K Means Clustering Project - Solutions




K Means Clustering Project - Solutions

For this project we will attempt to use KMeans Clustering to cluster Universities into to two groups, Private and Public.


It is very important to note, we actually have the labels for this data set, but we will NOT use them for the KMeans clustering algorithm, since that is an unsupervised learning algorithm.

When using the Kmeans algorithm under normal circumstances, it is because you don't have labels. In this case we will use the labels to try to get an idea of how well the algorithm performed, but you won't usually do this for Kmeans, so the classification report and confusion matrix at the end of this project, don't truly make sense in a real world setting!.


The Data

We will use a data frame with 777 observations on the following 18 variables.

  • Private A factor with levels No and Yes indicating private or public university
  • Apps Number of applications received
  • Accept Number of applications accepted
  • Enroll Number of new students enrolled
  • Top10perc Pct. new students from top 10% of H.S. class
  • Top25perc Pct. new students from top 25% of H.S. class
  • F.Undergrad Number of fulltime undergraduates
  • P.Undergrad Number of parttime undergraduates
  • Outstate Out-of-state tuition
  • Room.Board Room and board costs
  • Books Estimated book costs
  • Personal Estimated personal spending
  • PhD Pct. of faculty with Ph.D.’s
  • Terminal Pct. of faculty with terminal degree
  • S.F.Ratio Student/faculty ratio
  • perc.alumni Pct. alumni who donate
  • Expend Instructional expenditure per student
  • Grad.Rate Graduation rate

Import Libraries

Import the libraries you usually use for data analysis.


In [103]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

Get the Data

Read in the College_Data file using read_csv. Figure out how to set the first column as the index.


In [104]:
df = pd.read_csv('College_Data',index_col=0)

Check the head of the data


In [105]:
df.head()


Out[105]:
Private Apps Accept Enroll Top10perc Top25perc F.Undergrad P.Undergrad Outstate Room.Board Books Personal PhD Terminal S.F.Ratio perc.alumni Expend Grad.Rate
Abilene Christian University Yes 1660 1232 721 23 52 2885 537 7440 3300 450 2200 70 78 18.1 12 7041 60
Adelphi University Yes 2186 1924 512 16 29 2683 1227 12280 6450 750 1500 29 30 12.2 16 10527 56
Adrian College Yes 1428 1097 336 22 50 1036 99 11250 3750 400 1165 53 66 12.9 30 8735 54
Agnes Scott College Yes 417 349 137 60 89 510 63 12960 5450 450 875 92 97 7.7 37 19016 59
Alaska Pacific University Yes 193 146 55 16 44 249 869 7560 4120 800 1500 76 72 11.9 2 10922 15

Check the info() and describe() methods on the data.


In [106]:
df.info()


<class 'pandas.core.frame.DataFrame'>
Index: 777 entries, Abilene Christian University to York College of Pennsylvania
Data columns (total 18 columns):
Private        777 non-null object
Apps           777 non-null int64
Accept         777 non-null int64
Enroll         777 non-null int64
Top10perc      777 non-null int64
Top25perc      777 non-null int64
F.Undergrad    777 non-null int64
P.Undergrad    777 non-null int64
Outstate       777 non-null int64
Room.Board     777 non-null int64
Books          777 non-null int64
Personal       777 non-null int64
PhD            777 non-null int64
Terminal       777 non-null int64
S.F.Ratio      777 non-null float64
perc.alumni    777 non-null int64
Expend         777 non-null int64
Grad.Rate      777 non-null int64
dtypes: float64(1), int64(16), object(1)
memory usage: 115.3+ KB

In [107]:
df.describe()


Out[107]:
Apps Accept Enroll Top10perc Top25perc F.Undergrad P.Undergrad Outstate Room.Board Books Personal PhD Terminal S.F.Ratio perc.alumni Expend Grad.Rate
count 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.000000 777.00000
mean 3001.638353 2018.804376 779.972973 27.558559 55.796654 3699.907336 855.298584 10440.669241 4357.526384 549.380952 1340.642214 72.660232 79.702703 14.089704 22.743887 9660.171171 65.46332
std 3870.201484 2451.113971 929.176190 17.640364 19.804778 4850.420531 1522.431887 4023.016484 1096.696416 165.105360 677.071454 16.328155 14.722359 3.958349 12.391801 5221.768440 17.17771
min 81.000000 72.000000 35.000000 1.000000 9.000000 139.000000 1.000000 2340.000000 1780.000000 96.000000 250.000000 8.000000 24.000000 2.500000 0.000000 3186.000000 10.00000
25% 776.000000 604.000000 242.000000 15.000000 41.000000 992.000000 95.000000 7320.000000 3597.000000 470.000000 850.000000 62.000000 71.000000 11.500000 13.000000 6751.000000 53.00000
50% 1558.000000 1110.000000 434.000000 23.000000 54.000000 1707.000000 353.000000 9990.000000 4200.000000 500.000000 1200.000000 75.000000 82.000000 13.600000 21.000000 8377.000000 65.00000
75% 3624.000000 2424.000000 902.000000 35.000000 69.000000 4005.000000 967.000000 12925.000000 5050.000000 600.000000 1700.000000 85.000000 92.000000 16.500000 31.000000 10830.000000 78.00000
max 48094.000000 26330.000000 6392.000000 96.000000 100.000000 31643.000000 21836.000000 21700.000000 8124.000000 2340.000000 6800.000000 103.000000 100.000000 39.800000 64.000000 56233.000000 118.00000

EDA

It's time to create some data visualizations!

Create a scatterplot of Grad.Rate versus Room.Board where the points are colored by the Private column.


In [111]:
sns.set_style('whitegrid')
sns.lmplot('Room.Board','Grad.Rate',data=df, hue='Private',
           palette='coolwarm',size=6,aspect=1,fit_reg=False)


Out[111]:
<seaborn.axisgrid.FacetGrid at 0x11db9da90>

Create a scatterplot of F.Undergrad versus Outstate where the points are colored by the Private column.


In [112]:
sns.set_style('whitegrid')
sns.lmplot('Outstate','F.Undergrad',data=df, hue='Private',
           palette='coolwarm',size=6,aspect=1,fit_reg=False)


Out[112]:
<seaborn.axisgrid.FacetGrid at 0x144b90b38>

Create a stacked histogram showing Out of State Tuition based on the Private column. Try doing this using sns.FacetGrid. If that is too tricky, see if you can do it just by using two instances of pandas.plot(kind='hist').


In [109]:
sns.set_style('darkgrid')
g = sns.FacetGrid(df,hue="Private",palette='coolwarm',size=6,aspect=2)
g = g.map(plt.hist,'Outstate',bins=20,alpha=0.7)


Create a similar histogram for the Grad.Rate column.


In [110]:
sns.set_style('darkgrid')
g = sns.FacetGrid(df,hue="Private",palette='coolwarm',size=6,aspect=2)
g = g.map(plt.hist,'Grad.Rate',bins=20,alpha=0.7)


Notice how there seems to be a private school with a graduation rate of higher than 100%.What is the name of that school?


In [113]:
df[df['Grad.Rate'] > 100]


Out[113]:
Private Apps Accept Enroll Top10perc Top25perc F.Undergrad P.Undergrad Outstate Room.Board Books Personal PhD Terminal S.F.Ratio perc.alumni Expend Grad.Rate
Cazenovia College Yes 3847 3433 527 9 35 1010 12 9384 4840 600 500 22 47 14.3 20 7697 118

Set that school's graduation rate to 100 so it makes sense. You may get a warning not an error) when doing this operation, so use dataframe operations or just re-do the histogram visualization to make sure it actually went through.


In [93]:
df['Grad.Rate']['Cazenovia College'] = 100


/Users/marci/anaconda/lib/python3.5/site-packages/ipykernel/__main__.py:1: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
  if __name__ == '__main__':

In [94]:
df[df['Grad.Rate'] > 100]


Out[94]:
Private Apps Accept Enroll Top10perc Top25perc F.Undergrad P.Undergrad Outstate Room.Board Books Personal PhD Terminal S.F.Ratio perc.alumni Expend Grad.Rate

In [95]:
sns.set_style('darkgrid')
g = sns.FacetGrid(df,hue="Private",palette='coolwarm',size=6,aspect=2)
g = g.map(plt.hist,'Grad.Rate',bins=20,alpha=0.7)


K Means Cluster Creation

Now it is time to create the Cluster labels!

Import KMeans from SciKit Learn.


In [114]:
from sklearn.cluster import KMeans

Create an instance of a K Means model with 2 clusters.


In [115]:
kmeans = KMeans(n_clusters=2)

Fit the model to all the data except for the Private label.


In [116]:
kmeans.fit(df.drop('Private',axis=1))


Out[116]:
KMeans(copy_x=True, init='k-means++', max_iter=300, n_clusters=2, n_init=10,
    n_jobs=1, precompute_distances='auto', random_state=None, tol=0.0001,
    verbose=0)

What are the cluster center vectors?


In [117]:
kmeans.cluster_centers_


Out[117]:
array([[  1.81323468e+03,   1.28716592e+03,   4.91044843e+02,
          2.53094170e+01,   5.34708520e+01,   2.18854858e+03,
          5.95458894e+02,   1.03957085e+04,   4.31136472e+03,
          5.41982063e+02,   1.28033632e+03,   7.04424514e+01,
          7.78251121e+01,   1.40997010e+01,   2.31748879e+01,
          8.93204634e+03,   6.51195815e+01],
       [  1.03631389e+04,   6.55089815e+03,   2.56972222e+03,
          4.14907407e+01,   7.02037037e+01,   1.30619352e+04,
          2.46486111e+03,   1.07191759e+04,   4.64347222e+03,
          5.95212963e+02,   1.71420370e+03,   8.63981481e+01,
          9.13333333e+01,   1.40277778e+01,   2.00740741e+01,
          1.41705000e+04,   6.75925926e+01]])

Evaluation

There is no perfect way to evaluate clustering if you don't have the labels, however since this is just an exercise, we do have the labels, so we take advantage of this to evaluate our clusters, keep in mind, you usually won't have this luxury in the real world.

Create a new column for df called 'Cluster', which is a 1 for a Private school, and a 0 for a public school.


In [118]:
def converter(cluster):
    if cluster=='Yes':
        return 1
    else:
        return 0

In [119]:
df['Cluster'] = df['Private'].apply(converter)

In [122]:
df.head()


Out[122]:
Private Apps Accept Enroll Top10perc Top25perc F.Undergrad P.Undergrad Outstate Room.Board Books Personal PhD Terminal S.F.Ratio perc.alumni Expend Grad.Rate Cluster
Abilene Christian University Yes 1660 1232 721 23 52 2885 537 7440 3300 450 2200 70 78 18.1 12 7041 60 1
Adelphi University Yes 2186 1924 512 16 29 2683 1227 12280 6450 750 1500 29 30 12.2 16 10527 56 1
Adrian College Yes 1428 1097 336 22 50 1036 99 11250 3750 400 1165 53 66 12.9 30 8735 54 1
Agnes Scott College Yes 417 349 137 60 89 510 63 12960 5450 450 875 92 97 7.7 37 19016 59 1
Alaska Pacific University Yes 193 146 55 16 44 249 869 7560 4120 800 1500 76 72 11.9 2 10922 15 1

Create a confusion matrix and classification report to see how well the Kmeans clustering worked without being given any labels.


In [123]:
from sklearn.metrics import confusion_matrix,classification_report
print(confusion_matrix(df['Cluster'],kmeans.labels_))
print(classification_report(df['Cluster'],kmeans.labels_))


[[138  74]
 [531  34]]
             precision    recall  f1-score   support

          0       0.21      0.65      0.31       212
          1       0.31      0.06      0.10       565

avg / total       0.29      0.22      0.16       777

Not so bad considering the algorithm is purely using the features to cluster the universities into 2 distinct groups! Hopefully you can begin to see how K Means is useful for clustering un-labeled data!

Great Job!