// ref for sample mode: https://stats.stackexchange.com/a/3934/289542
public static double CalculateVariance(List <double> values, VarianceCalculationMode mode = VarianceCalculationMode.Sample)
{
if (values.Count < 0)
{
throw new ZeroSizeArrayException();
}
double result = 0;
double mean = Statistics.CalculateMean(values);
foreach (double item in values)
{
result += (item - mean) * (item - mean);
}
if (mode == VarianceCalculationMode.Sample)
{
return(result / (values.Count - 1));
}
else if (mode == VarianceCalculationMode.Population)
{
return(result / values.Count);
}
else
{
throw new NotImplementedException("Statistics > CalculateVariance");
}
}
// **********************************************************************
// Z score standardization is one of the most popular
// method to normalize data. In this case, we rescale
// an original variable to have a mean of zero and
// standard deviation of one.
// **********************************************************************
public static double[] NormalizeUsingZScore(double[] values, VarianceCalculationMode mode)
{
if (values.IsNullOrEmpty())
{
return(null);
}
double[] result = new double[values.Length];
//values.CopyTo(result, 0);
var mean = IRI.Msh.Statistics.Statistics.CalculateMean(values);
var std = IRI.Msh.Statistics.Statistics.CalculateStandardDeviation(values, mode);
// 1399.12.12
// to prevent divide by zero
if (std == 0)
{
std = 1;
}
for (int i = 0; i < values.Length; i++)
{
result[i] = (values[i] - mean) / std;
}
return(result);
}
public static double CalculateStandardDeviation(List <double> values, VarianceCalculationMode mode = VarianceCalculationMode.Sample)
{
if (values.Count < 0)
{
throw new ZeroSizeArrayException();
}
return(Math.Sqrt(Statistics.CalculateVariance(values, mode)));
}
public static Matrix NormalizeColumnsUsingZScore(Matrix values, VarianceCalculationMode mode)
{
if (values == null)
{
return(null);
}
int numberOfColumns = values.NumberOfColumns;
Matrix result = new Matrix(values.NumberOfRows, values.NumberOfColumns);
for (int i = 0; i < numberOfColumns; i++)
{
var columnValues = values.GetColumn(i);
result.SetColumn(i, NormalizeUsingZScore(columnValues, mode));
}
return(result);
}
// **********************************************************************
// In this method, we divide each value by the standard deviation.
// The idea is to have equal variance, but different means and ranges.
// **********************************************************************
public static double[] NormalizeUsingStandardDeviation(double[] values, VarianceCalculationMode mode)
{
if (values.IsNullOrEmpty())
{
return(null);
}
double[] result = new double[values.Length];
var std = Statistics.CalculateStandardDeviation(values, mode);
// to prevent divide by zero
if (std == 0)
{
std = 1;
}
for (int i = 0; i < values.Length; i++)
{
result[i] = (values[i]) / std;
}
return(result);
}
