104 lines
3.4 KiB
Python
104 lines
3.4 KiB
Python
|
import math
|
||
|
|
import random
|
||
|
|
import numpy as np
|
||
|
|
import matplotlib.pyplot as plt
|
||
|
|
|
||
|
|
|
||
|
|
def get_distance(first: np.ndarray, second: np.ndarray) -> float:
|
||
|
|
return math.sqrt(sum([(first[i] - second[i]) ** 2 for i in range(first.shape[0])])) + 1e-5
|
||
|
|
|
||
|
|
|
||
|
|
def affiliation_calculation(data: np.ndarray, centers: np.ndarray, k: int, m: int) -> np.ndarray:
|
||
|
|
data_len = data.shape[0]
|
||
|
|
u = np.zeros((data_len, k))
|
||
|
|
for i in range(data_len):
|
||
|
|
for j in range(k):
|
||
|
|
total = 0
|
||
|
|
distance = get_distance(data[i], centers[j])
|
||
|
|
for c in range(k):
|
||
|
|
total += (distance / get_distance(data[i], centers[c])) ** (2 / (m - 1))
|
||
|
|
u[i, j] = 1 / total
|
||
|
|
return u
|
||
|
|
|
||
|
|
|
||
|
|
def variance_calculation(data: np.ndarray, centers: np.ndarray, u: np.ndarray) -> float:
|
||
|
|
value = 0
|
||
|
|
for j in range(k):
|
||
|
|
for i in range(data.shape[0]):
|
||
|
|
value += get_distance(data[i], centers[j]) ** 2 * u[i, j]
|
||
|
|
return value
|
||
|
|
|
||
|
|
|
||
|
|
def center_update(data: np.ndarray, u: np.ndarray, k: int, m: int) -> np.ndarray:
|
||
|
|
centers = np.zeros((k, data.shape[1]))
|
||
|
|
for j in range(k):
|
||
|
|
total = 0
|
||
|
|
for i in range(data.shape[0]):
|
||
|
|
total += u[i, j] ** m * data[i]
|
||
|
|
centers[j] = total / np.sum(u[:, j] ** m)
|
||
|
|
return centers
|
||
|
|
|
||
|
|
|
||
|
|
def fuzzy_c_means(data: np.ndarray, k: int, m: int, max_iter: int = 100, tol: float = 1e-5) -> (
|
||
|
|
np.ndarray, np.ndarray, float):
|
||
|
|
centers = np.array([[random.randint(data.min(), data.max()) for i in range(data.shape[1])] for j in range(k)])
|
||
|
|
u = None
|
||
|
|
|
||
|
|
value = 0
|
||
|
|
|
||
|
|
for _ in range(max_iter):
|
||
|
|
u = affiliation_calculation(data, centers, k, m)
|
||
|
|
|
||
|
|
new_value = variance_calculation(data, centers, u)
|
||
|
|
if abs(new_value - value) <= tol:
|
||
|
|
return centers, u, value
|
||
|
|
|
||
|
|
value = new_value
|
||
|
|
|
||
|
|
centers = center_update(data, u, k, m)
|
||
|
|
|
||
|
|
return centers, u, value
|
||
|
|
|
||
|
|
|
||
|
|
def visualise_resout(centers: np.ndarray, u: np.ndarray):
|
||
|
|
center_colors = [[random.random(), random.random(), random.random()] for i in range(k)]
|
||
|
|
point_colors = []
|
||
|
|
for i in u:
|
||
|
|
tmp_color = [0, 0, 0]
|
||
|
|
for j in range(k):
|
||
|
|
tmp_color[0] += center_colors[j][0] * i[j]
|
||
|
|
tmp_color[1] += center_colors[j][1] * i[j]
|
||
|
|
tmp_color[2] += center_colors[j][1] * i[j]
|
||
|
|
point_colors.append(tmp_color)
|
||
|
|
|
||
|
|
plt.title("Нечёткая кластеризация")
|
||
|
|
plt.xlabel("Размер зарплаты")
|
||
|
|
|
||
|
|
if data.shape[1] == 1:
|
||
|
|
plt.scatter(data[:, 0], [0] * data.shape[0], c=point_colors)
|
||
|
|
plt.scatter(centers[:, 0], [0] * centers.shape[0], marker='*', edgecolor='black', s=100, c=center_colors)
|
||
|
|
plt.gca().axes.get_yaxis().set_visible(False)
|
||
|
|
else:
|
||
|
|
plt.scatter(data[:, 0], data[:, 1], c=point_colors)
|
||
|
|
plt.scatter(centers[:, 0], centers[:, 1], marker='*', edgecolor='black', s=100, c=center_colors)
|
||
|
|
plt.show()
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == '__main__':
|
||
|
|
data: np.ndarray = np.array(
|
||
|
|
[
|
||
|
|
[
|
||
|
|
random.randint(0, 500)
|
||
|
|
]
|
||
|
|
for i in range(random.randint(40, 100))
|
||
|
|
])
|
||
|
|
k = 3
|
||
|
|
m = 2
|
||
|
|
|
||
|
|
centers, u, value = fuzzy_c_means(data, k, m)
|
||
|
|
print(f"Значение функции отклонений: {value}")
|
||
|
|
print("Степени принадлежности первых 10 точек:")
|
||
|
|
print(*u[:10], sep="\n")
|
||
|
|
print("Центры всех кластеров:")
|
||
|
|
print(*centers, sep="\n")
|
||
|
|
visualise_resout(centers, u)
|