无监督学习

数据准备

%matplotlib notebook
import numpy as np
import pandas as pd
import seaborn as sn
import matplotlib.pyplot as plt
from sklearn.datasets import load_breast_cancer

# Breast cancer dataset
cancer = load_breast_cancer()
(X_cancer, y_cancer) = load_breast_cancer(return_X_y = True)

# Our sample fruits dataset
fruits = pd.read_table('fruit_data_with_colors.txt')
X_fruits = fruits[['mass','width','height', 'color_score']]
y_fruits = fruits[['fruit_label']] - 1

降维和流形学习

PCA

使用PCA查找乳腺癌数据集的前两个主要组成部分

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.datasets import load_breast_cancer

cancer = load_breast_cancer()
(X_cancer, y_cancer) = load_breast_cancer(return_X_y = True)

# Before applying PCA, each feature should be centered (zero mean) and with unit variance
X_normalized = StandardScaler().fit(X_cancer).transform(X_cancer)  
#n_components设置主成分个数
pca = PCA(n_components = 2).fit(X_normalized)

X_pca = pca.transform(X_normalized)
print(X_cancer.shape, X_pca.shape)

(569, 30) (569, 2)


绘制乳腺癌数据集的PCA转换版本

from adspy_shared_utilities import plot_labelled_scatter
plot_labelled_scatter(X_pca, y_cancer, ['malignant', 'benign'])

plt.xlabel('First principal component')
plt.ylabel('Second principal component')
plt.title('Breast Cancer Dataset PCA (n_components = 2)');

画出各个因素对两个主成分的影响大小

fig = plt.figure(figsize=(8, 4))
plt.imshow(pca.components_, interpolation = 'none', cmap = 'plasma')
feature_names = list(cancer.feature_names)

plt.gca().set_xticks(np.arange(-.5, len(feature_names)));
plt.gca().set_yticks(np.arange(0.5, 2));
plt.gca().set_xticklabels(feature_names, rotation=90, ha='left', fontsize=12);
plt.gca().set_yticklabels(['First PC', 'Second PC'], va='bottom', fontsize=12);

plt.colorbar(orientation='horizontal', ticks=[pca.components_.min(), 0, 
                                              pca.components_.max()], pad=0.65);

PCA用于水果数据集(用于比较)

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA

# each feature should be centered (zero mean) and with unit variance
X_normalized = StandardScaler().fit(X_fruits).transform(X_fruits)  

pca = PCA(n_components = 2).fit(X_normalized)
X_pca = pca.transform(X_normalized)

from adspy_shared_utilities import plot_labelled_scatter
plot_labelled_scatter(X_pca, y_fruits, ['apple','mandarin','orange','lemon'])

plt.xlabel('First principal component')
plt.ylabel('Second principal component')
plt.title('Fruits Dataset PCA (n_components = 2)');

多种学习方法

水果数据集上的多维缩放（MDS）

from adspy_shared_utilities import plot_labelled_scatter
from sklearn.preprocessing import StandardScaler
from sklearn.manifold import MDS

# each feature should be centered (zero mean) and with unit variance
X_fruits_normalized = StandardScaler().fit(X_fruits).transform(X_fruits)  

mds = MDS(n_components = 2)

X_fruits_mds = mds.fit_transform(X_fruits_normalized)

plot_labelled_scatter(X_fruits_mds, y_fruits, ['apple', 'mandarin', 'orange', 'lemon'])
plt.xlabel('First MDS feature')
plt.ylabel('Second MDS feature')
plt.title('Fruit sample dataset MDS');

 

乳腺癌上的多维缩放

t-SNE on the fruit dataset

（结果不是很好)

from sklearn.manifold import TSNE

tsne = TSNE(random_state = 0)

X_tsne = tsne.fit_transform(X_fruits_normalized)

plot_labelled_scatter(X_tsne, y_fruits, 
    ['apple', 'mandarin', 'orange', 'lemon'])
plt.xlabel('First t-SNE feature')
plt.ylabel('Second t-SNE feature')
plt.title('Fruits dataset t-SNE');

t-SNE on the breast cancer dataset

tsne = TSNE(random_state = 0)

X_tsne = tsne.fit_transform(X_normalized)

plot_labelled_scatter(X_tsne, y_cancer, 
    ['malignant', 'benign'])
plt.xlabel('First t-SNE feature')
plt.ylabel('Second t-SNE feature')
plt.title('Breast cancer dataset t-SNE');

聚类算法

k-means

#分成三个聚类中心
 1 from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from adspy_shared_utilities import plot_labelled_scatter

X, y = make_blobs(random_state = 10)

kmeans = KMeans(n_clusters = 3)
kmeans.fit(X)

plot_labelled_scatter(X, kmeans.labels_, ['Cluster 1', 'Cluster 2', 'Cluster 3'])

#分成4个聚类中心
 1 from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from adspy_shared_utilities import plot_labelled_scatter
from sklearn.preprocessing import MinMaxScaler

fruits = pd.read_table('fruit_data_with_colors.txt')
X_fruits = fruits[['mass','width','height', 'color_score']].as_matrix()
y_fruits = fruits[['fruit_label']] - 1

X_fruits_normalized = MinMaxScaler().fit(X_fruits).transform(X_fruits)  

kmeans = KMeans(n_clusters = 4, random_state = 0)
kmeans.fit(X_fruits_normalized)

plot_labelled_scatter(X_fruits_normalized, kmeans.labels_, 
                      ['Cluster 1', 'Cluster 2', 'Cluster 3', 'Cluster 4'])

Agglomerative clustering

from sklearn.datasets import make_blobs
from sklearn.cluster import AgglomerativeClustering
from adspy_shared_utilities import plot_labelled_scatter

X, y = make_blobs(random_state = 10)

cls = AgglomerativeClustering(n_clusters = 3)
cls_assignment = cls.fit_predict(X)

plot_labelled_scatter(X, cls_assignment, 
        ['Cluster 1', 'Cluster 2', 'Cluster 3'])

创建树状图（使用scipy）

此树形图是基于上一步中使用make_blobs创建的数据集，但为了清楚起见，本示例仅选择了10个样本，如下所示：

X, y = make_blobs(random_state = 10, n_samples = 10)
plot_labelled_scatter(X, y, 
        ['Cluster 1', 'Cluster 2', 'Cluster 3'])
print(X)

[[  5.69192445  -9.47641249]
 [  1.70789903   6.00435173]
 [  0.23621041  -3.11909976]
 [  2.90159483   5.42121526]
 [  5.85943906  -8.38192364]
 [  6.04774884 -10.30504657]
 [ -2.00758803  -7.24743939]
 [  1.45467725  -6.58387198]
 [  1.53636249   5.11121453]
 [  5.4307043   -9.75956122]]

这里的树状图对应于使用Ward方法的10点以上的凝聚聚类。 点的索引0..9对应于上面X数组中点的索引。 
例如，点0（5.69，-9.47）和点9（5.43，-9.76）是最接近的两个点，并且首先聚集在一起。

from scipy.cluster.hierarchy import ward, dendrogram
plt.figure()
dendrogram(ward(X))
plt.show()

DBSCAN集群(基于密度的聚类)

from sklearn.cluster import DBSCAN
from sklearn.datasets import make_blobs

X, y = make_blobs(random_state = 9, n_samples = 25)

dbscan = DBSCAN(eps = 2, min_samples = 2)

cls = dbscan.fit_predict(X)
print("Cluster membership values:
{}".format(cls))

plot_labelled_scatter(X, cls + 1, 
        ['Noise', 'Cluster 0', 'Cluster 1', 'Cluster 2'])

Cluster membership values:
[ 0  1  0  2  0  0  0  2  2 -1  1  2  0  0 -1  0  0  1 -1  1  1  2  2  2  1]