对于kmeans散点图，PCA输出看起来很奇怪

Question

在对我的数据进行PCA并绘制kmeans簇后，我的情节看起来很奇怪。群集的中心和点的散点图对我来说没有意义。这是我的代码：

#clicks, conversion, bounce and search are lists of values.
clicks=[2,0,0,8,7,...]
conversion = [1,0,0,6,0...]
bounce = [2,4,5,0,1....]

X = np.array([clicks,conversion, bounce]).T
y = np.array(search)

num_clusters = 5

pca=PCA(n_components=2, whiten=True)
data2D = pca.fit_transform(X)

print data2D
    >>> [[-0.07187948 -0.17784291]
     [-0.07173769 -0.26868727]
     [-0.07173789 -0.26867958]
     ..., 
     [-0.06942414 -0.25040886]
     [-0.06950897 -0.19591147]
     [-0.07172973 -0.2687937 ]]

km = KMeans(n_clusters=num_clusters, init='k-means++',n_init=10, verbose=1)
km.fit_transform(X)

labels=km.labels_
centers2D = pca.fit_transform(km.cluster_centers_)

colors=['#000000','#FFFFFF','#FF0000','#00FF00','#0000FF']
col_map=dict(zip(set(labels),colors))
label_color = [col_map[l] for l in labels]

plt.scatter( data2D[:,0], data2D[:,1], c=label_color)
plt.hold(True)
plt.scatter(centers2D[:,0], centers2D[:,1],  marker='x', c='r')
plt.show()

红色十字架是群集的中心。任何帮助都会很棒。

Answer 1

你订购的PCA和KMeans搞砸了......

以下是您需要做的事情：

1. 规范化您的数据。
2. 在PCA上执行X将尺寸从5缩小为2并生成Data2D
3. 再次标准化
4. 群集Data2D与KMeans
5. 在Centroids。{/ li>之上绘制Data2D

   在哪里，这是你上面所做的：

   1. 在PCA上执行X将尺寸从5缩小为2以生成Data2D
   2. 将原始数据X分为5个维度。
   3. 在群集质心上执行单独的PCA，这会为质心生成完全不同的2D子空间。
   4. 将PCA缩小Data2D并将PCA缩小的质心放在顶部，即使这些质心不再正确耦合。

   归一化：

   看看下面的代码，你会发现它将质心放在需要的位置。规范化是关键，完全可逆。群集时始终规范化数据，因为距离指标需要平均移动所有空间。聚类是规范化数据的最重要时刻之一，但总的来说......总是正常化： - ）

   超出原始问题的启发式讨论：

   降维的整个要点是使KMeans聚类更容易，并预测出不会增加数据方差的维度。因此，您应该将简化数据传递给聚类算法。我将补充说，很少有5D数据集可以投影到2D而不会产生很多差异，即查看PCA诊断以查看是否已保留90％的原始方差。如果没有，那么你可能不想在你的PCA中如此咄咄逼人。

   新代码：

   import pandas as pd
   import numpy as np
   import matplotlib.pyplot as plt
   from sklearn.decomposition import PCA
   from sklearn.cluster import KMeans
   import seaborn as sns
   %matplotlib inline
   
   # read your data, replace 'stackoverflow.csv' with your file path
   df = pd.read_csv('/Users/angus/Desktop/Downloads/stackoverflow.csv', usecols[0, 2, 4],names=['freq', 'visit_length', 'conversion_cnt'],header=0).dropna()
   
   df.describe()
   
   #Normalize the data
   df_norm = (df - df.mean()) / (df.max() - df.min())
   
   num_clusters = 5
   
   pca=PCA(n_components=2)
   UnNormdata2D = pca.fit_transform(df_norm)
   
   # Check the resulting varience
   var = pca.explained_variance_ratio_
   print "Varience after PCA: ",var
   
   #Normalize again following PCA: data2D
   data2D = (UnNormdata2D - UnNormdata2D.mean()) / (UnNormdata2D.max()-UnNormdata2D.min())
   
   print "Data2D: "
   print data2D
   
   km = KMeans(n_clusters=num_clusters, init='k-means++',n_init=10, verbose=1)
   km.fit_transform(data2D)
   
   labels=km.labels_
   centers2D = km.cluster_centers_
   
   colors=['#000000','#FFFFFF','#FF0000','#00FF00','#0000FF']
   col_map=dict(zip(set(labels),colors))
   label_color = [col_map[l] for l in labels]
   
   plt.scatter( data2D[:,0], data2D[:,1], c=label_color)
   plt.hold(True)
   plt.scatter(centers2D[:,0], centers2D[:,1],marker='x',s=150.0,color='purple')
   plt.show()
   

   简介：

   

   输出：

   Varience after PCA:  [ 0.65725709  0.29875307]
   Data2D: 
   [[-0.00338421 -0.0009403 ]
   [-0.00512081 -0.00095038]
   [-0.00512081 -0.00095038]
   ..., 
   [-0.00477349 -0.00094836]
   [-0.00373153 -0.00094232]
   [-0.00512081 -0.00095038]]
   Initialization complete
   Iteration  0, inertia 51.225
   Iteration  1, inertia 38.597
   Iteration  2, inertia 36.837
   ...
   ...
   Converged at iteration 31
   

   希望这有帮助！

Answer 2

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans

# read your data, replace 'stackoverflow.csv' with your file path
df = pd.read_csv('stackoverflow.csv', usecols=[0, 2, 4], names=['freq', 'visit_length', 'conversion_cnt'], header=0).dropna()
df.describe()

Out[3]: 
              freq  visit_length  conversion_cnt
count  289705.0000   289705.0000     289705.0000
mean        0.2624       20.7598          0.0748
std         0.4399       55.0571          0.2631
min         0.0000        1.0000          0.0000
25%         0.0000        6.0000          0.0000
50%         0.0000       10.0000          0.0000
75%         1.0000       21.0000          0.0000
max         1.0000     2500.0000          1.0000

# binarlize freq and conversion_cnt
df.freq = np.where(df.freq > 1.0, 1, 0)
df.conversion_cnt = np.where(df.conversion_cnt > 0.0, 1, 0)

feature_names = df.columns
X_raw = df.values

transformer = PCA(n_components=2)
X_2d = transformer.fit_transform(X_raw)
# over 99.9% variance captured by 2d data
transformer.explained_variance_ratio_

Out[4]: array([  9.9991e-01,   6.6411e-05])

# do clustering
estimator = KMeans(n_clusters=5, init='k-means++', n_init=10, verbose=1)
estimator.fit(X_2d)

labels = estimator.labels_
colors = ['#000000','#FFFFFF','#FF0000','#00FF00','#0000FF']
col_map=dict(zip(set(labels),colors))
label_color = [col_map[l] for l in labels]

fig, ax = plt.subplots()
ax.scatter(X_2d[:,0], X_2d[:,1], c=label_color)
ax.scatter(estimator.cluster_centers_[:,0], estimator.cluster_centers_[:,1], marker='x', s=50, c='r')

KMeans尝试最小化群内欧几里德距离，这可能适合您的数据，也可能不适合您的数据。只是基于图表，我会考虑使用Gaussian Mixture Model进行无监督的聚类。

此外，如果您对哪些观察可能归类为哪个类别/标签有更好的了解，则可以进行半监督学习。