数据聚类¶
K均值算法¶
In [3]:
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
# 分割训练集和测试集
digits_train = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/optdigits/optdigits.tra',header=None)
digits_test = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/optdigits/optdigits.tes',header=None)
In [4]:
x_train = digits_train[np.arange(64)]
y_train = digits_train[64]
x_test = digits_test[np.arange(64)]
y_test = digits_test[64]
In [24]:
# 训练集中存在空值，去除
#np.isnan(x_train).any()
#np.isnan(y_train).any()
x_train.dropna(inplace=True)
y_train.dropna(inplace=True)
x_train.shape, y_train.shape
Out[24]:
In [17]:
from sklearn.cluster import KMeans
kmeans = KMeans(n_clusters=10)
kmeans.fit(x_train)
y_pred = kmeans.predict(x_test)
In [26]:
# 性能测评
# 1.使用ARI
from sklearn import metrics
print metrics.adjusted_rand_score(y_test,y_pred)
In [53]:
# 2.使用轮廓系数SC。以下代码重新定义了数据集，包括2个数据特征，无标签
import numpy as np
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
import matplotlib.pyplot as plt
In [77]:
# 把窗口分成3*2个子图，并在第1个子图作图
plt.subplot(3,2,1)
# 初始化原始数据点
x1 = np.array([1,2,3,1,5,6,5,5,6,7,8,9,7,9])
x2 = np.array([1,3,2,2,8,6,7,6,7,1,2,1,1,3])
x = np.array(zip(x1,x2)).reshape(len(x1),2)
# 在1号子图做出原始数据点阵的分布
plt.xlim([0,10])
plt.ylim([0,10])
plt.title('Instances')
plt.scatter(x1,x2)
colors = ['b','g','r','c','m','y','k','b']
markers = ['o','s','D','v','^','p','*','+']
clusters = [2,3,4,5,8]
subplot_counter = 1
sc_scores = []
for t in clusters:
subplot_counter += 1
plt.subplot(3,2,subplot_counter)
kmeans_model = KMeans(n_clusters=t).fit(x)
for i, l in enumerate(kmeans_model.labels_):
plt.plot(x1[i],x2[i],color=colors[l],marker=markers[l],ls='None')
plt.xlim([0,10])
plt.ylim([0,10])
plt.subplots_adjust(top=1.5,wspace=0.5,hspace=0.5)
sc_score = silhouette_score(x,kmeans_model.labels_,metric='euclidean') ## 计算轮廓系数SC
sc_scores.append(sc_score)
plt.title('K=%s, sc=%0.03f' %(t,sc_score))
# 绘制sc与n的折线图
plt.figure()
plt.plot(clusters, sc_scores,'*-')
plt.xlabel('Number of Clusters')
plt.ylabel('Silhouette Coefficient Score')
plt.show()
特征降维¶
PCA主成分分析方法¶
In [2]:
# 计算2*2线性相关矩阵的秩
import numpy as np
M = np.array([[1,2],[2,4]])
np.linalg.matrix_rank(M,tol=None)
Out[2]:
In [31]:
# 以手写数字案例为例
x_digits = x_train
y_digits = y_train
# 降维
from sklearn.decomposition import PCA
estimator = PCA(n_components=2)
x_pca = estimator.fit_transform(x_digits)
# 显示降维后的分布
from matplotlib import pyplot as plt
def plot_pca_scatter():
#subplot_counter = 0
colors = ['black','blue','purple','yellow','deeppink','red','lime','cyan','orange','gray']
for i in xrange(len(colors)):
#subplot_counter += 1
#plt.subplot(5,2,subplot_counter)
px = x_pca[:,0][y_digits.as_matrix()==i]
py = x_pca[:,1][y_digits.as_matrix()==i]
plt.scatter(px,py,c=colors[i],s=3)
plt.legend(np.arange(0,10).astype(str))
plt.xlabel('First Principal Component')
plt.ylabel('Second Principal Component')
plt.show()
plot_pca_scatter()
In [33]:
# 比较降维前后的图像识别效果
# 使用相同配置的支持向量机
from sklearn.svm import LinearSVC
svc = LinearSVC()
svc.fit(x_train,y_train)
y_predict = svc.predict(x_test)
estimator = PCA(n_components=20)
pca_x_train = estimator.fit_transform(x_train)
pca_x_test = estimator.transform(x_test)
pca_svc = LinearSVC()
pca_svc.fit(pca_x_train,y_train)
pca_y_predict = pca_svc.predict(pca_x_test)
In [39]:
# 性能测评
from sklearn.metrics import classification_report
print svc.score(x_test,y_test)
print classification_report(y_test,y_predict,target_names=np.arange(10).astype(str))
print pca_svc.score(pca_x_test,y_test)
print classification_report(y_test,pca_y_predict,target_names=np.arange(10).astype(str))