def _cmeans0(data, u_old, c, m, metric):
"""
Single step in generic fuzzy c-means clustering algorithm.
Modified from Ross, Fuzzy Logic w/Engineering Applications (2010),
pages 352-353, equations 10.28 - 10.35.
Parameters inherited from cmeans()
"""
# Normalizing, then eliminating any potential zero values.
u_old = normalize_columns(u_old)
u_old = np.fmax(u_old, np.finfo(np.float64).eps)
um = u_old**m
# Calculate cluster centers
data = data.T
cntr = um.dot(data) / np.atleast_2d(um.sum(axis=1)).T
d = _distance(data, cntr, metric)
d = np.fmax(d, np.finfo(np.float64).eps)
jm = (um * d**2).sum()
u = normalize_power_columns(d, -2. / (m - 1))
return cntr, u, jm, d
def _cmeans_predict0(test_data, cntr, u_old, c, m, metric):
"""
Single step in fuzzy c-means prediction algorithm. Clustering algorithm
modified from Ross, Fuzzy Logic w/Engineering Applications (2010)
p.352-353, equations 10.28 - 10.35, but this method to generate fuzzy
predictions was independently derived by Josh Warner.
Parameters inherited from cmeans()
Very similar to initial clustering, except `cntr` is not updated, thus
the new test data are forced into known (trained) clusters.
"""
# Normalizing, then eliminating any potential zero values.
u_old = normalize_columns(u_old)
u_old = np.fmax(u_old, np.finfo(np.float64).eps)
um = u_old**m
test_data = test_data.T
# For prediction, we do not recalculate cluster centers. The test_data is
# forced to conform to the prior clustering.
d = _distance(test_data, cntr, metric)
d = np.fmax(d, np.finfo(np.float64).eps)
jm = (um * d**2).sum()
u = normalize_power_columns(d, -2. / (m - 1))
return u, jm, d
def _pfcm0(data, centers_old, gamma, c, m, eta, a, b):
""" Single step of pfcm"""
dist = _distance(data, centers_old)
dist = np.fmax(dist,
np.finfo(np.float64).eps
) #Nullen vorsichtshalber durch minimum Wert ersetzen"
#Zugehörigkeitsgrade berechnen (u_i_k)
u = normalize_power_columns(dist, -2. / (m - 1))
#Berechnung der Typischkeitswerte
#Wichtige Funktionen:
#np.reciprocal: reciprocal(x) entspricht 1/x, nur Elementweise
#np.ones: Matrix mit Dimension (x,y) mit Einsen gefüllt, x Anzahl der Zeilen, y Spalten
# Compute typicality values
d2 = dist**2
d2 = np.fmax(d2, np.finfo(np.float64).eps)
t = np.reciprocal(
np.add(np.ones((c, data.shape[0])),
(np.divide(np.multiply(d2, b).T, gamma).T**(1. / (eta - 1)))))
#Clusterzentroiden berechnen (v_i)
#ut entspricht der Summe (a*u_i_k**m + b*t_i_k**eta)
ut = np.add(np.multiply((u**m), a), np.multiply((t**eta), b))
centers = np.divide((ut.dot(data)).T, (ut.sum(axis=1)).T).T
#Berechnung der Zielfunktion J_m_eta
d_new = _distance(data, centers)
d_new = np.fmax(d_new, np.finfo(np.float64).eps)
d_new = d_new**2
d_new = np.fmax(d_new, np.finfo(np.float64).eps)
jm = np.multiply(ut, d_new).sum() + np.multiply(gamma, (np.subtract(
np.ones((c, data.shape[0])), t)**eta).sum(axis=1).T).sum()
return centers, u, t, jm