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