add: top cut model initial implementation

src/fitting.py

@@ -58,6 +58,36 @@ def fit_piece_wise_linear(d, C, M=1000):
     return m.X, c0.X, b.X, aic
 
 
+def fit_cut(d, C):
+    """
+    Fits a simple linear regression model to the given data.
+    However the top 10% of points are used to derive a constant which is added as a constraint to the optimization problem.
+    This results in a piece-wise linear function of two parts, where the first part is a linear function while the second function is a constant.
+
+    Parameters:
+    d (array-like): Distance values.
+    C (array-like): Corresponding centrality values.
+
+    Returns:
+    tuple: Optimize slope (m), intercept (t) and breaking point (b)
+    """
+    n = len(d)
+    cut = math.floor(n * 0.1)
+    b = sum(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)
+    for i in range(n - cut, n):
+        model.addConstr(b >= m * d[i] + t) 
+    model.optimize()
+
+    return m.X, t.X, b
+
+
 def fit_linear_regression(d, C):
     """
     Fits a simple linear regression model to the given data using optimization.