k-Means

In this project we begin unsupervised ML with K-means clustering.

Data head

** Crude data metrics**

<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

Data Exploration

** Scatterplot of Grad.Rate versus Room.Board where the points are colored by the Private column. **

<seaborn.axisgrid.FacetGrid at 0x11db9da90>

Scatterplot of F.Undergrad versus Outstate where the points are colored by the Private column. <seaborn.axisgrid.FacetGrid at 0x144b90b38>

** Stacked histogram showing Out of State Tuition based on the Private column.**

Similar histogram for the Grad.Rate column.

** There seems to be a private school with a graduation rate of higher than 100%.**

** Set school's graduation rate to 100 so it makes sense. **

** Cluster center vectors**

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]])

Model Evaluation

There is no perfect way to evaluate clustering if you don't have the labels, however for this data, we have the labels, so we take advantage of this to evaluate our clusters.

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

** Confusion matrix and classification report to see how well the Kmeans clustering worked without being given any 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

This is not so bad considering the algorithm purely uses the features to cluster the universities into 2 distinct groups.