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.
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
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.
Computing distances between vectors
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 0 0 0 1] [0 1 0 1 1] 0.42264973081037416 1.4142135623730951 0.6666666666666666 0.4
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.
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 1] [0 1 1] [0 0 0] [0 0 1] [1 0 0]] all row distances [0.66666667 1. 0.5 0.5 1. 0.5 1. 1. 1. 1. ] [[0. 0.66666667 1. 0.5 0.5 ] [0.66666667 0. 1. 0.5 1. ] [1. 1. 0. 1. 1. ] [0.5 0.5 1. 0. 1. ] [0.5 1. 1. 1. 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
x = x.reshape(1,5)
y = y.reshape(1,5)
sp_dist.cdist(x,y,'cosine')
array([[0.42264973]])
B = np.random.randint(2, size = (3,3))
print(A)
print(B)
D = sp_dist.cdist(A,B,'jaccard')
print(D)
[[1 0 1] [0 1 1] [0 0 0] [0 0 1] [1 0 0]] [[0 0 1] [1 1 0] [0 1 0]] [[0.5 0.66666667 1. ] [0.5 0.66666667 0.5 ] [1. 1. 1. ] [0. 1. 1. ] [1. 0.5 1. ]]
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 1] [0 1 1] [0 0 0] [0 0 1] [1 0 0]] the matrix of row distances [[0. 0.66666667 1. 0.5 0.5 ] [0.66666667 0. 1. 0.5 1. ] [1. 1. 0. 1. 1. ] [0.5 0.5 1. 0. 1. ] [0.5 1. 1. 1. 0. ]]
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\metrics\pairwise.py:1870: DataConversionWarning: Data was converted to boolean for metric jaccard warnings.warn(msg, DataConversionWarning)
Some similarity and distance metrics are directly computed in the pairwise library:
https://scikit-learn.org/stable/modules/classes.html#module-sklearn.metrics.pairwise
C = metrics.pairwise.cosine_similarity(A)
print('Cosine Similarity')
print(C)
Cosine Similarity [[1. 0.5 0. 0.70710678 0.70710678] [0.5 1. 0. 0.70710678 0. ] [0. 0. 0. 0. 0. ] [0.70710678 0.70710678 0. 1. 0. ] [0.70710678 0. 0. 0. 1. ]]
Compute distances between the rows of two tables
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 1] [0 1 1] [0 0 0] [0 0 1] [1 0 0]] [[0 0 1] [1 1 0] [0 1 0]] the matrix of distances between the rows of A and B [[0.5 0.66666667 1. ] [0.5 0.66666667 0.5 ] [1. 1. 1. ] [0. 1. 1. ] [1. 0.5 1. ]]
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\metrics\pairwise.py:1870: DataConversionWarning: Data was converted to boolean for metric jaccard warnings.warn(msg, DataConversionWarning)
We can apply everything to sparce matrices
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. ]]
v = np.random.randint(2, size = 6)
v = v.reshape(1,6)
print(v)
metrics.pairwise.pairwise_distances(v,s,metric = 'euclidean')
[[1 0 1 0 1 1]]
array([[34.82814953, 13.11487705, 22.06807649, 13.11487705]])
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
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])
<matplotlib.collections.PathCollection at 0x28e53f3d160>
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
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')
<matplotlib.collections.PathCollection at 0x28e540710b8>
Useful command: We will create a colormap of the distance matrix using the pcolormesh method of matplotlib.pyplot
euclidean_dists = metrics.euclidean_distances(X)
plt.pcolormesh(euclidean_dists,cmap=plt.cm.coolwarm)
<matplotlib.collections.QuadMesh at 0x28e540e9dd8>
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,
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 random initializations
max_iter: maximum number of iterations,
Important attributes:
labels_ the labels for each point
cluster_centers_: the cluster centroids
inertia_: the SSE value
import sklearn.cluster as sk_cluster
kmeans = sk_cluster.KMeans(init='k-means++', n_clusters=3, max_iter=100)
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: 729.3882206069677 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
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)
<matplotlib.collections.QuadMesh at 0x28e542699e8>
se = euclidean_dists[idx,:]
se = se[:,idx]
plt.pcolormesh(se,cmap=plt.cm.coolwarm)
<matplotlib.collections.QuadMesh at 0x28e56843898>
Confusion matrix: http://scikit-learn.org/stable/modules/generated/sklearn.metrics.confusion_matrix.html
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]]
<matplotlib.collections.QuadMesh at 0x28e568a27f0>
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.
These metrics are for classification, so they assume that row i is mapped to column i
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
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]]
<matplotlib.collections.QuadMesh at 0x28e5691bda0>
Compute different metrics for clustering quality
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)
[0.77348066 0.89403974 0.72619048] [0.83832335 0.80838323 0.73493976] [0.8045977 0.8490566 0.73053892] 0.7980470510548809 0.794 0.794859459999974
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
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)
0.44199547480098583 0.4430951461741084 0.44254462735008065
http://scikit-learn.org/stable/modules/generated/sklearn.metrics.silhouette_score.html
Create the silhouette plot, plotting the silhouette score against k
We see a peak at k = 3 and k = 6 indicating that these may be good values for the cluster number
The SSE plot
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)
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')
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\cluster\_kmeans.py:1040: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=2. "KMeans is known to have a memory leak on Windows "
Text(0, 0.5, 'Error')
The silhouette plot
plt.plot(range(2,len(sh_score)),sh_score[2:])
plt.xlabel('Number of clusters')
plt.ylabel('silhouette score')
Text(0, 0.5, 'silhouette score')
Plot of silhouette and SSE together in a plot with two different y axes. The red (left) is the silhouette score and the blue (right) is the SSE score. We can now study the two lines together.
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()
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)
<matplotlib.collections.PathCollection at 0x28e5929b5f8>
More on Agglomerative Clustering here: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html
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
import scipy.cluster.hierarchy as hr
Z = hr.linkage(X, method='complete', metric='euclidean')
print (Z.shape, X.shape)
(499, 4) (500, 2)
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.
fig = plt.figure(figsize=(10,10))
T = hr.dendrogram(Z,color_threshold=0.4, leaf_font_size=4)
fig.show()
C:\ProgramData\Anaconda3\lib\site-packages\ipykernel_launcher.py:3: UserWarning: Matplotlib is currently using module://ipykernel.pylab.backend_inline, which is a non-GUI backend, so cannot show the figure. This is separate from the ipykernel package so we can avoid doing imports until
Another way to do agglomerative clustering (and visualizing it): http://seaborn.pydata.org/generated/seaborn.clustermap.html
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:560: UserWarning: Clustering large matrix with scipy. Installing `fastcluster` may give better performance. warnings.warn(msg) C:\ProgramData\Anaconda3\lib\site-packages\seaborn\matrix.py:531: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix metric=self.metric)
[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]
More on DBSCAN here: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html
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]]
#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)
<matplotlib.collections.PathCollection at 0x28e5a3043c8>
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
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
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\\tsapa\\scikit_learn_data\\20news_home\\20news-bydate-train\\sci.space\\60940' 'C:\\Users\\tsapa\\scikit_learn_data\\20news_home\\20news-bydate-train\\comp.os.ms-windows.misc\\9955' 'C:\\Users\\tsapa\\scikit_learn_data\\20news_home\\20news-bydate-train\\comp.os.ms-windows.misc\\9846' ... 'C:\\Users\\tsapa\\scikit_learn_data\\20news_home\\20news-bydate-train\\sci.space\\60891' 'C:\\Users\\tsapa\\scikit_learn_data\\20news_home\\20news-bydate-train\\rec.sport.baseball\\104484' 'C:\\Users\\tsapa\\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
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'>
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)
array([1, 1, 1, ..., 1, 1, 1])
To understand the clusters we can print the words that have the highest values in the centroid
print("Top terms per cluster:")
asc_order_centroids = kmeans.cluster_centers_.argsort()#[:, ::-1]
order_centroids = asc_order_centroids[:,::-1]
terms = vectorizer.get_feature_names_out()
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: comp linux os unix fortran free robust list chris utilities Cluster 1: windows space like just know think don thanks year does Cluster 2: ami compress pro loading running causes fault drive times hard
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)
[[ 4 0 0] [587 597 593] [ 0 0 0]] [1. 0.33595948 0. ] [0.00676819 1. 0. ]
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\metrics\_classification.py:1308: UndefinedMetricWarning: Precision is ill-defined and being set to 0.0 in labels with no predicted samples. Use `zero_division` parameter to control this behavior. _warn_prf(average, modifier, msg_start, len(result))
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)
C:\ProgramData\Anaconda3\lib\site-packages\sklearn\utils\validation.py:590: FutureWarning: np.matrix usage is deprecated in 1.0 and will raise a TypeError in 1.2. Please convert to a numpy array with np.asarray. For more information see: https://numpy.org/doc/stable/reference/generated/numpy.matrix.html FutureWarning,
[[574 595 482] [ 17 0 2] [ 0 2 109]]
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]]