Лаба 11 сдана

lab11/lab11.py

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+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
+
+
+# Расчёт степени принадлежности
+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
+
+
+# Расчёт отклонения
+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
+
+
+# Обновление центров кластеров
+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
+
+
+# Работа с plt для визуализации результата
+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")
+
+    # Визуализация
+    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)