/// <summary>
/// Convert one user's preference relations into position matrix
/// See: Brun, A., Hamad, A., Buffet, O., & Boyer, A. (2010).
/// Towards preference relations in recommender systems. Workshop in ECML-PKDD.
/// </summary>
/// <param name="userPreferences"></param>
/// <returns></returns>
public static Vector<double> PreferencesToPositions(SparseMatrix userPreferences)
{
// Count for each preference type
// Actually the original paper count the strict preferred and less preferred by exact match
// but here we just compare with the EquallyPreferred, because the preferences can be
// scalar with Bradley-Terry model. However, it won't affect the result when it is discrete preference relations.
SparseVector preferredCountByItem = SparseVector.OfEnumerable(userPreferences.FoldByRow((count, pref) =>
count + (pref == Config.Preferences.Preferred ? 1 : 0), 0.0));
SparseVector lessPreferredCountByItem = SparseVector.OfEnumerable(userPreferences.FoldByRow((count, pref) =>
count + (pref == Config.Preferences.LessPreferred ? 1 : 0), 0.0));
// Note that we assume the diagonal are left empty
// otherwise the equally count needs to be offset by 1 for each, i.e. item itself does not count
Debug.Assert(userPreferences.Trace() == 0);
SparseVector equallyPreferredCountByItem = SparseVector.OfEnumerable(userPreferences.FoldByRow((count, pref) =>
count + (pref == Config.Preferences.EquallyPreferred ? 1 : 0), 0.0));
// Note that if the position is value zero then it won't appear in positionByItem
// because the use of SparseVector.OfVector() will ignore all zero values
Vector<double> positionByItem =
(preferredCountByItem - lessPreferredCountByItem)
.PointwiseDivide(lessPreferredCountByItem + preferredCountByItem + equallyPreferredCountByItem) + Config.Preferences.PositionShift;
Vector<double> indicatorOfSeenItems = userPreferences.RowSums(); // If zero, then this item has never been seen
for(int i = 0; i < indicatorOfSeenItems.Count; i++)
{
if(indicatorOfSeenItems[i] == 0)
{
positionByItem[i] = SparseVector.Zero;
}
}
// Note that the positions do not add up to 0
// because we shifted all values
Debug.Assert(
Math.Abs(positionByItem.Sum()- ((SparseVector)positionByItem).NonZerosCount * Config.Preferences.PositionShift)
< 0.001);
//+Config.Preferences.PositionShift;
// TODO: May improve later. Some items have position 0 and we dont want to mix
// up the position 0 and the 0 in sparsematrix.
// So we use a constant to hold the space for position value 0
// it should be reverted back when use
//Vector<double> indicatorVector = userPreferences.RowSums();
//for (int i = 0; i < indicatorVector.Count; i++)
//{
//if (indicatorVector[i] != 0 && positionByItem[i] != 0)
//{
// Debug.Assert(true, "By using the PositionShift constant, we should not be in here.");
// positionByItem[i] = Config.ZeroInSparseMatrix;
// }
//}
return positionByItem;
}