5-11、高斯核函数RBF
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import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from matplotlib.colors import ListedColormap
from sklearn.preprocessing import StandardScaler
from sklearn.svm import SVC
from sklearn.pipeline import Pipeline
from sklearn.model_selection import train_test_split
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
x, y = datasets.make_moons(n_samples=1000, noise=0.25, random_state=2020) # 生成1000个数据样本
plt.figure()
plt.scatter(x[y == 0, 0], x[y == 0, 1], color="r")
plt.scatter(x[y == 1, 0], x[y == 1, 1], color="g")
plt.title('散点图')
plt.show()
x_train, x_test, y_train, y_test = train_test_split(x, y, random_state=2020)
# 绘制边界曲线
def plot_decision_boundary(model, axis):
x0, x1 = np.meshgrid(
np.linspace(axis[0], axis[1], int((axis[1] - axis[0]) * 100)).reshape(-1, 1),
np.linspace(axis[2], axis[3], int((axis[3] - axis[2]) * 100)).reshape(-1, 1)
)
x_new = np.c_[x0.ravel(), x1.ravel()]
y_pre = model.predict(x_new)
zz = y_pre.reshape(x0.shape)
# 设置颜色
cus = ListedColormap(["#BA55D3", "#FF69B4", "#FFE4C4"])
plt.contourf(x0, x1, zz, cmap=cus)
def RBFkernelSVC(gamma):#高斯核函数RBF
return Pipeline([
("std", StandardScaler()),
("svc", SVC(kernel="rbf", gamma=gamma))
])
sv = RBFkernelSVC(gamma=1)
sv.fit(x_train, y_train)
plot_decision_boundary(sv, axis=([-1.8, 2.5, -1.4, 1.8]))
plt.scatter(x[y == 0, 0], x[y == 0, 1], color="r")
plt.scatter(x[y == 1, 0], x[y == 1, 1], color="g")
plt.title('高斯核函数RBF')
plt.show()
# 打印出分数
print(sv.score(x_test, y_test))
d = datasets.load_iris()
x = d.data
y = d.target
x_train, x_test, y_train, y_test = train_test_split(x, y, random_state=2020)
sv = RBFkernelSVC(gamma=10)
sv.fit(x_train, y_train)
# 打印出分数
print(sv.score(x_test, y_test))
径向基（RBF）神经网络python实现
1 from numpy import array, append, vstack, transpose, reshape, \
2 dot, true_divide, mean, exp, sqrt, log, \
3 loadtxt, savetxt, zeros, frombuffer
4 from numpy.linalg import norm, lstsq
5 from multiprocessing import Process, Array
6 from random import sample
7 from time import time
8 from sys import stdout
9 from ctypes import c_double
10 from h5py import File
11
12
13 def metrics(a, b):
14 return norm(a - b)
15
16
17 def gaussian (x, mu, sigma):
18 return exp(- metrics(mu, x)**2 / (2 * sigma**2))
21 def multiQuadric (x, mu, sigma):
22 return pow(metrics(mu,x)**2 + sigma**2, 0.5)
23
24
25 def invMultiQuadric (x, mu, sigma):
26 return pow(metrics(mu,x)**2 + sigma**2, -0.5)
27
28
29 def plateSpine (x,mu):
30 r = metrics(mu,x)
31 return (r**2) * log(r)
32
33
34 class Rbf:
35 def __init__(self, prefix = 'rbf', workers = 4, extra_neurons = 0, from_files = None):
36 self.prefix = prefix
37 self.workers = workers
38 self.extra_neurons = extra_neurons
39
40 # Import partial model
41 if from_files is not None:
42 w_handle = self.w_handle = File(from_files['w'], 'r')
43 mu_handle = self.mu_handle = File(from_files['mu'], 'r')
44 sigma_handle = self.sigma_handle = File(from_files['sigma'], 'r')
45
46 self.w = w_handle['w']
47 self.mu = mu_handle['mu']
48 self.sigmas = sigma_handle['sigmas']
49
50 self.neurons = self.sigmas.shape[0]
51
52 def _calculate_error(self, y):
53 self.error = mean(abs(self.os - y))
54 self.relative_error = true_divide(self.error, mean(y))
55
56 def _generate_mu(self, x):
57 n = self.n
58 extra_neurons = self.extra_neurons
59
60 # TODO: Make reusable
61 mu_clusters = loadtxt('clusters100.txt', delimiter='\t')
62
63 mu_indices = sample(range(n), extra_neurons)
64 mu_new = x[mu_indices, :]
65 mu = vstack((mu_clusters, mu_new))
66
67 return mu
68
69 def _calculate_sigmas(self):
70 neurons = self.neurons
71 mu = self.mu
72
73 sigmas = zeros((neurons, ))
74 for i in xrange(neurons):
75 dists = [0 for _ in xrange(neurons)]
76 for j in xrange(neurons):
77 if i != j:
78 dists[j] = metrics(mu[i], mu[j])
79 sigmas[i] = mean(dists)* 2
80 # max(dists) / sqrt(neurons * 2))
81 return sigmas
82
83 def _calculate_phi(self, x):
84 C = self.workers
85 neurons = self.neurons
86 mu = self.mu
87 sigmas = self.sigmas
88 phi = self.phi = None
89 n = self.n
90
91
92 def heavy_lifting(c, phi):
93 s = jobs[c][1] - jobs[c][0]
94 for k, i in enumerate(xrange(jobs[c][0], jobs[c][1])):
95 for j in xrange(neurons):
96 # phi[i, j] = metrics(x[i,:], mu[j])**3)
97 # phi[i, j] = plateSpine(x[i,:], mu[j]))
98 # phi[i, j] = invMultiQuadric(x[i,:], mu[j], sigmas[j]))
99 phi[i, j] = multiQuadric(x[i,:], mu[j], sigmas[j])
100 # phi[i, j] = gaussian(x[i,:], mu[j], sigmas[j]))
101 if k % 1000 == 0:
102 percent = true_divide(k, s)*100
103 print(c, ': {:2.2f}%'.format(percent))
104 print(c, ': Done')
105
106 # distributing the work between 4 workers
107 shared_array = Array(c_double, n * neurons)
108 phi = frombuffer(shared_array.get_obj())
109 phi = phi.reshape((n, neurons))
110
111 jobs = []
112 workers = []
113
114 p = n / C
115 m = n % C
116 for c in range(C):
117 jobs.append((c*p, (c+1)*p + (m if c == C-1 else 0)))
118 worker = Process(target = heavy_lifting, args = (c, phi))
119 workers.append(worker)
120 worker.start()
121
122 for worker in workers:
123 worker.join()
124
125 return phi
126
127 def _do_algebra(self, y):
128 phi = self.phi
129
130 w = lstsq(phi, y)[0]
131 os = dot(w, transpose(phi))
132 return w, os
133 # Saving to HDF5
134 os_h5 = os_handle.create_dataset('os', data = os)
135
136 def train(self, x, y):
137 self.n = x.shape[0]
138
139 ## Initialize HDF5 caches
140 prefix = self.prefix
141 postfix = str(self.n) + '-' + str(self.extra_neurons) + '.hdf5'
142 name_template = prefix + '-{}-' + postfix
143 phi_handle = self.phi_handle = File(name_template.format('phi'), 'w')
144 os_handle = self.w_handle = File(name_template.format('os'), 'w')
145 w_handle = self.w_handle = File(name_template.format('w'), 'w')
146 mu_handle = self.mu_handle = File(name_template.format('mu'), 'w')
147 sigma_handle = self.sigma_handle = File(name_template.format('sigma'), 'w')
148
149 ## Mu generation
150 mu = self.mu = self._generate_mu(x)
151 self.neurons = mu.shape[0]
152 print('({} neurons)'.format(self.neurons))
153 # Save to HDF5
154 mu_h5 = mu_handle.create_dataset('mu', data = mu)
155
156 ## Sigma calculation
157 print('Calculating Sigma...')
158 sigmas = self.sigmas = self._calculate_sigmas()
159 # Save to HDF5
160 sigmas_h5 = sigma_handle.create_dataset('sigmas', data = sigmas)
161 print('Done')
162
163 ## Phi calculation
164 print('Calculating Phi...')
165 phi = self.phi = self._calculate_phi(x)
166 print('Done')
167 # Saving to HDF5
168 print('Serializing...')
169 phi_h5 = phi_handle.create_dataset('phi', data = phi)
170 del phi
171 self.phi = phi_h5
172 print('Done')
173
174 ## Algebra
175 print('Doing final algebra...')
176 w, os = self.w, _ = self._do_algebra(y)
177 # Saving to HDF5
178 w_h5 = w_handle.create_dataset('w', data = w)
179 os_h5 = os_handle.create_dataset('os', data = os)
180
181 ## Calculate error
182 self._calculate_error(y)
183 print('Done')
184
185 def predict(self, test_data):
186 mu = self.mu = self.mu.value
187 sigmas = self.sigmas = self.sigmas.value
188 w = self.w = self.w.value
189
190 print('Calculating phi for test data...')
191 phi = self._calculate_phi(test_data)
192 os = dot(w, transpose(phi))
193 savetxt('iok3834.txt', os, delimiter='\n')
194 return os
195
196 @property
197 def summary(self):
198 return '\n'.join( \
199 ['-----------------',
200 'Training set size: {}'.format(self.n),
201 'Hidden layer size: {}'.format(self.neurons),
202 '-----------------',
203 'Absolute error : {:02.2f}'.format(self.error),
204 'Relative error : {:02.2f}%'.format(self.relative_error * 100)])
205
206
207 def predict(test_data):
208 mu = File('rbf-mu-212243-2400.hdf5', 'r')['mu'].value
209 sigmas = File('rbf-sigma-212243-2400.hdf5', 'r')['sigmas'].value
210 w = File('rbf-w-212243-2400.hdf5', 'r')['w'].value
211
212 n = test_data.shape[0]
213 neur = mu.shape[0]
214
215 mu = transpose(mu)
216 mu.reshape((n, neur))
217
218 phi = zeros((n, neur))
219 for i in range(n):
220 for j in range(neur):
221 phi[i, j] = multiQuadric(test_data[i,:], mu[j], sigmas[j])
222
223 os = dot(w, transpose(phi))
224 savetxt('iok3834.txt', os, delimiter='\n')
225 return os
preface：做着最近的任务，对数据处理，做些简单的提特征，用机器学习算法跑下程序得出结果，看看哪些特征的组合较好，这一系列流程必然要用到很多函数，故将自己常用函数记录上。应该说这些函数基本上都会用到，像是数据预处理，处理完了后特征提取、降维、训练预测、通过混淆矩阵看分类效果，得出报告。
1.输入
从数据集开始，提取特征转化为有标签的数据集，转为向量。拆分成训练集和测试集，这里不多讲，在上一篇博客中谈到用StratifiedKFold()函数即可。在训练集中有data和target开始。
2.处理
[python] view plain copy
def my_preprocessing(train_data):
from sklearn import preprocessing
X_normalized = preprocessing.normalize(train_data ,norm = "l2",axis=0)#使用l2范式，对特征列进行正则
return X_normalized
def my_feature_selection(data, target):
from sklearn.feature_selection import SelectKBest
from sklearn.feature_selection import chi2
data_new = SelectKBest(chi2, k= 50).fit_transform(data,target)
return data_new
def my_PCA(data):#data without target, just train data, withou train target.
from sklearn import decomposition
pca_sklearn = decomposition.PCA()
pca_sklearn.fit(data)
main_var = pca_sklearn.explained_variance_
print sum(main_var)*0.9
import matplotlib.pyplot as plt
n = 15
plt.plot(main_var[:n])
plt.show()
def clf_train(data,target):
from sklearn import svm
#from sklearn.linear_model import LogisticRegression
clf = svm.SVC(C=100,kernel="rbf",gamma=0.001)
clf.fit(data,target)
#clf_LR = LogisticRegression()
#clf_LR.fit(x_train, y_train)
#y_pred_LR = clf_LR.predict(x_test)
return clf
def my_confusion_matrix(y_true, y_pred):
from sklearn.metrics import confusion_matrix
labels = list(set(y_true))
conf_mat = confusion_matrix(y_true, y_pred, labels = labels)
print "confusion_matrix(left labels: y_true, up labels: y_pred):"
print "labels\t",
for i in range(len(labels)):
print labels[i],"\t",
for i in range(len(conf_mat)):
print i,"\t",
for j in range(len(conf_mat[i])):
print conf_mat[i][j],'\t',
def my_classification_report(y_true, y_pred):
from sklearn.metrics import classification_report
print "classification_report(left: labels):"
print classification_report(y_true, y_pred)
my_preprocess()函数：
主要使用sklearn的preprocessing函数中的normalize()函数，默认参数为l2范式，对特征列进行正则处理。即每一个样例，处理标签，每行的平方和为1.
my_feature_selection()函数：
使用sklearn的feature_selection函数中SelectKBest()函数和chi2()函数，若是用词袋提取了很多维的稀疏特征，有必要使用卡方选取前k个有效的特征。
my_PCA()函数：
主要用来观察前多少个特征是主要特征，并且画图。看看前多少个特征占据主要部分。
clf_train()函数：
可用多种机器学习算法，如SVM, LR, RF, GBDT等等很多，其中像SVM需要调参数的，有专门调试参数的函数如StratifiedKFold()（见前几篇博客）。以达到最优。
my_confusion_matrix()函数：
主要是针对预测出来的结果，和原来的结果对比，算出混淆矩阵，不必自己计算。其对每个类别的混淆矩阵都计算出来了，并且labels参数默认是排序了的。
my_classification_report()函数：
主要通过sklearn.metrics函数中的classification_report()函数，针对每个类别给出详细的准确率、召回率和F-值这三个参数和宏平均值，用来评价算法好坏。另外ROC曲线的话，需要是对二分类才可以。多类别似乎不行。
主要参考sklearn官网
5-2、利用RBF作为核函数
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
iris = datasets.load_iris()
# 为简单起见，选取前两个特征作为分类的输入特征，
# 以便在二维空间画出决策曲线
X = iris.data[:, :2]
y = iris.target
# 设置分类器SVC，核函数为rbf,gamma设置为自动调整
svc = svm.SVC(kernel="rbf", C=1, gamma="auto").fit(X, y)
# 绘图参数
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
h = (x_max / x_min) / 100
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
plt.subplot(1, 1, 1)
# 利用已有分类器进行预测
Z = svc.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
# 绘制等高线并填充轮廓
plt.contourf(xx, yy, Z, cmap=plt.cm.Paired, alpha=0.8)
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Paired)
plt.xlabel('花萼长度')
plt.ylabel('花萼宽度')
# 限制x的取值范围，便于显示
plt.xlim(xx.min(), xx.max())
plt.title('利用RBF作为核函数')
plt.show()