FCM算法

全名为Fuzzy C-Means，是一种聚类算法。

Fuzzy c-means (FCM) is a method of clustering which allows one piece of data to belong to two or more clusters. This method (developed by Dunn in 1973 and improved by Bezdek in 1981) is frequently used in pattern recognition. It is based on minimization of the following objective function:
FCM是一种聚类的方法，可以允许一个数据属于两个或以上的类。这种方法（由Dunn在1973年提出，由Bezdek在1981年改进。）被频繁地用于模式识别。

• J. C. Dunn (1973): “A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters”, Journal of Cybernetics 3: 32-57
• J. C. Bezdek (1981): “Pattern Recognition with Fuzzy Objective Function Algoritms”, Plenum Press, New York

基于最小化下面的目标函数:

Jm=∑i=1N∑j=1Cuijm∣∣xi−cj∣∣2J_m = \sum^{N}_{i=1}{\sum^{C}_{j=1}{u_{ij}^m||x_i-c_j||^2}}Jm​=i=1∑N​j=1∑C​uijm​∣∣xi​−cj​∣∣2

• m是任何大于1的实数
• uiju_{ij}uij​是xix_ixi​在类j上隶属度
• 其中xix_ixi​是第i个d维测量向量
• cjc_jcj​是一个d维的类中心

FCM主要通过迭代更新u和c来得到最终的解。

迭代终点一般选取两个：

• 当u变化的无穷范数小于某个值时
• 当迭代次数达到某个极限时候

这个过程可能会收敛到局部最小值或者是鞍点上

算法流程

1. 初始化矩阵U （描述每个点在不同的类中的概率）
2. 通过U算类中心
   Cj=∑i=1Nuijm∗xi∑i=1NuijmC_j=\frac{\sum^{N}_{i=1}{u_{ij}^m * x_i}}{\sum^{N}_{i=1}{u_{ij}^m}}Cj​=∑i=1N​uijm​∑i=1N​uijm​∗xi​​
3. 更新U，通过之前算出来的类中心
   uij=1∑k=1C(∣∣xi−cj∣∣∣∣xi−ck∣∣)2m−1u_{ij} = \frac{1}{\sum^{C}_{k=1}{(\frac{||x_i-c_j||}{||x_i-c_k||})^{\frac{2}{m-1}}}}uij​=∑k=1C​(∣∣xi​−ck​∣∣∣∣xi​−cj​∣∣​)m−12​1​
4. 如果u变化的无穷范小于某个值的时候，就停下来，否者就转到第2步

其实看到这里，一般来说直接公式来做，就可以把算法实现了。

但我偷了个懒，找了一份代码，原始的代码有些问题，我做了修改后，然后写上了备注（部分备注我写的是英文的~）

Python代码实现

• accuracy函数是用来验证的
• 其他函数都是实现fcm的部分
• 数据文件我放到后面，大家复制之后另存为“SPECTF_New.csv”即可

import pandas as pd
import numpy as np
import random
import operator
import mathdf_full = pd.read_csv("SPECTF_New.csv")
columns = list(df_full.columns)
features = columns[:len(columns) - 1]
class_labels = list(df_full[columns[-1]])
df = df_full[features]# Number of Attributes
num_attr = len(df.columns) - 1# Number of Clusters
k = 2# Maximum number of iterations
MAX_ITER = 100# Number of data points
n = len(df)# Fuzzy parameter
m = 2.00def accuracy(cluster_labels, class_labels):county = [0, 0]countn = [0, 0]tp = [0, 0]tn = [0, 0]fp = [0, 0]fn = [0, 0]for i in range(len(df)):# Yes = 1, No = 0if cluster_labels[i] == 1 and class_labels[i] == 'Yes':tp[0] = tp[0] + 1if cluster_labels[i] == 0 and class_labels[i] == 'No':tn[0] = tn[0] + 1if cluster_labels[i] == 1 and class_labels[i] == 'No':fp[0] = fp[0] + 1if cluster_labels[i] == 0 and class_labels[i] == 'Yes':fn[0] = fn[0] + 1for i in range(len(df)):# Yes = 0, No = 1if cluster_labels[i] == 0 and class_labels[i] == 'Yes':tp[1] = tp[1] + 1if cluster_labels[i] == 1 and class_labels[i] == 'No':tn[1] = tn[1] + 1if cluster_labels[i] == 0 and class_labels[i] == 'No':fp[1] = fp[1] + 1if cluster_labels[i] == 1 and class_labels[i] == 'Yes':fn[1] = fn[1] + 1a0 = float((tp[0] + tn[0])) / (tp[0] + tn[0] + fn[0] + fp[0])a1 = float((tp[1] + tn[1])) / (tp[1] + tn[1] + fn[1] + fp[1])p0 = float(tp[0]) / (tp[0] + fp[0])p1 = float(tp[1]) / (tp[1] + fp[1])r0 = float(tp[0]) / (tp[0] + fn[0])r1 = float(tp[1]) / (tp[1] + fn[1])accuracy = [a0 * 100, a1 * 100]precision = [p0 * 100, p1 * 100]recall = [r0 * 100, r1 * 100]return accuracy, precision, recall# 返回的矩阵是每个点属于不同的集群的概率（隶属度）
# 随机生成
def initializeMembershipMatrix():membership_mat = list()for i in range(n):random_num_list = [random.random() for i in range(k)]summation = sum(random_num_list)temp_list = [x / summation for x in random_num_list]membership_mat.append(temp_list)return membership_matdef calculateClusterCenter(membership_mat):cluster_mem_val = list(zip(*membership_mat))# cluster_mem_val 's shape is (k, n)cluster_centers = list()for j in range(k):  # 选定一个类别x = cluster_mem_val[j]xraised = [e ** m for e in x]  # m is a Fuzzy parameterdenominator = sum(xraised)  # 求和# 将对应点向量乘上它在该类别上的概率 得到概率向量temp_num = list()for i in range(n):data_point = list(df.iloc[i])prod = [xraised[i] * val for val in data_point]temp_num.append(prod)# 将所有点在对应特征下的概率累积求和numerator = map(sum, zip(*temp_num))center = [z / denominator for z in numerator]# the shape of center is (num_attr,) , which is the number of the features.# 本质上做的是加权平均，关于不同的特征，在不同的点上做加权。权重即为初始概率cluster_centers.append(center)return cluster_centersdef updateMembershipValue(membership_mat, cluster_centers):# m is the Fuzzy parameter.p = float(2 / (m - 1))# cluster_centers : (k, num_attr)for i in range(n):x = list(df.iloc[i])# 算和两个中心的距离，这里采用的是二范数distances = [np.linalg.norm(list(map(operator.sub, x, cluster_centers[j]))) for j in range(k)]# 更新概率矩阵for j in range(k):den = sum([math.pow(float(distances[j] / distances[c]), p) for c in range(k)])membership_mat[i][j] = float(1 / den)return membership_matdef getClusters(membership_mat):cluster_labels = list()for i in range(n):max_val, idx = max((val, idx) for (idx, val) in enumerate(membership_mat[i]))cluster_labels.append(idx)return cluster_labelsdef fuzzyCMeansClustering():# Membership Matrixmembership_mat = initializeMembershipMatrix()curr = 0while curr <= MAX_ITER:cluster_centers = calculateClusterCenter(membership_mat)# cluster_centers: (k, num_attr). k means k clusters. And num_attr means num_attr features.# 更新 membership_mat 矩阵membership_mat = updateMembershipValue(membership_mat, cluster_centers)cluster_labels = getClusters(membership_mat)curr += 1# print(membership_mat)return cluster_labels, cluster_centerslabels, centers = fuzzyCMeansClustering()
print(labels)
print(len(labels))
# a, p, r = accuracy(labels, class_labels)
#
# print("Accuracy = " + str(a))
# print("Precision = " + str(p))
# print("Recall = " + str(r))

• 数据

Attr_1,Attr_2,Attr_3,Attr_4,Attr_5,Attr_6,Attr_7,Attr_8,Attr_9,Attr_10,Attr_11,Attr_12,Attr_13,Attr_14,Attr_15,Attr_16,Attr_17,Attr_18,Attr_19,Attr_20,Attr_21,Attr_22,Attr_23,Attr_24,Attr_25,Attr_26,Attr_27,Attr_28,Attr_29,Attr_30,Attr_31,Attr_32,Attr_33,Attr_34,Attr_35,Attr_36,Attr_37,Attr_38,Attr_39,Attr_40,Attr_41,Attr_42,Attr_43,Attr_44,Class
57,69,68,75,69,74,73,71,57,61,72,74,73,69,61,58,60,55,71,62,79,70,77,71,65,63,69,55,61,68,75,74,63,64,63,58,69,67,79,77,72,70,61,65,Yes
76,59,82,76,80,56,74,67,67,58,77,71,56,68,60,64,66,66,66,66,82,79,40,45,49,48,75,70,64,35,71,60,39,28,71,66,73,61,71,49,53,45,29,15,Yes
65,62,67,68,65,67,71,71,64,56,73,72,68,69,56,57,67,62,74,66,80,76,80,78,53,47,48,36,68,65,74,73,60,60,67,63,74,63,77,79,68,70,59,56,Yes
70,54,66,66,76,46,74,58,68,52,81,58,67,58,68,32,73,59,76,51,82,57,76,54,58,30,69,41,59,59,67,73,62,55,60,55,65,56,65,44,73,36,51,28,Yes
64,64,70,75,70,71,74,71,59,60,62,68,70,66,69,72,69,69,61,63,56,60,62,66,69,71,62,63,67,65,62,58,52,51,67,66,61,56,64,65,71,73,57,63,Yes
65,67,69,76,62,68,65,66,65,64,74,73,60,75,66,63,64,62,73,65,77,74,69,69,66,59,68,59,69,69,76,79,65,63,60,60,69,64,69,74,69,70,62,57,No
68,70,69,74,65,70,72,73,71,68,73,70,68,74,63,65,65,63,70,67,74,70,69,72,62,63,63,61,66,66,74,80,70,72,69,67,60,57,69,62,66,75,50,50,No
64,66,68,71,62,64,74,73,63,67,66,74,70,74,59,64,75,73,70,66,79,81,79,78,61,62,76,72,67,67,71,75,65,62,70,69,68,65,75,72,62,64,57,54,No
58,63,80,71,76,70,70,71,64,63,74,78,77,75,62,61,62,56,71,52,82,71,84,85,71,71,57,47,42,39,70,70,50,70,50,46,58,60,76,73,82,77,65,66,No
77,79,79,77,74,76,76,81,65,68,66,66,74,73,72,68,67,73,63,62,72,67,76,69,68,64,64,61,69,68,73,75,70,66,64,70,70,70,73,76,79,73,65,63,No
54,53,73,68,77,65,65,72,60,50,69,64,73,75,74,76,69,72,66,60,74,67,68,69,69,78,56,67,69,61,76,71,67,64,73,70,55,49,70,61,73,70,61,61,Yes
59,57,67,71,66,68,68,70,56,62,77,61,67,71,75,71,67,64,62,54,64,75,71,72,76,79,75,70,71,77,71,69,56,54,62,64,56,53,71,68,64,63,56,56,No
68,64,74,80,76,72,78,75,67,64,75,80,78,77,66,64,67,67,70,60,78,82,70,68,63,60,64,60,54,56,70,73,59,65,55,58,50,51,73,70,69,65,42,41,No
78,73,68,74,68,69,63,74,68,67,73,73,66,71,64,67,66,68,61,66,75,71,60,62,64,66,65,67,66,62,74,75,61,61,63,66,68,65,71,62,69,67,61,59,Yes
64,72,70,74,63,70,73,74,61,69,65,75,61,71,65,67,73,69,72,71,74,81,69,69,65,65,78,75,67,71,66,74,54,60,64,68,64,68,69,71,65,65,56,58,Yes
70,64,68,67,76,68,76,69,67,64,69,65,62,65,70,67,74,68,65,65,74,75,64,69,63,63,64,64,56,61,62,68,66,66,62,58,57,48,75,64,79,74,59,58,No
71,75,78,78,68,67,75,72,67,68,72,75,74,74,67,66,66,67,66,66,78,80,73,75,67,72,67,67,67,65,77,78,61,64,63,66,51,57,77,67,78,76,60,59,No
56,56,63,66,76,76,68,73,62,54,65,62,70,65,74,72,65,64,64,53,64,56,63,61,73,64,66,60,66,74,76,75,65,61,71,73,60,53,61,73,67,68,59,56,No
72,66,75,67,61,59,64,63,61,67,75,76,66,48,61,56,69,68,68,68,68,75,69,67,68,71,70,68,48,47,74,79,63,75,62,62,64,67,56,52,69,83,59,73,Yes
71,76,74,79,71,69,77,75,64,64,75,78,69,70,59,52,71,62,47,50,68,65,67,62,56,48,58,50,65,63,75,75,64,62,60,56,64,63,61,65,64,58,51,38,Yes
68,70,66,72,63,71,77,82,61,63,61,62,61,65,65,62,72,77,69,73,72,78,74,77,69,69,77,74,64,63,66,70,58,60,65,69,75,77,77,77,69,77,65,64,No
64,53,74,70,65,63,70,70,57,57,64,64,73,74,65,59,65,63,63,62,72,73,79,76,75,68,60,58,69,66,72,76,64,65,63,65,63,65,75,80,74,67,71,67,No
74,73,72,79,66,61,76,66,65,64,78,74,62,57,48,36,62,50,67,63,79,70,61,57,52,36,69,49,55,65,74,73,58,60,64,62,73,69,62,67,60,56,53,46,Yes
69,64,73,72,49,70,66,71,57,56,64,62,76,74,65,62,63,58,63,63,75,76,78,80,75,77,51,62,74,68,77,77,70,68,68,64,59,58,69,66,74,75,62,59,No
70,75,72,72,67,71,71,78,63,67,73,76,71,74,59,61,67,64,74,71,77,77,70,72,61,61,62,58,63,69,76,75,64,65,66,67,68,70,70,71,64,67,56,54,No
63,63,69,72,67,62,65,57,68,53,68,71,73,78,64,58,61,54,70,61,72,67,72,68,57,55,61,53,66,60,76,77,73,66,66,58,75,70,77,67,78,68,64,58,Yes
63,58,66,55,56,58,69,74,44,48,63,60,76,67,73,73,58,66,68,63,72,74,70,72,77,75,70,71,71,67,75,73,60,59,71,70,65,62,70,69,71,70,58,61,Yes
71,61,74,74,76,74,69,56,68,78,71,78,58,64,70,72,71,68,72,71,79,78,67,68,63,60,67,67,76,74,67,79,67,71,71,64,70,74,83,76,74,73,54,54,No
67,57,73,78,63,68,72,73,61,59,59,76,71,72,69,66,70,68,65,77,79,68,71,75,62,66,70,78,68,69,70,76,65,65,66,67,62,72,69,72,70,68,60,59,No
62,67,68,70,65,70,73,77,69,70,69,73,71,74,71,71,76,75,66,67,73,73,70,74,63,67,58,68,66,69,78,79,69,70,71,73,72,71,73,77,72,76,64,66,No
70,72,65,64,71,69,75,76,65,68,69,79,65,74,62,67,73,73,53,51,72,69,74,68,49,44,52,48,65,68,64,72,57,58,66,69,64,69,76,73,66,69,50,53,Yes
70,64,52,58,75,89,70,72,26,30,46,55,54,59,40,40,39,37,35,17,59,52,66,72,23,46,8,31,17,20,49,72,61,70,31,13,40,23,31,30,57,67,41,57,Yes
67,65,77,74,67,66,67,70,65,64,75,78,66,74,62,60,65,65,73,72,75,76,74,81,66,65,65,63,63,67,76,80,63,64,63,64,73,72,76,75,72,74,65,64,No
76,72,73,69,67,73,74,72,60,65,73,66,66,73,68,67,69,70,60,58,66,76,69,75,65,64,63,60,74,71,77,79,61,68,71,70,62,63,73,76,62,69,52,59,No
61,63,58,62,56,60,67,75,61,57,64,71,56,59,66,62,73,76,71,75,83,84,69,71,69,69,69,71,49,43,59,64,56,61,64,72,70,73,69,70,65,68,65,62,Yes
74,81,80,78,70,69,74,77,69,71,73,76,68,68,62,61,68,68,67,70,74,80,68,74,57,62,57,65,61,65,71,76,63,65,67,67,70,74,63,72,68,70,61,64,No
75,71,54,51,53,50,68,69,46,55,11,12,43,48,61,60,73,77,46,45,68,59,65,73,54,60,55,66,54,41,53,52,58,63,72,65,33,23,64,54,36,46,45,52,Yes
68,64,65,68,63,64,77,73,75,72,80,77,70,71,61,61,73,68,63,62,76,73,69,69,48,59,62,44,66,59,75,74,64,64,63,61,70,69,74,67,51,48,45,45,Yes
70,72,70,70,65,69,70,65,69,72,77,78,68,71,63,70,69,71,68,74,75,74,69,65,71,68,63,64,66,68,73,75,67,67,69,65,66,71,69,65,78,75,66,63,No
76,75,68,78,71,72,72,75,61,65,67,70,67,75,60,58,63,67,59,63,67,72,74,73,56,56,52,52,67,68,73,78,65,68,61,67,69,74,77,75,74,70,63,61,No
69,66,62,75,67,71,72,76,69,70,66,69,71,80,66,64,71,77,65,61,72,67,71,69,65,57,69,65,68,65,76,73,63,64,69,70,72,72,69,68,70,73,63,59,Yes
80,76,75,75,69,68,74,75,77,77,76,78,74,70,66,65,67,75,74,73,74,77,68,67,61,58,60,67,61,63,75,75,66,62,59,61,77,74,69,67,65,66,61,58,No
72,62,69,67,78,82,74,65,69,63,70,70,72,74,70,71,72,75,66,65,73,78,74,79,74,69,69,70,71,69,72,70,62,65,65,71,63,60,69,73,67,71,56,58,Yes
71,75,76,74,71,68,67,68,69,75,75,74,59,58,71,69,70,74,74,72,71,78,69,72,69,72,63,61,59,70,72,75,61,66,70,71,59,64,64,60,72,61,55,63,Yes
60,51,75,60,65,45,64,55,55,61,66,74,61,50,62,41,70,63,60,62,76,69,70,54,51,47,77,80,69,48,74,59,72,57,76,68,69,63,62,53,57,31,46,30,Yes
74,73,72,75,63,62,67,67,73,74,75,79,70,71,64,67,65,69,79,78,81,80,71,73,60,62,69,67,69,69,75,75,66,67,67,66,71,73,66,69,62,65,55,56,No
75,75,70,77,67,75,75,75,67,66,74,73,68,72,64,70,76,70,67,63,74,75,72,68,69,68,75,69,71,74,75,76,63,70,71,69,66,63,70,73,66,68,58,59,No
62,67,64,70,59,58,67,74,60,66,68,68,73,71,60,63,64,74,64,65,74,77,69,73,59,58,58,67,65,69,78,76,61,62,64,67,72,74,71,71,71,69,66,61,No
61,60,60,62,64,72,68,67,74,68,76,70,74,71,76,74,74,70,75,66,69,62,65,60,66,65,68,59,64,59,72,65,55,56,66,66,66,60,60,58,60,67,49,52,Yes
78,76,71,72,65,71,75,74,70,64,65,76,65,73,59,57,65,65,73,73,81,80,68,66,59,44,62,63,62,59,71,74,59,60,64,61,77,76,62,67,44,42,44,30,Yes
70,66,61,66,61,58,69,69,72,68,62,71,71,71,63,59,74,75,70,69,83,77,73,70,41,37,39,40,58,46,75,73,65,66,67,69,70,66,70,64,60,55,49,41,Yes
73,74,65,66,69,69,67,81,65,62,69,65,67,68,70,67,72,68,66,66,78,61,67,70,67,63,68,66,70,70,69,70,66,66,66,69,72,70,74,76,75,72,67,63,No
79,78,66,63,69,62,78,70,72,71,73,78,75,65,68,62,76,71,68,68,72,71,52,48,23,26,66,59,66,66,72,74,56,58,67,63,66,69,70,74,34,33,11,12,Yes
66,81,75,72,69,67,74,81,67,73,76,75,69,64,58,57,74,74,56,62,74,78,55,50,37,38,65,73,61,61,73,73,61,63,67,66,60,71,46,58,35,37,24,20,Yes
76,77,69,70,64,69,76,80,50,56,70,74,61,55,54,59,65,65,53,72,76,73,51,47,43,46,66,80,73,73,71,65,60,53,69,70,54,62,64,66,51,42,28,22,Yes
66,64,64,66,67,72,72,77,65,66,64,64,57,61,70,66,74,78,73,72,77,75,60,58,58,61,63,60,59,60,65,65,58,58,69,73,76,75,73,75,72,72,62,62,No
72,63,68,62,72,63,79,61,57,49,76,75,55,57,43,37,54,52,57,56,78,78,57,55,35,37,57,57,41,35,67,70,75,72,53,46,63,62,53,43,38,35,32,26,Yes
32,41,76,34,65,53,30,54,16,51,61,43,74,70,62,21,34,42,61,37,58,66,54,49,17,19,11,42,53,30,71,9,61,16,31,43,67,61,29,31,17,8,18,11,Yes
69,78,74,76,70,67,69,73,68,75,75,76,71,77,58,61,66,70,67,72,76,72,56,62,56,61,57,62,67,73,76,74,58,63,64,68,66,76,70,72,64,68,60,56,No
40,73,61,74,61,67,56,75,64,71,75,76,63,61,56,67,70,73,69,60,74,63,65,73,57,63,66,69,60,66,72,71,57,64,64,69,67,68,59,66,55,62,51,60,Yes
65,66,71,72,67,75,76,83,70,74,70,76,70,68,63,71,69,76,72,73,76,80,69,68,57,59,59,56,62,68,75,73,65,61,69,73,66,70,63,65,65,67,53,42,Yes
80,74,82,77,74,74,73,77,64,61,73,73,73,72,62,66,66,68,63,61,69,75,70,75,59,64,63,69,66,66,70,77,62,62,60,65,67,66,74,71,66,71,59,62,Yes
67,64,73,75,77,77,74,70,65,62,74,75,65,67,68,70,66,69,67,60,74,75,62,64,66,71,62,61,64,69,73,76,64,66,61,64,65,60,68,75,74,80,67,68,No
71,71,69,71,65,65,76,73,67,66,69,79,76,76,63,62,74,71,58,66,76,78,78,74,68,66,69,68,68,68,71,74,59,57,65,66,73,71,78,74,68,70,57,55,No
63,61,75,72,68,71,69,70,64,56,70,75,76,73,70,72,76,73,68,68,79,76,68,76,66,73,58,68,72,75,72,75,65,61,66,67,58,57,72,72,68,71,57,58,No
70,69,67,66,68,60,76,77,70,67,71,71,79,79,70,64,77,76,63,54,68,65,72,67,59,52,56,50,67,61,74,72,67,59,68,66,73,68,74,68,77,69,65,62,Yes
59,75,70,76,62,70,65,74,65,67,75,76,70,73,63,61,74,67,78,69,75,73,70,68,67,64,79,68,70,75,76,77,59,63,72,69,64,64,65,72,61,61,51,55,No
64,58,70,78,66,66,74,72,66,63,72,74,72,65,59,58,64,67,63,61,75,74,67,58,60,53,61,58,62,61,76,72,64,65,62,64,77,71,74,72,74,73,70,59,No
59,58,69,74,71,73,70,68,57,55,64,68,76,75,67,66,66,63,72,67,77,75,80,75,73,69,65,61,71,75,71,77,65,66,66,66,61,56,74,71,72,69,62,60,No
72,70,75,80,73,70,76,73,66,56,72,70,73,75,67,65,69,69,73,72,81,77,80,79,67,64,64,66,69,68,70,75,63,59,66,63,74,77,81,78,79,75,65,66,No
68,59,77,69,77,64,75,71,64,53,67,63,66,74,74,62,67,65,70,61,73,66,78,75,72,67,67,53,72,64,71,77,66,60,73,73,70,58,70,59,77,71,70,63,Yes
61,68,62,70,76,79,71,71,73,77,75,77,68,73,72,72,71,68,72,75,81,80,72,73,61,67,62,61,66,68,72,71,67,67,69,69,66,71,67,66,74,71,58,58,No
75,73,72,77,68,67,76,73,67,65,76,78,66,74,67,62,70,69,66,64,77,74,75,73,67,69,73,69,68,68,72,74,61,61,70,67,72,71,79,75,77,75,67,71,No
70,66,66,68,71,69,64,61,68,67,50,53,73,71,73,63,71,73,80,81,82,82,67,71,52,47,67,64,66,67,66,75,58,62,65,65,71,67,70,71,67,64,52,53,Yes
69,68,75,74,78,72,75,72,61,57,72,71,75,72,70,68,68,62,62,66,67,67,74,78,64,68,62,62,64,63,75,77,66,67,69,65,62,63,64,59,74,75,63,67,Yes
73,80,78,78,75,73,78,75,70,66,77,77,67,71,60,63,71,74,77,75,74,76,61,67,60,60,64,63,62,58,72,77,59,58,65,70,68,69,64,64,63,63,56,51,No
55,66,58,75,71,77,68,73,63,69,77,78,60,69,59,60,69,69,67,70,72,80,67,72,53,60,70,58,46,67,68,84,69,79,70,74,62,71,67,66,63,61,53,60,Yes
66,67,63,70,69,70,73,72,61,62,68,68,70,71,71,67,71,69,65,65,76,78,71,70,65,64,68,71,70,71,73,74,58,63,68,71,70,72,77,79,79,79,66,66,No
70,69,60,62,58,60,71,77,69,69,73,68,68,70,69,65,76,75,63,64,67,74,56,60,54,44,68,69,68,68,74,73,61,59,68,67,64,68,64,76,64,61,54,49,Yes
75,72,75,79,72,68,79,77,69,66,73,77,67,73,57,58,69,69,67,65,77,68,69,65,58,54,68,60,67,66,75,78,63,66,68,64,72,69,73,61,52,44,34,37,Yes
61,76,71,68,77,69,77,69,64,75,71,81,75,72,71,69,70,73,61,71,69,79,64,65,62,66,61,65,71,68,67,71,59,64,66,65,60,68,74,71,69,68,63,59,No
76,73,74,76,60,69,76,76,68,69,78,79,57,62,69,69,67,66,73,69,80,81,58,68,75,69,73,70,58,65,79,76,74,71,66,64,65,62,78,68,75,68,62,60,No
59,62,72,74,66,66,74,76,63,67,72,76,71,74,66,64,70,69,63,66,70,72,70,76,65,69,61,66,64,65,67,72,57,63,65,71,67,69,77,78,77,76,70,70,No
69,71,70,78,61,63,67,65,59,59,66,69,71,75,65,58,60,55,62,59,67,66,74,74,64,60,57,54,70,73,69,76,62,64,61,61,66,65,72,73,68,68,59,63,Yes
62,66,66,68,73,76,68,71,62,62,63,68,74,75,63,68,71,68,58,58,65,66,65,76,64,70,63,60,70,72,71,77,67,69,72,71,63,63,70,72,75,79,62,59,No
59,68,69,67,69,59,78,73,66,65,77,73,74,66,66,55,71,66,69,68,75,73,80,79,69,65,69,66,68,65,75,71,59,61,65,64,73,71,81,75,74,65,69,66,No
70,65,65,62,68,67,77,74,62,61,66,61,69,74,64,62,71,71,74,70,77,78,69,70,67,65,67,70,49,48,73,71,65,73,73,73,75,71,73,72,73,70,65,64,Yes
59,52,70,67,73,66,72,61,58,52,72,71,70,77,66,65,67,55,61,57,68,66,72,74,63,64,56,54,67,54,76,74,65,67,66,56,62,56,72,62,74,74,64,67,Yes
62,56,66,57,74,75,68,59,65,59,74,66,71,65,67,69,66,66,71,72,80,74,71,63,62,72,62,66,66,61,73,68,59,59,63,62,73,73,76,67,77,71,62,58,Yes
74,69,75,70,70,74,77,77,65,67,73,72,69,73,68,66,69,68,67,63,78,74,71,63,66,61,68,63,74,69,74,75,65,61,66,67,63,61,71,68,66,65,54,57,No
67,66,65,77,66,70,72,72,72,67,76,72,73,76,74,71,74,73,69,61,78,70,76,73,70,70,62,51,70,68,79,77,75,68,72,71,69,63,65,61,73,73,64,67,Yes
71,62,70,64,67,64,79,65,70,69,72,71,68,65,61,61,73,71,75,74,80,74,54,47,53,37,77,68,72,59,72,68,60,60,73,70,66,65,64,55,61,41,51,46,Yes
64,60,71,69,71,65,66,64,68,59,63,67,68,64,73,59,73,60,72,56,77,68,69,69,66,59,57,40,55,53,69,63,71,63,66,55,66,58,65,65,75,64,61,56,Yes
64,70,71,69,72,70,75,78,61,66,69,68,68,70,71,70,75,76,73,72,80,78,79,81,74,70,72,79,73,75,77,73,65,64,72,72,59,62,71,74,68,67,58,57,No
72,74,67,69,69,70,74,81,66,70,73,78,69,80,65,65,70,77,69,70,73,79,64,68,56,58,67,64,68,68,69,74,62,67,66,70,73,77,74,77,71,72,63,65,No
62,71,78,84,64,68,72,74,53,57,71,70,71,72,54,53,63,67,54,57,71,71,70,74,54,57,54,57,62,64,75,72,62,65,60,64,64,67,72,77,62,62,61,65,No
77,61,62,68,62,58,72,68,77,71,76,77,72,75,62,57,77,74,61,58,72,76,69,68,56,53,57,54,69,70,73,79,65,70,66,68,67,66,71,67,60,60,53,57,Yes
65,68,70,78,65,72,72,74,64,69,71,73,72,68,62,62,65,62,72,75,79,78,72,76,66,67,62,61,68,76,72,78,65,64,67,63,64,67,67,77,66,66,59,57,No
76,69,78,73,68,67,75,70,77,70,79,73,79,75,74,71,76,68,81,79,77,78,75,76,66,76,65,67,67,57,68,75,50,62,62,59,47,49,75,65,74,70,51,48,Yes
68,65,72,72,47,74,76,74,67,66,71,69,69,67,63,64,68,68,70,74,77,77,73,60,49,48,42,69,70,69,76,79,63,66,64,69,71,73,73,75,68,56,58,44,No
72,61,64,66,64,59,68,66,76,66,77,75,71,72,72,62,72,68,77,78,77,81,67,67,69,68,65,68,69,64,72,73,56,56,69,64,67,71,69,68,65,73,56,52,No
65,69,66,76,58,67,65,72,66,64,77,75,64,62,63,59,71,61,67,45,74,45,66,46,64,48,62,27,65,67,72,72,62,66,71,64,71,70,72,69,70,65,63,61,Yes
67,51,73,65,69,56,72,63,64,56,68,67,70,62,70,58,68,62,65,59,77,69,68,59,64,55,65,60,70,60,72,65,58,51,66,59,71,62,74,60,76,65,62,56,Yes
73,76,68,74,56,59,73,76,54,48,75,78,47,53,25,19,60,56,56,54,80,79,47,53,19,14,58,50,67,71,63,54,49,48,66,65,62,58,57,72,31,30,15,11,Yes
59,65,53,60,72,74,67,69,64,67,64,65,71,70,68,71,72,70,70,70,75,78,72,71,71,71,67,64,67,71,71,74,62,66,72,73,57,57,64,71,70,69,53,49,No
76,65,60,40,32,34,65,50,53,37,66,53,33,31,30,30,69,75,64,45,68,65,57,43,23,23,53,77,48,32,55,32,48,23,62,51,65,59,43,39,35,30,24,21,Yes
70,71,71,74,68,66,72,70,66,69,74,72,70,69,64,66,73,72,75,73,81,81,76,75,71,70,74,82,69,72,76,74,60,56,66,66,64,64,73,72,66,63,54,58,No
68,76,79,78,63,73,68,78,64,71,73,77,67,71,58,57,61,63,52,64,64,74,53,72,36,44,52,54,49,56,73,81,65,80,53,60,63,70,58,64,52,57,49,50,Yes
64,63,62,59,60,61,70,74,68,63,66,68,64,66,67,66,72,68,63,59,75,72,67,62,63,55,66,56,65,64,70,71,61,63,67,63,69,69,77,65,74,62,60,54,Yes
66,54,69,66,69,69,75,72,63,62,68,66,68,70,71,68,70,69,66,68,73,72,65,73,67,63,60,57,70,68,75,75,65,67,69,65,65,64,67,69,71,68,59,59,No

FCM算法理论及其Python实现相关推荐

1. 一个简单好用的磨皮祛斑算法理论和python实现

   前言 最近看了一个磨皮算法祛斑感觉效果不错,效果图看文末就行,个人觉得效果非常不错滴. 国际惯例,参考博客: 磨皮算法的源码:YUCIHighPassSkinSmoothing How To Smoo ...

2. DBSCAN算法理论和Python实现

   https://github.com/Sean16SYSU/MachineLearningImplement DBSCAN算法 基于密度的聚类方法DBSCAN算法,是相当经典. 算法思路很简单. 简述 ...

3. 模糊C均值聚类（FCM）算法介绍及其Python实现

   这篇文章是楼主老早之前做课后作业写的,如果有问题的话建议米娜桑自行解决哦~ 目录 一.理论介绍 二.算法实现思路 三.FCM算法核心代码的python实现 四.使用示例 1.对数据进行聚类 2.图片分 ...

4. FCM算法实现Python（简洁版）

   FCM算法 关于聚类的所有项目都放到了这个上面 https://github.com/Sean16SYSU/MachineLearningImplement/tree/master/Clusterin ...

5. 模拟退火算法理论+Python解决函数极值+C++实现解决TSP问题

   简述 算法设计课这周的作业: 赶紧写了先,不然搞不完了. 文章目录 简述 算法理论部分 变量简单分析 从状态转移概率到状态概率 推导 理解当温度收敛到接近0的时候,收敛到结果 理论部分的后记 pyth ...

6. 非线性有限元：基本理论与算法及基于Python、Fortran程序实现与案例分析实践技术

   有限单元法在岩土工程问题中应用非常广泛,很多商业软件如Plaxis/Abaqus/Comsol等都采用有限单元解法.尽管各类商业软件使用方便,但其使用对用户来说往往是一个"黑箱子" ...

7. 非线性有限元：基本理论与算法及基于Python、Fortran程序实现与案例分析

   非线性有限元:基本理论与算法及基于Python.Fortran程序实现与案例分析 (qq.com) 有限单元法在岩土工程问题中应用非常广泛,很多商业软件如Plaxis/Abaqus/Comsol等都采 ...

8. 岩土工程--非线性有限元：基本理论与算法及基于Python、Fortran程序实现与案例分析

   非线性有限元:基本理论与算法及基于Python.Fortran程序实现与案例分析实践技术 有限单元法在岩土工程问题中应用非常广泛,很多商业软件如Plaxis/Abaqus/Comsol等都采用有限单元 ...

9. 非线性有限元：基本理论与算法及基于Python、Fortran程序实现

   **前言:**有限单元法在岩土工程问题中应用非常广泛,很多商业软件如Plaxis/Abaqus/Comsol等都采用有限单元解法.尽管各类商业软件使用方便,但其使用对用户来说往往是一个"黑箱 ...

10. FCM聚类算法详解(Python实现iris数据集)

    参考:https://blog.csdn.net/on2way/article/details/47087201 模糊C均值(Fuzzy C-means)算法简称FCM算法,是一种基于目标函数的模糊聚 ...

最新文章

1. 测试lazy_enable_if的所有变体
2. SpringMVC学习记录--Validator验证分析
3. C++PrimerPlus学习——第十一章编程练习
4. tensorflow 学习资料汇总
5. 计算机游戏无法运行程序包,一体电脑显示或声音不正常，某些软件或游戏无法正常运行怎么办...
6. 易助erp系统服务器安装,易助ERP系统操作培训教程
7. deepin和UOS sunpinyin 皮肤添加
8. Android完全关闭（退出）应用程序
9. win10的js文件-bat脚本-开启移动热点
10. 测试用例入门（二） - 使用等价类划分法编写测试用例
11. 简述与机器学习相关的十大常用Python库，极简化算法编程
12. js使用input上传文件夹、拖拽上传文件夹并将文件夹结构展示为树形结构
13. MyBatis源码的学习（9）---映射器mappers的的XML解析
14. u3m8缓存文件.ts合成mp4
15. word常见问题_2 添加不同的页码
16. 升级到win11后VMware不能开启虚拟机了
17. 使用Vivado生成ADI的ADC例程（以AD9680为例）
18. [JVM]了断局: 类加载机制
19. 《鹰猎长空》探析日本电影业在东西方文化间的摇摆
20. [渝粤教育] 西南交通大学 体育健康课程Ⅰ—奥运裁判带你学规则 参考 资料

热门文章

1. AOSP 隐藏 su
2. pip卸载旧版本后安装新版本（我是Python3）
3. AltiumDesigner16安装教程
4. 从生活中领悟设计模式（Python）
5. idea添加注释模板
6. PLSQL代码美化配置
7. ofdm导频信道估计matlab,基于导频的OFDM系统信道估计
8. 3ds Max 文件修改版本工具
9. atx20pin电源短接_ATX电源20针及24针接口定义
10. 全流程OA系统集成对接案例实例