/// <summary>
/// Group answer sheets in each answer strategy.
/// Hierarchical clustering / Group average method
/// </summary>
/// <param name="answers"></param>
/// <param name="feature">Using feature</param>
/// <returns></returns>
private HierarchicalClusteringResult ClusteringAnswerSheets(List<AnswerSheet> answers, ClassificationFeature feature)
{
Stopwatch sw = new Stopwatch();
Console.WriteLine("Start answer process grouping: " + feature.ToString());
sw.Start();
AnswerDendrogramTreeNode treeParent = null;
// Cache matrix of answer step grouping results
List<List<AnswerStep>> answerSteps = new List<List<AnswerStep>>();
if (feature == ClassificationFeature.Proposed)
{
Console.WriteLine("Answer Step Grouping...");
for (int i = 0, ilen = answers.Count; i < ilen; i++)
{
List<AnswerStep> s = GroupAnswerStep(answers[i].Strokes);
answerSteps.Add(s);
}
Console.WriteLine("Finished: " + sw.Elapsed);
}
// Cache matrix of answer process distance results
Console.WriteLine("Creating answer process similarity table...");
double[,] answerDistances = new double[answers.Count, answers.Count];
double[,] answerDistances_Time = new double[answers.Count, answers.Count];
double adAvg = 0.0;
double adStd = 0.0;
double adTimeAvg = 0.0;
double adTimeStd = 0.0;
int adNum = 0;
for (int i = 0, ilen = answers.Count; i < ilen; i++)
{
answerDistances[i, i] = 0.0;
answerDistances_Time[i, i] = 0.0;
}
for (int i = 0, ilen = answers.Count; i < ilen; i++)
{
for (int k = i + 1; k < ilen; k++)
{
// proposed method
if (feature == ClassificationFeature.Proposed)
{
answerDistances[i, k] = CalcAnswerProcessSimilarity(answerSteps[i], answerSteps[k]).Distance;
answerDistances[k, i] = answerDistances[i, k];
adAvg += answerDistances[i, k];
adStd += answerDistances[i, k] * answerDistances[i, k];
}
// answering time
if (feature == ClassificationFeature.AnswerTime)
{
// answering time
answerDistances_Time[i, k] = Math.Abs((long)(answers[i].AnswerTime - answers[k].AnswerTime));
// writing time
//answerDistances_Time[i, k] = Math.Abs((long)(answers[i].WritingTime - answers[k].WritingTime));
answerDistances_Time[k, i] = answerDistances_Time[i, k];
adTimeAvg += answerDistances_Time[i, k];
adTimeStd += answerDistances_Time[i, k] * answerDistances_Time[i, k];
}
adNum++;
}
}
adAvg /= (double)adNum;
adStd -= adAvg * adAvg;
adStd = Math.Sqrt(adStd);
adTimeAvg /= (double)adNum;
adTimeStd -= adTimeAvg * adTimeAvg;
adTimeStd = Math.Sqrt(adTimeStd);
// standardization of answer process similarity distance matrix
// subtract average and devide standard deviation: average 0 and variance 1
double[,] stdDistanceTable = new double[answers.Count, answers.Count];
for (int i = 0, ilen = answers.Count; i < ilen; i++)
{
for (int k = i + 1; k < ilen; k++)
{
switch (feature)
{
case ClassificationFeature.Proposed:
stdDistanceTable[i, k] = (answerDistances[i, k] - adAvg) / adStd;
break;
case ClassificationFeature.AnswerTime:
stdDistanceTable[i, k] = (answerDistances_Time[i, k] - adTimeAvg) / adTimeStd;
break;
}
stdDistanceTable[k, i] = stdDistanceTable[i, k];
}
}
Console.WriteLine("Finished: " + sw.Elapsed);
// Initial condition -> 1 element in 1 cluster
// bottom up hierarchical clustering
Console.WriteLine("Clustering answersheets (Group Average Method)...");
List<AnswerDendrogramTreeNode> treeElements = new List<AnswerDendrogramTreeNode>();
foreach (AnswerSheet answer in answers)
{
AnswerDendrogramTreeNode node = new AnswerDendrogramTreeNode();
node.AnswerData = answer;
treeElements.Add(node);
}
while (treeElements.Count != 1)
{
// Join clusters that indicate minimum distance combination
int minPair1 = 0;
int minPair2 = 0;
double minDistance = double.MaxValue;
for (int i = 0, ilen = treeElements.Count; i < ilen; i++)
{
for (int k = i + 1; k < ilen; k++)
{
// calculate group average
List<AnswerSheet> cluster1 = treeElements[i].GetClusterAnswerSheets();
List<AnswerSheet> cluster2 = treeElements[k].GetClusterAnswerSheets();
double d = CalcAnswersGroupAverage(cluster1, cluster2, stdDistanceTable);
if (d < minDistance)
{
minPair1 = i;
minPair2 = k;
minDistance = d;
}
}
}
// join nodes
AnswerDendrogramTreeNode child1 = treeElements[minPair1];
AnswerDendrogramTreeNode child2 = treeElements[minPair2];
AnswerDendrogramTreeNode[] children = new AnswerDendrogramTreeNode[] { child1, child2 };
AnswerDendrogramTreeNode node = new AnswerDendrogramTreeNode(children, minDistance, stdDistanceTable);
treeElements.Add(node);
treeElements.Remove(child1);
treeElements.Remove(child2);
}
treeParent = treeElements[0];
sw.Stop();
Console.WriteLine("Finished: " + sw.Elapsed);
HierarchicalClusteringResult result = new HierarchicalClusteringResult();
result.RootTree = treeParent;
result.AnswerSheetDistances = stdDistanceTable;
return result;
}
/// <summary>
/// Get cluster tree height
/// </summary>
/// <returns></returns>
public int GetClusterTreeHeight(ClassificationFeature feature)
{
int height = 0;
switch (feature)
{
case ClassificationFeature.Proposed:
height = this.hierarchicalResult.RootTree.GetHeight();
break;
case ClassificationFeature.AnswerTime:
height = this.hierarchicalResultAnswerTime.RootTree.GetHeight();
break;
}
return height;
}
