Dimension reduction¶

● More efficient storage and computation

● Remove less-informative "noise" features

● ... which cause problems for prediction tasks, e.g. classification, regression

Principal Component Analysis¶

● PCA = "Principal Component Analysis"

● Fundamental dimension reduction technique

● First step "decorrelation" (considered here)

● Second step reduces dimension (considered later)

In [1]:
from sklearn import datasets
from sklearn.decomposition import PCA
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

%matplotlib inline


iris data set¶

In [2]:
iris = datasets.load_iris()
print iris.feature_names

['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']


PCA follows the fit/transform pattern¶

● PCA a scikit-learn component like KMeans or StandardScaler

● fit() learns the transformation from given data

● transform() applies the learned transformation

● transform() can also be applied to new data

In [3]:
data = iris.data
print data.shape
print data[:4]

plt.scatter(data[:,0], data[:,2], c=iris.target)
plt.axhline(color='r', y=0, linewidth=5)
plt.axvline(color='r')

(150L, 4L)
[[ 5.1  3.5  1.4  0.2]
[ 4.9  3.   1.4  0.2]
[ 4.7  3.2  1.3  0.2]
[ 4.6  3.1  1.5  0.2]]

Out[3]:
<matplotlib.lines.Line2D at 0xcf06a90>

PCA aligns data with axes¶

● Rotates data samples to be aligned with axes

● Shifs data samples so they have mean 0

● No information is lost

after pca, data algins with 0, 0¶

In [4]:
pca = PCA(2)
pca_data = pca.fit_transform(data[:,[0,2]])

plt.scatter(pca_data[:,0], pca_data[:,1], c=iris.target)
plt.axhline(color='b')
plt.axvline(color='b')

Out[4]:
<matplotlib.lines.Line2D at 0xd29eac8>

PCA features¶

● Rows of transformed correspond to samples

● Columns of transformed are the "PCA features"

● Row gives PCA feature values of corresponding sample

Pearson correlation¶

● Measures linear correlation of features

● Value between -1 and 1

● Value of 0 means no linear correlation

PCA features are not correlated¶

● Features of dataset are o"en correlated, e.g. total_phenols and od280

● PCA aligns the data with axes

● Resulting PCA features are not linearly correlated ("decorrelation") PCA

statistics by scipy¶

from scipy.stats import pearsonr¶

In [5]:
from scipy.stats import pearsonr

# Calculate the Pearson correlation
correlation, pvalue = pearsonr(data[:,0], data[:,2])
print pvalue
print correlation

1.03845406279e-47
0.871754157305


before PCA correlation is not 0¶

In [6]:
np.corrcoef(data[:,0], data[:,2])

Out[6]:
array([[ 1.        ,  0.87175416],
[ 0.87175416,  1.        ]])
In [7]:
pd.DataFrame(data[:,[0,2]]).corr()

Out[7]:
0 1
0 1.000000 0.871754
1 0.871754 1.000000

plot linear correlation with Seaborn¶

In [8]:
df = pd.DataFrame(data[:,[0,2]], columns= ['x','y'])

Out[8]:
x y
0 5.1 1.4
1 4.9 1.4
2 4.7 1.3
In [9]:
sns.lmplot('x','y',data=df, size=4, aspect=1.5)

Out[9]:
<seaborn.axisgrid.FacetGrid at 0xce10d30>
In [10]:
plt.scatter(data[:,0], data[:,2], alpha=.6, c ='gold')
plt.axis('equal')

Out[10]:
(4.0, 8.5, 0.0, 8.0)

after PCA correlation is 0¶

In [11]:
np.corrcoef(pca_data[:,0], pca_data[:,1])

Out[11]:
array([[  1.00000000e+00,   2.49817039e-17],
[  2.49817039e-17,   1.00000000e+00]])
In [12]:
pd.DataFrame(pca_data).corr()

Out[12]:
0 1
0 1.000000e+00 1.769537e-17
1 1.769537e-17 1.000000e+00

for numpy ndarray, similar to R cbind and rbind¶

rbind : np.hstack([ arr1, arr2,...])¶

In [13]:
print data[:,[0,2]].shape, pca_data.shape
pair = np.hstack([data[:,[0,2]], pca_data])
print pair.shape

(150L, 2L) (150L, 2L)
(150L, 4L)


so binding rows in pd as DataFrame and add a new category for two distinct groups¶

In [14]:
df2 = pd.DataFrame(pca_data, columns= ['x','y'])

Out[14]:
x y
0 -2.460806 -0.245533
1 -2.539563 -0.061692
2 -2.710240 0.082770
In [15]:
df['cat']='before_pca'
df2['cat']='after_pca'

In [16]:
df3 = pd.concat([df,df2])
print df3.shape
df3.tail(3)

(300, 3)

Out[16]:
x y cat
147 1.583463 -0.036035 after_pca
148 1.649168 0.318483 after_pca
149 1.255272 0.476108 after_pca

plotting dataset of linear relationship¶

• after PCA, there is NO correlation
In [17]:
sns.lmplot('x','y',data=df3, size=4, aspect=1.5, hue = 'cat')

Out[17]:
<seaborn.axisgrid.FacetGrid at 0xcf575c0>
In [18]:
sns.lmplot('x','y',data=df3, size=3.5, col = 'cat')

Out[18]:
<seaborn.axisgrid.FacetGrid at 0xe7d7e10>

Principal components¶

● "Principal components" = directions of variance

● PCA aligns principal components with the axes

Available as components_attribute of PCA object

● Each row defines displacement from mean

In [19]:
print pca.components_

[[ 0.39378459  0.91920275]
[-0.91920275  0.39378459]]


Intrinsic dimension¶

Intrinsic dimension of a flight path

● 2 features: longitude and latitude at points along a flight path

● Dataset appears to be 2-dimensional

● But can approximate using one feature: displacement along flight path

● Is intrinsically 1-dimensional

In [20]:
plt.imshow(plt.imread('ch3_slides.jpg'))
plt.grid('off')


The first principal component¶

The first principal component of the data is the direction in which the data varies the most.¶

• In this exercise, your job is to use PCA to find the first principal component of the length and width measurements of the iris petal , and represent it as an arrow on the scatter plot.
In [21]:
print iris.feature_names

['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']

In [22]:
# Make a scatter plot of the untransformed points
plt.scatter(iris.data[:,2], iris.data[:,3], alpha=.7, c='g')

# Create a PCA instance: model
model = PCA()

# Fit model to points
model.fit(iris.data[:,2:4])

# Get the mean of the grain samples: mean
mean = model.mean_
print mean

# Get the first principal component: first_pc
first_pc = model.components_[0,:]
print first_pc

# Plot first_pc as an arrow, starting at mean
plt.arrow(mean[0], mean[1], first_pc[0], first_pc[1], color='red', width=0.01)

sec_pc = model.components_[1,:]
print sec_pc

# Plot second_pc as an arrow, starting at mean
plt.arrow(mean[0], mean[1], sec_pc[0], sec_pc[1], color='b', width=0.01)

# Keep axes on same scale
plt.axis('equal')
plt.show()

[ 3.75866667  1.19866667]
[ 0.92154695  0.38826694]
[-0.38826694  0.92154695]


Intrinsic dimension¶

● Intrinsic dimension = number of features needed to approximate the dataset

● Essential idea behind dimension reduction

● What is the most compact representation of the samples?

● Can be detected with PCA

Versicolor dataset¶

● "versicolor", one of the iris species

● Only 3 features: sepal length, sepal width, and petal width

● Samples are points in 3D space

create verisocolor dataset¶

In [23]:
print iris.target_names
print iris.feature_names

['setosa' 'versicolor' 'virginica']
['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']

In [24]:
iri = pd.DataFrame(iris.data, columns = ['sepal_l','sepal_w','petal_l','petal_w'])
iri['target']=iris.target
versicolor = iri[iri['target']==1]
versicolor = versicolor.iloc[:,[0,1,3]]

In [25]:
versicolor.head()

Out[25]:
sepal_l sepal_w petal_w
50 7.0 3.2 1.4
51 6.4 3.2 1.5
52 6.9 3.1 1.5
53 5.5 2.3 1.3
54 6.5 2.8 1.5

Versicolor dataset has intrinsic dimension 2¶

● Samples lie close to a flat 2-dimensional sheet

● So can be approximated using 2 features

the easiest 3D plotting¶

In [26]:
from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure(figsize=(6,4))

ax = Axes3D(fig)

ax.scatter(versicolor.iloc[:, 1], versicolor.iloc[:, 1], versicolor.iloc[:, 2])

Out[26]:
<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x10630b00>

PCA identifies intrinsic dimension¶

● Scatter plots work only if samples have 2 or 3 features

● PCA identifies intrinsic dimension when samples have any number of features

● Intrinsic dimension = number of PCA features with significant variance

In [27]:
pca2 = PCA()
pca2.fit(versicolor)
versicolor_pca = pca2.transform(versicolor)
versicolor_pca[:3]

Out[27]:
array([[-1.13236543,  0.09514055, -0.17654689],
[-0.62150644, -0.20612416, -0.04140747],
[-1.02792193,  0.10180149, -0.03853535]])
In [28]:
fig = plt.figure(figsize=(10,4))

l1 = ax.scatter(versicolor.iloc[:, 1], versicolor.iloc[:, 1], versicolor.iloc[:, 2])
ax.set_title('before PCA')

l2 = ax.scatter(versicolor_pca[:, 1], versicolor_pca[:, 1], versicolor_pca[:, 2])
ax.set_title('after PCA')

plt.show()


Variance and intrinsic dimension¶

● Intrinsic dimension is number of PCA features with significant variance

● In our example: the first two PCA features

● So intrinsic dimension is 2

In [29]:
plt.figure(figsize=(4,4))
features = range(pca2.n_components_)

plt.bar(features, pca2.explained_variance_, alpha = .6, color='r')
plt.xticks(features)
plt.ylabel('variance')
plt.xlabel('PCA feature')

Out[29]:
<matplotlib.text.Text at 0x10cba4a8>

Intrinsic dimension can be ambiguous¶

● Intrinsic dimension is an idealization

● … there is not always one correct answer!

● Boston data from sklearn: could argue for 2, or for 3, or more

NOT standardize feature so the dimension is ambiguous¶

In [30]:
bos = datasets.load_boston()
bos_data = bos.data
bos_data.shape

Out[30]:
(506L, 13L)
In [31]:
pca3 = PCA()
pca3.fit(bos_data)

Out[31]:
PCA(copy=True, iterated_power='auto', n_components=None, random_state=None,
svd_solver='auto', tol=0.0, whiten=False)
In [32]:
plt.figure(figsize=(7,4))
features = range(pca3.n_components_)

plt.bar(features, pca3.explained_variance_, alpha = .6, color='g')
plt.xticks(features)
plt.ylabel('variance')
plt.xlabel('PCA feature')

plt.axvline(x=2, ls = '--', c='r')
plt.axvline(x=3, ls = '--', c='r')

Out[32]:
<matplotlib.lines.Line2D at 0xd2deda0>

standardize features first¶

Variance of the PCA features¶

The Boston dataset is 13-dimensional. But what is its intrinsic dimension?

Make a plot of the variances of the PCA features to find out.

As before, samples is a 2D array, where each row represents a fish. You'll need to standardize the features first.

In [33]:
# Perform the necessary imports
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import make_pipeline
import matplotlib.pyplot as plt

# Create scaler: scaler
scaler = StandardScaler()

# Create a PCA instance: pca
pca4 = PCA()

# Create pipeline: pipeline
pipeline = make_pipeline(scaler, pca4)

# Fit the pipeline to 'samples'
pipeline.fit(bos_data)

# Plot the explained variances
features = range(pca4.n_components_)

plt.figure(figsize=(9,4))

plt.bar(features, pca4.explained_variance_, color='r', alpha=.6)
plt.xlabel('PCA feature')
plt.ylabel('variance')
plt.xticks(features)
plt.show()


Dimension reduction with PCA¶

Dimension reduction

● Represents same data, using less features

● Important part of machine-learning pipelines

● Can be performed using PCA

Dimension reduction with PCA¶

● PCA features are in decreasing order of variance

● Assumes the low variance features are "noise"

● … and high variance features are informative informative noisy

Specify how many features to keep¶

● E.g. PCA(n_components=2)

● Keeps the first 2 PCA features

● Intrinsic dimension is a good choice

Dimension reduction of iris dataset¶

● samples = array of iris measurements (4 features)

● species = list of iris species numbers

In [34]:
pca5 = PCA(2)
pca5.fit(iris.data)

transform = pca5.transform(iris.data)
print (transform.shape)

(150L, 2L)


Iris dataset in 2 dimensions¶

● PCA has reduced the dimension to 2

● Retained the 2 PCA features with highest variance

● Important information preserved: species remain distinct

In [35]:
plt.scatter(transform[:,0], transform[:,1], c=iris.target)

Out[35]:
<matplotlib.collections.PathCollection at 0x10f34f60>

Dimension reduction with PCA¶

● Discards low variance PCA features

● Assumes the high variance features are informative

● Assumption typically holds in practice (e.g. for iris)

Word frequency arrays¶

● Rows represent documents, columns represent words

● Entries measure presence of each word in each document

● ... measure using "tf-idf" (more later)

In [36]:
plt.imshow(plt.imread('tfidf.jpg'))
plt.grid('off')
plt.axis('off')

Out[36]:
(-0.5, 542.5, 292.5, -0.5)

A tf-idf word-frequency array¶

• create a tf-idf word frequency array for a toy collection of documents.

• For this, use the TfidfVectorizer from sklearn. It transforms a list of documents into a word frequency array, which it outputs as a csr_matrix.

• It has fit() and transform() methods like other sklearn objects.

• You are given a list documents of toy documents about pets. It's contents have been printed in the IPython Shell.
In [37]:
documents = ['cats say meow', 'dogs say woof', 'dogs chase cats']

In [38]:
# Import TfidfVectorizer
from sklearn.feature_extraction.text import TfidfVectorizer

# Create a TfidfVectorizer: tfidf
tfidf = TfidfVectorizer()

# Apply fit_transform to document: csr_mat
csr_mat = tfidf.fit_transform(documents)

# Print result of toarray() method
print(csr_mat.toarray())

# Get the words: words
words = tfidf.get_feature_names()

# Print words
print
print(words)

[[ 0.51785612  0.          0.          0.68091856  0.51785612  0.        ]
[ 0.          0.          0.51785612  0.          0.51785612  0.68091856]
[ 0.51785612  0.68091856  0.51785612  0.          0.          0.        ]]

[u'cats', u'chase', u'dogs', u'meow', u'say', u'woof']

In [39]:
csr_mat

Out[39]:
<3x6 sparse matrix of type '<type 'numpy.float64'>'
with 9 stored elements in Compressed Sparse Row format>
In [40]:
print csr_mat

  (0, 0)	0.517856116168
(0, 4)	0.517856116168
(0, 3)	0.680918560399
(1, 4)	0.517856116168
(1, 2)	0.517856116168
(1, 5)	0.680918560399
(2, 0)	0.517856116168
(2, 2)	0.517856116168
(2, 1)	0.680918560399

In [ ]:



Sparse arrays and csr_matrix¶

● Array is "sparse": most entries are zero

● Can use scipy.sparse.csr_matrix instead of NumPy array

● csr_matrix remembers only the non-zero entries (saves space!)

TruncatedSVD and csr_matrix¶

● scikit-learn PCA doesn't support csr_matrix

● Performs same transformation

In [41]:
plt.imshow(plt.imread('svd.jpg'))
plt.grid('off')
plt.axis('off')

Out[41]:
(-0.5, 717.5, 247.5, -0.5)

TruncatedSVD is able to perform PCA on sparse arrays in csr_matrix format¶

• such as word-frequency arrays.
• Combine your knowledge of TruncatedSVD and k-means to cluster some popular pages from Wikipedia.
• build the pipeline.
• Create a Pipeline object consisting of a TruncatedSVD followed by KMeans.
In [42]:
# Perform the necessary imports
from sklearn.decomposition import TruncatedSVD
from sklearn.cluster import KMeans
from sklearn.pipeline import make_pipeline

# Create a TruncatedSVD instance: svd
svd = TruncatedSVD(n_components=50)

# Create a KMeans instance: kmeans
kmeans = KMeans(n_clusters=6)

# Create a pipeline: pipeline
pipeline = make_pipeline(svd, kmeans)


In [43]:
twi = pd.read_csv('tweets.csv')
twi.shape

Out[43]:
(615, 33)
In [44]:
text = twi['text']
text.shape

Out[44]:
(615L,)
In [45]:
text.head()

Out[45]:
0    RT @MeckeringBoy: Does Pauline secretly wear h...
1    RT @lordaedonis: if you a grown man afraid of ...
2    RT @alaskantexanQCT: I'm not "White" but still...
3    We dont discriminate like Libs, divede by sex,...
4    @TMattis7 @babsmarshall1 @Randazzoj @realDonal...
Name: text, dtype: object
In [46]:
# Import TfidfVectorizer
from sklearn.feature_extraction.text import TfidfVectorizer

# Create a TfidfVectorizer: tfidf
tfidf = TfidfVectorizer()

# Apply fit_transform to document: csr_mat
tweet_mat = tfidf.fit_transform(text)

# Get the words: words
word = tfidf.get_feature_names()

# Print words

In [47]:
len(word)

Out[47]:
1286
In [48]:
tweet_mat

Out[48]:
<615x1286 sparse matrix of type '<type 'numpy.float64'>'
with 10947 stored elements in Compressed Sparse Row format>

clustering¶

label is the group of the post¶

In [69]:
# Import pandas
import pandas as pd

# Fit the pipeline to articles
pipeline.fit(tweet_mat)

# Calculate the cluster labels: labels
labels = pipeline.predict(tweet_mat)

# Create a DataFrame aligning labels and titles: df
df = pd.DataFrame({'label': labels, 'article': range(1,616)})

# Display df sorted by cluster label
df['label'].unique()

     article  label
247      248      0
276      277      0
287      288      0
238      239      0
19        20      0

Out[69]:
array([2, 0, 1, 3, 5, 4], dtype=int64)

the results show there are 6 categories in total, the biggest group has 322 twitter posts¶

In [70]:
df['label'].value_counts(ascending = False)

Out[70]:
2    320
1    149
3     90
5     23
0     23
4     10
Name: label, dtype: int64
In [71]:
df.head()

Out[71]:
article label
0 1 2
1 2 0
2 3 1
3 4 2
4 5 2

check out the group with the least posts¶

In [72]:
index = list(df[df['label']==4]['article'])
index

Out[72]:
[52, 82, 84, 132, 249, 327, 357, 359, 407, 607]
In [76]:
text.iloc[index]

Out[76]:
52     RT @DebraJenson: Marine veteran pushing @jason...
82     RT @PhDdropout: Reminder that Chaffetz wouldn'...
84     RT @PhDdropout: Reminder that Chaffetz wouldn'...
132    RT @PhDdropout: Reminder that Chaffetz wouldn'...
249    RT @alaskantexanQCT: I'm not "White" but still...
327    RT @DebraJenson: Marine veteran pushing @jason...
357    RT @PhDdropout: Reminder that Chaffetz wouldn'...
359    RT @PhDdropout: Reminder that Chaffetz wouldn'...
407    RT @PhDdropout: Reminder that Chaffetz wouldn'...
607    RT @alaskantexanQCT: I'm not "White" but still...
Name: text, dtype: object
In [77]:
for i in text.iloc[index]: print i+'\n'

RT @DebraJenson: Marine veteran pushing @jasoninthehouse to defend his flip-flop on Trump and pussy-grabbing, VAWA, and Session. #chaffetzt…

RT @PhDdropout: Reminder that Chaffetz wouldn't endorse Trump after pussy tape, only to reverse. Not the spine you'd want in ethics chair #…

RT @PhDdropout: Reminder that Chaffetz wouldn't endorse Trump after pussy tape, only to reverse. Not the spine you'd want in ethics chair #…

RT @PhDdropout: Reminder that Chaffetz wouldn't endorse Trump after pussy tape, only to reverse. Not the spine you'd want in ethics chair #…

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…

RT @DebraJenson: Marine veteran pushing @jasoninthehouse to defend his flip-flop on Trump and pussy-grabbing, VAWA, and Session. #chaffetzt…

RT @PhDdropout: Reminder that Chaffetz wouldn't endorse Trump after pussy tape, only to reverse. Not the spine you'd want in ethics chair #…

RT @PhDdropout: Reminder that Chaffetz wouldn't endorse Trump after pussy tape, only to reverse. Not the spine you'd want in ethics chair #…

RT @PhDdropout: Reminder that Chaffetz wouldn't endorse Trump after pussy tape, only to reverse. Not the spine you'd want in ethics chair #…

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…



check out the group with the second least posts¶

In [84]:
text.iloc[df[df['label']==0]['article'].values]

Out[84]:
2      RT @alaskantexanQCT: I'm not "White" but still...
7      @juliahosack @Marina_Sirtis  your the problem ...
13     RT @alaskantexanQCT: I'm not "White" but still...
20     RT @alaskantexanQCT: I'm not "White" but still...
90     RT @LEngelhorn: You can do "things" in Russia ...
135    RT @PhDdropout: Reminder that Chaffetz wouldn'...
239    Trump is China's bitch. They're definitely gra...
242    RT @lordaedonis: if you a grown man afraid of ...
243    Immigration kills black AMERICANS more than an...
245    RT @lordaedonis: if you a grown man afraid of ...
246    RT @alaskantexanQCT: I'm not "White" but still...
248    RT @daylinleach: @XGrabMyY @realDonaldTrump Ci...
255    RT @lordaedonis: if you a grown man afraid of ...
256    RT @alaskantexanQCT: I'm not "White" but still...
264    RT @bavegan2951: 👍👍👍👍😂😂😂😂😂😂😂🇺🇸🇮�...
268    RT @Caycioldman: If you were upset by Trump's ...
271    Donald is now seen as such a pussy that Access...
277    RT @alaskantexanQCT: I'm not "White" but still...
282    @juliahosack @Marina_Sirtis  your the problem ...
288    RT @alaskantexanQCT: I'm not "White" but still...
295    RT @alaskantexanQCT: I'm not "White" but still...
365    RT @LEngelhorn: You can do "things" in Russia ...
410    RT @PhDdropout: Reminder that Chaffetz wouldn'...
Name: text, dtype: object
In [83]:
for i in text.iloc[df[df['label']==0]['article'].values]: print i+'\n'

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…

RT @LEngelhorn: You can do "things" in Russia you can't get away with here. Think Thailand. Children. Pussy grabbers are welcomed.…

RT @PhDdropout: Reminder that Chaffetz wouldn't endorse Trump after pussy tape, only to reverse. Not the spine you'd want in ethics chair #…

Trump is China's bitch. They're definitely grabbing him by the pussy. Pathetic.

RT @lordaedonis: if you a grown man afraid of a Trump presidency please do not speak to me. the only pussy I like around me is on women.

Immigration kills black AMERICANS more than any other group. This guy gets it! https://t.co/yiDmuauje5

RT @lordaedonis: if you a grown man afraid of a Trump presidency please do not speak to me. the only pussy I like around me is on women.

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…

RT @daylinleach: @XGrabMyY @realDonaldTrump Civil to Trump? You know he calls your gender "disgusting pigs" and "filthy animals" whose puss…

RT @lordaedonis: if you a grown man afraid of a Trump presidency please do not speak to me. the only pussy I like around me is on women.

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…

RT @bavegan2951: 👍👍👍👍😂😂😂😂😂😂😂🇺🇸🇮🇱 https://t.co/yPpGIdVETg

RT @Caycioldman: If you were upset by Trump's "grab her by the pussy" comment but are defending our ASUN speaker saying "people change" I w…

Donald is now seen as such a pussy that Access Hollywood has released a tape of President Xi saying that he "grabbe… https://t.co/kdrkvYxVw6

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…

RT @alaskantexanQCT: I'm not "White" but still I think that "pussy hats", burning a college campus, attacking Trump supporters and obstr…

RT @LEngelhorn: You can do "things" in Russia you can't get away with here. Think Thailand. Children. Pussy grabbers are welcomed.…

RT @PhDdropout: Reminder that Chaffetz wouldn't endorse Trump after pussy tape, only to reverse. Not the spine you'd want in ethics chair #…


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