fix: correct implementation of top cut model

Model assumes that top 10% of centrality values are not effected by the boundary.
This means that they form the basis for the constant part of the two-part function:
  - linear function determined through simple linear regression for the remaining
    points that are below the calculated threshold
  - constant consistenting of the threshold

The threshold describes the median of the centrality values of the top 10% of the
values.

src/fitting.py

@@ -69,23 +69,30 @@ def fit_cut(d, C):
     C (array-like): Corresponding centrality values.
 
     Returns:
-    tuple: Optimize slope (m), intercept (t) and breaking point (b)
+    tuple: Optimize slope (m), intercept (t) and breaking point (b) as well as AIC score
     """
     n = len(d)
-    cut = math.floor(n * 0.1)
+    cut = math.ceil(n * 0.1)
-    b = sum(C[n - cut..n]) / cut
+    b_c = sum(sorted(C[n - cut:n])) / cut
 
     model = gp.Model("Top Cut")
 
     m = model.addVar(vtype=GRB.CONTINUOUS, name="m")
     t = model.addVar(vtype=GRB.CONTINUOUS, name="t")
 
-    model.setObjective(gp.quicksum((C[i] - t - m * d[i])**2 for i in range(n - cut, n)), GRB.MINIMIZE)
+    model.setObjective(gp.quicksum((C[i] - t - m * d[i])**2 for i in range(n) if C[i] <= b_c), GRB.MINIMIZE)
-    for i in range(n - cut, n):
+    for i in range(n - cut):
-        model.addConstr(b >= m * d[i] + t) 
+        model.addConstr(b_c >= m * d[i] + t) 
     model.optimize()
 
-    return m.X, t.X, b
+    b = (b_c - t.X) / m.X
+    print(f"b_c: {b_c} | b: {b}")
+
+    # AIC
+    k = 2
+    aic = 2. * k + n * math.log(model.ObjVal)
+
+    return m.X, t.X, b, aic
 
 
 def fit_linear_regression(d, C):