Introduction to Sci-Kit Learn and Clustering¶
In this tutorial we will introduce the Sci-Kit Learn library:https://scikit-learn.org/stable/
This is a very important library with a huge toolkit for data processing, unsupervised and supervised learning. It is one of the core tools for data science.
We will see some of the capabilities of this toolkit and focus on clustering.
In [26]:
import numpy as np
import scipy as sp
import scipy.sparse as sp_sparse
import scipy.spatial.distance as sp_dist
import matplotlib.pyplot as plt
import sklearn as sk
import sklearn.datasets as sk_data
import sklearn.metrics as metrics
from sklearn import preprocessing
import sklearn.cluster as sk_cluster
import sklearn.feature_extraction.text as sk_text
import scipy.cluster.hierarchy as hr
import time
import seaborn as sns
%matplotlib inline
Computing distances¶
For the computation of distances there are libraries in Scipy
http://docs.scipy.org/doc/scipy-0.15.1/reference/spatial.distance.html#module-scipy.spatial.distance
but also in SciKit metrics library:
https://scikit-learn.org/stable/modules/generated/sklearn.metrics.pairwise_distances.html
Most of these work with sparse data as well.
Compute distances using scipy¶
Computing distances between vectors
In [28]:
import scipy.spatial.distance as sp_dist
x = np.random.randint(2, size = 5)
y = np.random.randint(2, size = 5)
print (x)
print (y)
print (sp_dist.cosine(x,y))
print (sp_dist.euclidean(x,y))
print (sp_dist.jaccard(x,y))
print (sp_dist.hamming(x,y))
# When computing jaccard similarity of 0/1 matrices,
# 1 means that the element corresponding to the column is in the set,
# 0 that the element is not in the set
[0 1 1 1 1] [0 1 1 0 1] 0.1339745962155614 1.0 0.25 0.2
Compute pairwise distances in a table using pdist of scipy.
When given a matrix, it computes all pairwise distances between its rows. The output is a vector with N(N-1)/2 entries (N number of rows). We can transform it into an NxN distance matrix using squareform.
In [30]:
A = np.random.randint(2, size = (5,3))
# computes the matrix of all pairwise distances of rows
# returns a vector with N(N-1)/2 entries (N number of rows)
D = sp_dist.pdist(A, 'jaccard')
print (A)
print('\n all row distances')
print (D)
print(sp_dist.squareform(D))
[[1 0 0] [0 0 1] [1 1 1] [1 0 1] [1 1 0]] all row distances [1. 0.66666667 0.5 0.5 0.66666667 0.5 1. 0.33333333 0.33333333 0.66666667] [[0. 1. 0.66666667 0.5 0.5 ] [1. 0. 0.66666667 0.5 1. ] [0.66666667 0.66666667 0. 0.33333333 0.33333333] [0.5 0.5 0.33333333 0. 0.66666667] [0.5 1. 0.33333333 0.66666667 0. ]]
We can compute all pairwise distances between the rows of two tables A and B, using the cdist function of scipy. If A has N rows and B has M rows the result is an NxM matrix with all the distances
In [33]:
B = np.random.randint(2, size = (3,3))
print(B)
D = sp_dist.cdist(A,B,'jaccard')
print(D)
[[1 1 1] [1 0 1] [1 1 0]] [[0.66666667 0.5 0.5 ] [0.66666667 0.5 1. ] [0. 0.33333333 0.33333333] [0.33333333 0. 0.66666667] [0.33333333 0.66666667 0. ]]
Compute distances using sklearn¶
In [34]:
import sklearn.metrics as metrics
#computes the matrix of all pairwise distances of rows
# returns a NxN matrix (N number of rows)
print(A)
D2 = metrics.pairwise_distances(A,metric = 'jaccard')
print('\n the matrix of row distances')
print(D2)
[[1 0 0] [0 0 1] [1 1 1] [1 0 1] [1 1 0]]
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\metrics\pairwise.py:1765: DataConversionWarning: Data was converted to boolean for metric jaccard warnings.warn(msg, DataConversionWarning)
the matrix of row distances [[0. 1. 0.66666667 0.5 0.5 ] [1. 0. 0.66666667 0.5 1. ] [0.66666667 0.66666667 0. 0.33333333 0.33333333] [0.5 0.5 0.33333333 0. 0.66666667] [0.5 1. 0.33333333 0.66666667 0. ]]
Some similarity and distance metrics are directly computed in the pairwise library:
https://scikit-learn.org/stable/modules/classes.html#module-sklearn.metrics.pairwise
In [35]:
C = metrics.pairwise.cosine_similarity(A)
print('Cosine Similarity')
print(C)
Cosine Similarity [[1. 0. 0.57735027 0.70710678 0.70710678] [0. 1. 0.57735027 0.70710678 0. ] [0.57735027 0.57735027 1. 0.81649658 0.81649658] [0.70710678 0.70710678 0.81649658 1. 0.5 ] [0.70710678 0. 0.81649658 0.5 1. ]]
Compute distances between the rows of two tables
In [36]:
print(A)
print (B)
#computes the matrix of all pairwise distances of rows of A with rows of B
# returns an NxM matrix (N rows of A, M rows of B)
D3 = metrics.pairwise_distances(A,B,metric = 'jaccard')
print('\n the matrix of distances between the rows of A and B')
print(D3)
[[1 0 0] [0 0 1] [1 1 1] [1 0 1] [1 1 0]] [[1 1 1] [1 0 1] [1 1 0]] the matrix of distances between the rows of A and B [[0.66666667 0.5 0.5 ] [0.66666667 0.5 1. ] [0. 0.33333333 0.33333333] [0.33333333 0. 0.66666667] [0.33333333 0.66666667 0. ]]
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\metrics\pairwise.py:1765: DataConversionWarning: Data was converted to boolean for metric jaccard warnings.warn(msg, DataConversionWarning)
We can apply everything to sparce matrices
In [37]:
d = np.array([[0, 0, 12],
[0, 1, 1],
[0, 5, 34],
[1, 3, 12],
[1, 2, 6],
[2, 0, 23],
[3, 4, 14],
])
s = sp_sparse.csr_matrix((d[:,2],(d[:,0],d[:,1])), shape=(4,6))
D4 = metrics.pairwise.pairwise_distances(s,metric = 'euclidean')
print(s.toarray())
print(D4)
[[12 1 0 0 0 34] [ 0 0 6 12 0 0] [23 0 0 0 0 0] [ 0 0 0 0 14 0]] [[ 0. 38.48376281 35.74912586 38.69108424] [38.48376281 0. 26.62705391 19.39071943] [35.74912586 26.62705391 0. 26.92582404] [38.69108424 19.39071943 26.92582404 0. ]]
Clustering¶
You can read more about clustering in SciKit here:
Generate data from Gaussian distributions.
More on data generation here: http://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_blobs.html
In [39]:
centers = [[1,1], [-1, -1], [1, -1]]
X, true_labels = sk_data.make_blobs(n_samples=500, centers=centers, n_features=2,
center_box=(-10.0, 10.0),random_state=0)
plt.scatter(X[:,0], X[:,1])
Out[39]:
<matplotlib.collections.PathCollection at 0x26ba1eaa4c0>
In [40]:
print(type(X))
print(true_labels)
print(len(true_labels[true_labels==0]),len(true_labels[true_labels==1]),len(true_labels[true_labels==2]))
<class 'numpy.ndarray'> [2 0 1 1 0 1 1 2 2 2 1 0 0 1 1 0 0 2 2 0 0 0 2 2 0 1 0 2 0 2 0 0 0 2 1 1 0 0 2 2 0 2 1 0 2 2 0 0 1 2 2 0 0 1 0 2 1 1 1 2 2 1 0 0 2 1 1 2 2 2 2 1 2 0 0 0 2 2 0 0 0 0 0 2 1 2 2 0 0 2 2 1 0 2 1 0 1 2 1 1 2 2 1 2 1 0 1 1 0 2 2 2 0 2 0 2 2 0 1 1 0 1 2 1 1 2 2 1 2 0 0 0 1 2 2 0 2 0 2 1 2 1 0 0 1 0 2 1 0 1 2 2 2 0 1 0 1 0 2 2 0 1 0 0 1 2 1 1 1 2 1 2 1 0 1 0 2 2 0 2 1 0 2 2 0 1 2 0 0 2 1 2 2 2 0 2 2 1 2 1 0 2 1 2 1 2 0 0 0 1 2 0 0 2 1 1 2 2 0 1 2 0 0 1 1 1 0 2 2 2 1 2 1 1 1 0 1 2 0 2 1 2 0 2 1 1 2 2 1 2 0 0 1 0 1 0 2 1 2 1 1 1 1 0 0 1 0 1 1 1 1 2 1 0 0 0 0 2 1 2 2 0 0 1 0 2 1 0 2 2 1 0 0 1 0 2 1 2 1 0 0 0 1 2 0 0 2 2 1 0 0 1 1 0 2 1 0 1 2 1 1 0 2 0 2 1 2 1 0 0 0 1 0 2 2 1 0 2 2 2 0 1 1 1 0 1 0 0 0 2 0 2 0 2 2 0 2 2 2 2 1 1 1 2 2 2 2 0 0 0 1 2 0 1 0 1 0 1 2 2 0 2 1 0 1 2 2 0 1 2 1 2 0 0 0 1 2 0 0 1 2 2 0 2 1 0 2 0 1 0 2 0 0 1 0 0 0 0 1 0 2 2 2 1 0 1 2 1 2 1 0 1 1 1 1 1 0 2 1 2 0 0 1 2 0 2 1 0 0 1 1 2 1 2 1 1 1 1 2 0 1 1 0 1 2 0 1 1 0 2 0 0 1 1 1 0 1 0 1 1 1 1 0 1 1 2 2 2 1 1 1 0 1 2 2 2 1 0 0 2] 167 167 166
In [41]:
plt.scatter(X[true_labels==1,0], X[true_labels==1,1],c = 'r')
plt.scatter(X[true_labels==2,0], X[true_labels==2,1],c = 'b')
plt.scatter(X[true_labels==0,0], X[true_labels==0,1],c = 'g')
Out[41]:
<matplotlib.collections.PathCollection at 0x26ba1f09430>
Useful command: We will create a colormap of the distance matrix using the pcolormesh method of matplotlib.pyplot
In [42]:
euclidean_dists = metrics.euclidean_distances(X)
plt.pcolormesh(euclidean_dists,cmap=plt.cm.coolwarm)
Out[42]:
<matplotlib.collections.QuadMesh at 0x26ba1f63bb0>
Clustering Algorithms¶
scikit-learn has a huge set of tools for unsupervised learning generally, and clustering specifically. These are in sklearn.cluster. http://scikit-learn.org/stable/modules/clustering.html
There are 3 functions in all the clustering classes,
- fit(): builds the model from the training data (e.g. for kmeans, it finds the centroids)
- predict(): assigns labels to the data after building the model
- fit_predict(): does both at the same data (e.g in kmeans, it finds the centroids and assigns the labels to the dataset)
K-means clustering¶
More on the k-means clustering here: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html#sklearn.cluster.KMeans
Important parameters
init: determines the way the initialization is done. kmeans++ is the default.
n_init: number of iterations
Important attributes:
labels_ the labels for each point
cluster_centers_: the cluster centroids
inertia_: the SSE value
In [43]:
import sklearn.cluster as sk_cluster
kmeans = sk_cluster.KMeans(init='k-means++', n_clusters=3, n_init=10)
kmeans.fit_predict(X)
centroids = kmeans.cluster_centers_
kmeans_labels = kmeans.labels_
error = kmeans.inertia_
print ("The total error of the clustering is: ", error)
print ('\nCluster labels')
print(kmeans_labels)
print ('\n Cluster Centroids')
print (centroids)
The total error of the clustering is: 729.3882206069684 Cluster labels [1 1 1 0 2 0 0 1 1 1 0 2 2 0 0 2 2 2 0 1 2 2 1 2 2 0 2 0 2 1 1 2 2 1 0 0 2 2 1 1 2 1 0 2 1 1 2 2 1 1 0 2 2 0 2 2 0 0 2 2 1 0 2 2 2 0 0 0 1 1 2 0 1 2 1 2 0 1 2 2 2 2 2 1 0 1 2 2 2 1 0 0 2 1 1 1 0 1 2 0 2 1 1 1 0 2 0 0 2 1 1 1 2 1 1 1 1 2 0 0 2 0 1 0 0 1 1 0 1 2 2 2 0 1 1 2 1 2 1 1 1 0 1 1 0 2 1 1 2 0 2 1 1 2 0 2 0 1 2 1 2 1 1 2 0 1 0 0 0 1 1 1 0 2 0 2 0 1 2 1 0 2 2 1 2 0 1 2 2 2 0 1 1 1 2 1 1 0 1 0 2 1 0 1 0 1 2 2 2 0 1 2 2 0 2 0 1 1 2 0 1 2 2 0 0 2 2 1 2 1 0 1 0 2 0 2 0 2 2 2 0 1 2 1 0 1 1 2 0 1 2 1 0 2 0 2 1 0 1 0 0 0 1 2 2 2 2 0 0 2 0 1 0 2 2 2 2 1 0 1 1 2 2 0 2 1 0 2 0 1 0 1 2 0 2 2 0 1 0 2 2 2 0 1 2 2 2 1 0 1 2 0 0 2 1 0 2 0 2 1 0 2 1 2 1 0 2 1 2 2 2 0 2 2 1 0 1 1 1 1 2 0 0 0 1 2 2 2 2 1 2 0 1 1 0 2 2 1 0 0 0 1 0 2 1 1 1 2 2 2 1 2 2 0 2 0 1 2 0 1 2 1 0 2 0 1 1 2 0 1 0 1 2 1 2 0 1 2 2 0 1 1 2 1 0 2 1 1 0 0 2 2 2 0 2 2 2 2 1 2 2 1 1 0 2 1 1 1 1 0 2 0 0 1 0 0 2 0 0 1 2 2 0 1 2 1 0 2 1 1 0 1 0 1 0 0 0 0 1 1 0 0 2 0 1 2 0 0 2 1 1 2 0 0 2 1 0 1 0 0 2 0 2 0 0 1 2 1 0 0 0 2 2 2 1 1 1 1 1 2] Cluster Centroids [[-1.3362657 -1.28432839] [ 1.14789815 -1.17752675] [ 0.78589165 1.17781335]]
Useful command: numpy.argsort sorts a set of values and returns the sorted indices
In [44]:
idx = np.argsort(kmeans_labels) # returns the indices in sorted order
rX = X[idx,:]
r_euclid = metrics.euclidean_distances(rX)
#r_euclid = euclidean_dists[idx,:][:,idx]
plt.pcolormesh(r_euclid,cmap=plt.cm.coolwarm)
Out[44]:
<matplotlib.collections.QuadMesh at 0x26ba1fb6850>
In [49]:
se = euclidean_dists[idx,:]
se = se[:,idx]
plt.pcolormesh(se,cmap=plt.cm.coolwarm)
Out[49]:
<matplotlib.collections.QuadMesh at 0x26ba6c2e2e0>
Confusion matrix: http://scikit-learn.org/stable/modules/generated/sklearn.metrics.confusion_matrix.html
Important: In the produced confusion matrix, the first list defines the rows and the second the columns. The matrix is always square, regarless if the number of classes and clusters are not the same. The extra rows or columns are filled with zeros.
Homogeneity and completeness: http://scikit-learn.org/stable/modules/clustering.html#homogeneity-completeness
Homogeneity and completeness are computed using the conditional entropy of the labels given the cluster, and the conditional entropy of the cluster labels given the class label. The V-measure combines these in a similar way like F-measure
Silhouette score: http://scikit-learn.org/stable/modules/generated/sklearn.metrics.silhouette_score.html
In [50]:
C= metrics.confusion_matrix(kmeans_labels,true_labels)
print (C)
plt.pcolormesh(C,cmap=plt.cm.Reds)
[[ 1 135 15] [ 26 20 122] [140 12 29]]
Out[50]:
<matplotlib.collections.QuadMesh at 0x26ba6c7ca90>
Compute precision and recall.
These metrics are for classification, so they assume that row i is mapped to column i
In [51]:
p = metrics.precision_score(true_labels,kmeans_labels, average=None)
print(p)
r = metrics.recall_score(true_labels,kmeans_labels, average = None)
print(r)
[0.00662252 0.11904762 0.16022099] [0.00598802 0.11976048 0.1746988 ]
Create a function that maps each cluster to the class that has the most points.
You need to be careful if many clusters map to the same class. It will not work in this case
Useful command: numpy.argmax returns the index of the max element
In [52]:
def cluster_class_mapping(kmeans_labels,true_labels):
C= metrics.confusion_matrix(kmeans_labels,true_labels)
mapping = list(np.argmax(C,axis=1)) #for each row (cluster) find the best class in the confusion matrix
mapped_kmeans_labels = [mapping[l] for l in kmeans_labels]
C2= metrics.confusion_matrix(mapped_kmeans_labels,true_labels)
return mapped_kmeans_labels,C2
mapped_kmeans_labels,C = cluster_class_mapping(kmeans_labels,true_labels)
print(C)
plt.pcolormesh(C, cmap=plt.cm.Reds)
[[140 12 29] [ 1 135 15] [ 26 20 122]]
Out[52]:
<matplotlib.collections.QuadMesh at 0x26ba6d247c0>
Compute different metrics for clustering quality
In [53]:
h = metrics.homogeneity_score(true_labels,mapped_kmeans_labels)
print(h)
c = metrics.completeness_score(true_labels,mapped_kmeans_labels)
print(c)
v = metrics.v_measure_score(true_labels,mapped_kmeans_labels)
print(v)
p = metrics.precision_score(true_labels,mapped_kmeans_labels, average=None)
print(p)
r = metrics.recall_score(true_labels,mapped_kmeans_labels, average = None)
print(r)
f = metrics.f1_score(true_labels,mapped_kmeans_labels, average = None)
print(f)
p = metrics.precision_score(true_labels,mapped_kmeans_labels, average='weighted')
print(p)
r = metrics.recall_score(true_labels,mapped_kmeans_labels, average = 'weighted')
print(r)
f = metrics.f1_score(true_labels,mapped_kmeans_labels, average = 'weighted')
print(f)
0.44199547480098583 0.4430951461741084 0.44254462735008065 [0.77348066 0.89403974 0.72619048] [0.83832335 0.80838323 0.73493976] [0.8045977 0.8490566 0.73053892] 0.7980470510548809 0.794 0.794859459999974
The SSE plot
In [54]:
error = np.zeros(11)
sh_score = np.zeros(11)
for k in range(1,11):
kmeans = sk_cluster.KMeans(init='k-means++', n_clusters=k, n_init=10)
kmeans.fit_predict(X)
error[k] = kmeans.inertia_
if k>1: sh_score[k]= metrics.silhouette_score(X, kmeans.labels_)
plt.plot(range(1,len(error)),error[1:])
plt.xlabel('Number of clusters')
plt.ylabel('Error')
Out[54]:
Text(0, 0.5, 'Error')
The silhouette plot
We see a peak at k = 3 and k = 6 indicating that these may be good values for the cluster number
In [55]:
plt.plot(range(2,len(sh_score)),sh_score[2:])
plt.xlabel('Number of clusters')
plt.ylabel('silhouette score')
Out[55]:
Text(0, 0.5, 'silhouette score')
In [56]:
fig, ax1 = plt.subplots()
color = 'tab:red'
ax1.set_xlabel('number of clusters')
ax1.set_ylabel('silhoutte score', color=color)
ax1.plot(range(2,len(sh_score)),sh_score[2:], color=color)
ax1.tick_params(axis='y', labelcolor=color)
ax2 = ax1.twinx() # instantiate a second axes that shares the same x-axis
color = 'tab:blue'
ax2.set_ylabel('SSE', color=color) # we already handled the x-label with ax1
ax2.plot(range(2,len(error)),error[2:], color=color)
ax2.tick_params(axis='y', labelcolor=color)
fig.tight_layout()
In [57]:
colors = np.array([x for x in 'bgrcmykbgrcmykbgrcmykbgrcmyk'])
colors = np.hstack([colors] * 20)
plt.scatter(X[:, 0], X[:, 1], color=colors[kmeans_labels].tolist(), s=10, alpha=0.8)
Out[57]:
<matplotlib.collections.PathCollection at 0x26ba71e40a0>
Agglomerative Clustering¶
More on Agglomerative Clustering here: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html
In [58]:
agglo = sk_cluster.AgglomerativeClustering(linkage = 'complete', n_clusters = 3)
agglo_labels = agglo.fit_predict(X)
C_agglo= metrics.confusion_matrix(agglo_labels,true_labels)
print (C_agglo)
#plt.pcolor(C_agglo,cmap=plt.cm.coolwarm)
plt.pcolormesh(C_agglo,cmap=plt.cm.Reds)
mapped_agglo_labels,C_agglo = cluster_class_mapping(agglo_labels,true_labels)
print(C_agglo)
p = metrics.precision_score(true_labels,mapped_agglo_labels, average='weighted')
print(p)
r = metrics.recall_score(true_labels,mapped_agglo_labels, average = 'weighted')
print(r)
[[ 33 156 108] [126 10 16] [ 8 1 42]] [[126 10 16] [ 33 156 108] [ 8 1 42]] 0.7257145291928573 0.648
Another way to do agglomerative clustering using SciPy:
https://docs.scipy.org/doc/scipy/reference/cluster.hierarchy.html
In [59]:
import scipy.cluster.hierarchy as hr
Z = hr.linkage(X, method='complete', metric='euclidean')
print (Z.shape, X.shape)
(499, 4) (500, 2)
In [60]:
import scipy.spatial.distance as sp_dist
D = sp_dist.pdist(X, 'euclidean')
Z = hr.linkage(D, method='complete')
print (Z.shape, X.shape)
(499, 4) (500, 2)
Hierarchical clustering returns a 4 by (n-1) matrix Z. At the i-th iteration, clusters with indices Z[i, 0] and Z[i, 1] are combined to form cluster n + i. A cluster with an index less than n corresponds to one of the n original observations. The distance between clusters Z[i, 0] and Z[i, 1] is given by Z[i, 2]. The fourth value Z[i, 3] represents the number of original observations in the newly formed cluster.
In [61]:
fig = plt.figure(figsize=(10,10))
T = hr.dendrogram(Z,color_threshold=0.4, leaf_font_size=4)
fig.show()
<ipython-input-61-ddcad35f0acd>:3: UserWarning: Matplotlib is currently using module://ipykernel.pylab.backend_inline, which is a non-GUI backend, so cannot show the figure. fig.show()
Another way to do agglomerative clustering (and visualizing it): http://seaborn.pydata.org/generated/seaborn.clustermap.html
In [62]:
distances = metrics.euclidean_distances(X)
cg = sns.clustermap(distances, method="complete", figsize=(13,13), xticklabels=False)
print (cg.dendrogram_col.reordered_ind)
C:\ProgramData\Anaconda3\lib\site-packages\seaborn\matrix.py:659: UserWarning: Clustering large matrix with scipy. Installing `fastcluster` may give better performance. warnings.warn(msg) C:\ProgramData\Anaconda3\lib\site-packages\seaborn\matrix.py:629: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix linkage = hierarchy.linkage(self.array, method=self.method,
[177, 469, 83, 179, 343, 61, 34, 124, 3, 466, 252, 490, 442, 312, 354, 230, 240, 476, 302, 57, 317, 154, 438, 167, 71, 472, 232, 399, 450, 35, 236, 454, 172, 478, 219, 107, 320, 455, 283, 434, 244, 426, 425, 121, 123, 25, 335, 432, 254, 6, 174, 127, 388, 423, 267, 53, 435, 257, 197, 209, 481, 415, 491, 264, 206, 294, 181, 411, 275, 12, 117, 208, 226, 187, 332, 444, 238, 274, 263, 310, 75, 355, 374, 4, 424, 465, 95, 114, 142, 309, 281, 129, 468, 471, 80, 250, 200, 266, 419, 235, 436, 383, 194, 462, 28, 160, 441, 301, 412, 40, 11, 173, 242, 380, 100, 350, 221, 330, 392, 410, 36, 499, 287, 394, 88, 31, 54, 43, 155, 182, 347, 20, 222, 295, 369, 32, 15, 188, 440, 326, 316, 447, 24, 82, 137, 92, 480, 168, 223, 431, 382, 484, 492, 52, 345, 363, 58, 300, 47, 78, 51, 387, 356, 145, 207, 346, 416, 62, 329, 37, 305, 98, 321, 153, 178, 247, 348, 306, 417, 112, 148, 163, 405, 367, 81, 255, 323, 304, 131, 313, 135, 218, 402, 120, 16, 482, 63, 205, 333, 474, 443, 231, 1, 403, 150, 108, 397, 45, 19, 376, 140, 357, 23, 282, 189, 398, 237, 239, 175, 212, 276, 284, 420, 372, 414, 26, 368, 318, 46, 299, 87, 211, 273, 430, 253, 17, 55, 477, 196, 319, 33, 279, 385, 277, 427, 364, 192, 195, 307, 38, 41, 29, 258, 136, 453, 115, 220, 458, 365, 400, 143, 157, 111, 475, 289, 216, 422, 97, 324, 159, 8, 353, 86, 265, 158, 225, 409, 204, 149, 213, 130, 340, 371, 79, 214, 233, 377, 73, 292, 486, 64, 269, 21, 328, 70, 105, 184, 228, 59, 493, 245, 251, 327, 7, 291, 344, 485, 103, 496, 370, 74, 401, 165, 249, 384, 94, 375, 147, 448, 30, 49, 198, 69, 201, 68, 459, 186, 134, 418, 243, 497, 72, 379, 185, 215, 13, 99, 351, 268, 373, 413, 90, 479, 106, 360, 463, 144, 166, 10, 56, 298, 362, 224, 234, 65, 488, 42, 202, 156, 50, 483, 311, 437, 278, 404, 118, 489, 325, 66, 457, 395, 270, 429, 91, 260, 67, 248, 14, 456, 358, 446, 296, 164, 96, 452, 199, 272, 315, 104, 308, 341, 261, 290, 141, 259, 342, 467, 180, 390, 190, 27, 460, 349, 210, 361, 76, 378, 109, 60, 116, 421, 193, 227, 138, 133, 101, 126, 44, 122, 151, 433, 2, 48, 113, 84, 408, 461, 288, 18, 473, 5, 119, 293, 132, 359, 176, 139, 286, 331, 449, 183, 336, 170, 191, 161, 381, 77, 262, 246, 439, 39, 171, 256, 280, 89, 366, 352, 470, 93, 322, 393, 498, 297, 396, 285, 203, 391, 314, 406, 464, 0, 407, 338, 152, 22, 271, 303, 128, 241, 487, 110, 162, 217, 229, 389, 494, 339, 146, 337, 102, 451, 386, 445, 9, 428, 169, 125, 495, 85, 334]
DBSCAN Algorithm¶
More on DBSCAN here: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html
In [63]:
dbscan = sk_cluster.DBSCAN(eps=0.3)
dbscan_labels = dbscan.fit_predict(X)
print(dbscan_labels) #label -1 corresponds to noise
renamed_dbscan_labels = [x+1 for x in dbscan_labels]
C = metrics.confusion_matrix(renamed_dbscan_labels,true_labels)
#print(C)
print (C[:,:max(true_labels)+1])
[ 5 0 0 -1 -1 0 -1 0 0 3 0 0 -1 -1 0 -1 0 0 0 0 0 0 5 0 0 -1 0 -1 -1 0 0 0 -1 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 -1 1 -1 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 -1 0 2 0 0 -1 0 3 0 0 0 -1 0 0 -1 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 -1 0 0 0 -1 0 -1 -1 3 0 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 4 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 -1 -1 3 0 -1 -1 0 -1 0 0 -1 0 -1 0 -1 0 0 0 0 0 -1 -1 0 -1 0 0 0 0 0 0 -1 0 0 2 0 0 -1 0 0 -1 0 -1 -1 -1 0 0 0 0 -1 0 -1 0 0 0 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 2 0 0 -1 0 0 5 0 0 -1 0 0 0 0 0 2 0 -1 0 -1 0 -1 -1 0 0 0 0 0 -1 -1 0 2 -1 0 0 0 5 0 0 -1 -1 0 0 0 0 -1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 -1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 0 3 -1 0 4 5 4 0 0 0 -1 0 1 0 0 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 -1 0 1 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 -1 2 0 0 0 -1 -1 4 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 5 0 0 0 -1 0 0 0 -1 0 0 0 2 0 -1 0 -1 -1 -1 -1 0 3 0 0 -1 -1 0 0 -1 2 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 -1 0 0 0 -1 -1 -1 0 -1 -1 -1 2 -1 0 0 0 0 0 -1 0 -1 -1 0 0 -1 0 0 5 0 0 -1 -1 1 0 4 3 0 0 0 0] [[ 48 47 26] [106 117 120] [ 3 3 1] [ 9 0 0] [ 0 0 7] [ 0 0 5] [ 1 0 7]]
In [64]:
#colors = np.array([x for x in 'bgrcmykbgrcmykbgrcmykbgrcmyk'])
#colors = np.hstack([colors] * 20)
colors = np.array([x for x in 'bgrcmywk'*10])
plt.scatter(X[:, 0], X[:, 1], color=colors[dbscan_labels].tolist(), s=10, alpha=0.8)
Out[64]:
<matplotlib.collections.PathCollection at 0x26ba86f88b0>
Clustering text data¶
An example of what we want to do: http://scikit-learn.org/stable/auto_examples/text/document_clustering.html
SciKit datasets: http://scikit-learn.org/stable/datasets/
We will use the 20-newsgroups datasets which consists of postings on 20 different newsgroups.
More information here: http://scikit-learn.org/stable/datasets/#the-20-newsgroups-text-dataset
In [65]:
from sklearn.datasets import fetch_20newsgroups
categories = ['comp.os.ms-windows.misc', 'sci.space','rec.sport.baseball']
#categories = ['alt.atheism', 'sci.space','rec.sport.baseball']
news_data = sk_data.fetch_20newsgroups(subset='train',
remove=('headers', 'footers', 'quotes'),
categories=categories)
print (news_data.target)
print (len(news_data.target))
[2 0 0 ... 2 1 2] 1781
In [66]:
print (type(news_data))
print (news_data.filenames)
print (news_data.target[:10])
print (news_data.data[1])
print (len(news_data.data))
<class 'sklearn.utils.Bunch'> ['C:\\Users\\tsap\\scikit_learn_data\\20news_home\\20news-bydate-train\\sci.space\\60940' 'C:\\Users\\tsap\\scikit_learn_data\\20news_home\\20news-bydate-train\\comp.os.ms-windows.misc\\9955' 'C:\\Users\\tsap\\scikit_learn_data\\20news_home\\20news-bydate-train\\comp.os.ms-windows.misc\\9846' ... 'C:\\Users\\tsap\\scikit_learn_data\\20news_home\\20news-bydate-train\\sci.space\\60891' 'C:\\Users\\tsap\\scikit_learn_data\\20news_home\\20news-bydate-train\\rec.sport.baseball\\104484' 'C:\\Users\\tsap\\scikit_learn_data\\20news_home\\20news-bydate-train\\sci.space\\61110'] [2 0 0 2 0 0 1 2 2 1] Recently the following problem has arrisen. The first time I turn on my computer when windows starts (from my autoexec) after the win31 title screen the computer reboots on its own. Usually the second time (after reboot) or from the DOS prompt everything works fine. s far as I remember I have not changed my config.sys or autoxec.bat or win.ini. I can't remember whether this problem occured before I optimized/defragmented my disk and created a larger swap file (Thank you MathCAD 4 :( ) System 386sx, 4MB, stacker 2.0, win31, DOS 5 --- --------------------------------------------------------------------- 1781
In [67]:
vectorizer = sk_text.TfidfVectorizer(stop_words='english',
#max_features = 1000,
min_df=4, max_df=0.8)
data = vectorizer.fit_transform(news_data.data)
print(type(data))
<class 'scipy.sparse.csr.csr_matrix'>
In [68]:
import sklearn.cluster as sk_cluster
k=3
kmeans = sk_cluster.KMeans(n_clusters=k, init='k-means++', max_iter=100, n_init=1)
kmeans.fit_predict(data)
Out[68]:
array([2, 0, 0, ..., 1, 2, 1])
To understand the clusters we can print the words that have the highest values in the centroid
In [75]:
print("Top terms per cluster:")
asc_order_centroids = kmeans.cluster_centers_.argsort()#[:, ::-1]
order_centroids = asc_order_centroids[:,::-1]
terms = vectorizer.get_feature_names()
for i in range(k):
print ("Cluster %d:" % i)
for ind in order_centroids[i, :10]:
print (' %s' % terms[ind])
print
Top terms per cluster: Cluster 0: year team game games runs baseball think good hit pitching Cluster 1: space like just think nasa know don thanks does people Cluster 2: windows file dos files drivers driver thanks card use problem
In [69]:
C = metrics.confusion_matrix(kmeans.labels_,news_data.target)
mapped_kmeans_labels,C = cluster_class_mapping(kmeans.labels_,news_data.target)
print (C)
p = metrics.precision_score(news_data.target,mapped_kmeans_labels, average=None)
print(p)
r = metrics.recall_score(news_data.target,mapped_kmeans_labels, average = None)
print(r)
[[419 1 5] [170 596 384] [ 2 0 204]] [0.98588235 0.51826087 0.99029126] [0.70896785 0.99832496 0.34401349]
In [70]:
agglo = sk_cluster.AgglomerativeClustering(linkage = 'complete', n_clusters = 3,)
dense = data.todense()
agglo_labels = agglo.fit_predict(dense) # agglomerative needs dense data
C_agglo= metrics.confusion_matrix(agglo_labels,news_data.target)
print (C_agglo)
[[574 595 482] [ 17 0 2] [ 0 2 109]]
In [71]:
dbscan = sk_cluster.DBSCAN(eps=0.1)
dbscan_labels = dbscan.fit_predict(data)
C = metrics.confusion_matrix(dbscan.labels_,news_data.target)
print (C)
[[ 0 556 567 576] [ 0 9 0 0] [ 0 26 30 17] [ 0 0 0 0]]
In [ ]: