numberOfExplanatoryFeatures: 6);
},
expectedType: typeof(ArgumentException),
expectedPartialMessage:
STR_EXCEPT_PAR_MUST_BE_LESS_THAN_OTHER_COLUMNS,
expectedParameterName: parameterName);
}
// Valid input
{
const int numberOfItems = 12;
var source = DoubleMatrix.Dense(numberOfItems, 1,
new double[numberOfItems]
{
0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2
});
var partition = IndexPartition.Create(source);
var data = DoubleMatrix.Dense(numberOfItems, 7);
// features 0 to 4
var g = new GaussianDistribution(mu: 0, sigma: .1);
for (int j = 0; j < 5; j++)
{
data[":", j] = g.Sample(sampleSize: numberOfItems);
}
var partIdentifiers = partition.Identifiers;
// feature 5 to 6
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;
}
IndexCollection actualFeatureIndexes =
Clusters.Explain(
data: data,
partition: partition,
numberOfExplanatoryFeatures: 2);
IndexCollectionAssert.AreEqual(
expected: IndexCollection.Range(5, 6),
actual: actualFeatureIndexes);
}
}
public void Main()
{
// Set the number of items and features under study.
const int numberOfItems = 12;
int numberOfFeatures = 7;
// Create a matrix that will represent
// an artificial data set,
// having 12 items (rows) and 7 features (columns).
// This will store the observations which
// partition discovery will be based on.
var data = DoubleMatrix.Dense(
numberOfRows: numberOfItems,
numberOfColumns: numberOfFeatures);
// Fill the data rows by sampling from a different
// distribution while, respectively, drawing observations
// for items 0 to 3, 4 to 7, and 8 to 11: these will be the
// three different parts expected to be included in the
// optimal partition.
double mu = 1.0;
var g = new GaussianDistribution(mu: mu, sigma: .01);
IndexCollection range = IndexCollection.Range(0, 3);
for (int j = 0; j < numberOfFeatures; j++)
{
data[range, j] = g.Sample(sampleSize: range.Count);
}
mu += 5.0;
g.Mu = mu;
range = IndexCollection.Range(4, 7);
for (int j = 0; j < numberOfFeatures; j++)
{
data[range, j] = g.Sample(sampleSize: range.Count);
}
mu += 5.0;
g.Mu = mu;
range = IndexCollection.Range(8, 11);
for (int j = 0; j < numberOfFeatures; j++)
{
data[range, j] = g.Sample(sampleSize: range.Count);
}
Console.WriteLine("The data set:");
Console.WriteLine(data);
// Define the maximum number of parts allowed in the
// partition to be discovered.
int maximumNumberOfParts = 3;
// Select the best partition.
IndexPartition <double> optimalPartition =
Clusters.Discover(
data,
maximumNumberOfParts);
// Show the results.
Console.WriteLine();
Console.WriteLine(
"The optimal partition:");
Console.WriteLine(optimalPartition);
Console.WriteLine();
Console.WriteLine("The Davies-Bouldin Index for the optimal partition:");
var dbi = IndexPartition.DaviesBouldinIndex(
data,
optimalPartition);
Console.WriteLine(dbi);
}