/// <summary>
/// Returns LrNorm distance between frequency distributions of two lists
/// </summary>
/// <typeparam name="T">Type of the item, e.g. int or string</typeparam>
/// <param name="l1">First list of items</param>
/// <param name="l2">Second list of items</param>
/// <param name="r">Power to use 2 = Euclidean, 1 = Manhattan</param>
/// <returns>Distance, 0 - identical</returns>
public static double DoLrNorm <T>(List <T> l1, List <T> l2, int r)
{
// find distinct list of values from both lists.
List <T> dvs = FrequencyDist <T> .GetDistinctValues(l1, l2);
// create frequency distributions aligned to list of descrete values
FrequencyDist <T> fd1 = new FrequencyDist <T>(l1, dvs);
FrequencyDist <T> fd2 = new FrequencyDist <T>(l2, dvs);
if (fd1.ItemFreq.Count != fd2.ItemFreq.Count)
{
throw new Exception("Lists of different length for LrNorm calculation");
}
double sumsq = 0.0;
for (int i = 0; i < fd1.ItemFreq.Count; i++)
{
if (!EqualityComparer <T> .Default.Equals(fd1.ItemFreq.Values[i].value, fd2.ItemFreq.Values[i].value))
{
throw new Exception("Mismatched values in frequency distribution for LrNorm calculation");
}
if (r == 1) // Manhattan optimization
{
sumsq += Math.Abs((fd1.ItemFreq.Values[i].count - fd2.ItemFreq.Values[i].count));
}
else
{
sumsq += Math.Pow((double)Math.Abs((fd1.ItemFreq.Values[i].count - fd2.ItemFreq.Values[i].count)), r);
}
}
if (r == 1) // Manhattan optimization
{
return(sumsq);
}
else
{
return(Math.Pow(sumsq, 1.0 / r));
}
}
/// <summary>
/// Calculates the distance between frequency distributions calculated from lists of items
/// </summary>
/// <typeparam name="T">Type of the list item, e.g. int or string</typeparam>
/// <param name="l1">First list of items</param>
/// <param name="l2">Second list of items</param>
/// <returns>Distance in degrees. 90 is totally different, 0 exactly the same</returns>
public static double Distance <T>(List <T> l1, List <T> l2)
{
if (!l1.Any() || !l2.Any())
{
throw new Exception("Cosine Distance: lists cannot be zero length");
}
// find distinct list of items from two lists, used to align frequency distributions from two lists
List <T> dvs = FrequencyDist <T> .GetDistinctValues(l1, l2);
// calculate frequency distributions for each list.
FrequencyDist <T> fd1 = new FrequencyDist <T>(l1, dvs);
FrequencyDist <T> fd2 = new FrequencyDist <T>(l2, dvs);
if (fd1.ItemFreq.Count() != fd2.ItemFreq.Count)
{
throw new Exception("Cosine Distance: Frequency count vectors must be same length");
}
double dotProduct = 0.0;
double l2norm1 = 0.0;
double l2norm2 = 0.0;
for (int i = 0; i < fd1.ItemFreq.Values.Count(); i++)
{
if (!EqualityComparer <T> .Default.Equals(fd1.ItemFreq.Values[i].value, fd2.ItemFreq.Values[i].value))
{
throw new Exception("Mismatched values in frequency distribution for Cosine distance calculation");
}
dotProduct += fd1.ItemFreq.Values[i].count * fd2.ItemFreq.Values[i].count;
l2norm1 += fd1.ItemFreq.Values[i].count * fd1.ItemFreq.Values[i].count;
l2norm2 += fd2.ItemFreq.Values[i].count * fd2.ItemFreq.Values[i].count;
}
double cos = dotProduct / (Math.Sqrt(l2norm1) * Math.Sqrt(l2norm2));
// convert cosine value to radians then to degrees
return(Math.Acos(cos) * 180.0 / Math.PI);
}