In this project we begin unsupervised ML with K-means clustering.
Data head
| 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 |
** 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
| 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 |
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%.**
| 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 school's graduation rate to 100 so it makes sense. **
| 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 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.**
| 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 |
** 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.
