Unsupervised Learning - Kmeans Week 11 Challenge
1) How does similarity is calculated if data is categorical in nature
Categorical data (also known as nominal data) has been studied for a long time in various contexts. However, computing similarity between categorical data instances is not straightforward owing to the fact that there is no explicit notion of ordering between categorical values. To overcome this problem, several data-driven similarity measures have been proposed for categorical data. The behavior of such measures directly depends on the data. The simplest way to find similarity between two categorical attributes is to assign a similarity of 1 if the values are identical and similarity of 0 if the values are not identical.
Measuring the similarity or distance between two entities is a key step for several data mining and knowledge discovery tasks. The notion of similarity for continuous data is relatively well-understood, but for categorical data, the similarity computation is not straightforward. Several data-driven similarity measures have been proposed in the literature to compute the similarity between two categorical data instances but their relative performance has not been evaluated. In this paper, we study the performance of a variety of similarity measures in the context of a specific data mining task: outlier detection. Results on a variety of data sets show that while no one measure dominates others for all types of problems, some measures are able to have consistently high performance.
the similarity in categorical data is not as direct when it comes to numerical data. the categorical data is first transformed into numerical values and both are standardized to make sense of the similarity and dissimilarities between/among those features. For continuous data sets, the Minkowski Distance is a general method used to compute the distance between two multivariate points. In particular, the Minkowski Distance of order 1 (Manhattan) and order 2 (Euclidean)
are the two most widely used distance measures for continuous data.
The notion of similarity or distance for categorical data is not as straightforward as for continuous data.
The key characteristic of categorical data is that the different values that a categorical attribute takes are
not inherently ordered. Thus, it is not possible to directly compare two different categorical values. The simplest way to find similarity between two categorical attributes is to assign a similarity of 1 if the values are identical and similarity of 0 if the values are not identical.
2) Implement K-means for “Car dataset” and come up with the business insights
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
df=pd.read_csv('CarPrice_Assignment.csv')
print(df)
car_ID symboling CarName fueltype aspiration \
0 1 3 alfa-romero giulia gas std
1 2 3 alfa-romero stelvio gas std
2 3 1 alfa-romero Quadrifoglio gas std
3 4 2 audi 100 ls gas std
4 5 2 audi 100ls gas std
.. ... ... ... ... ...
200 201 -1 volvo 145e (sw) gas std
201 202 -1 volvo 144ea gas turbo
202 203 -1 volvo 244dl gas std
203 204 -1 volvo 246 diesel turbo
204 205 -1 volvo 264gl gas turbo
doornumber carbody drivewheel enginelocation wheelbase ... \
0 two convertible rwd front 88.6 ...
1 two convertible rwd front 88.6 ...
2 two hatchback rwd front 94.5 ...
3 four sedan fwd front 99.8 ...
4 four sedan 4wd front 99.4 ...
.. ... ... ... ... ... ...
200 four sedan rwd front 109.1 ...
201 four sedan rwd front 109.1 ...
202 four sedan rwd front 109.1 ...
203 four sedan rwd front 109.1 ...
204 four sedan rwd front 109.1 ...
enginesize fuelsystem boreratio stroke compressionratio horsepower \
0 130 mpfi 3.47 2.68 9.0 111
1 130 mpfi 3.47 2.68 9.0 111
2 152 mpfi 2.68 3.47 9.0 154
3 109 mpfi 3.19 3.40 10.0 102
4 136 mpfi 3.19 3.40 8.0 115
.. ... ... ... ... ... ...
200 141 mpfi 3.78 3.15 9.5 114
201 141 mpfi 3.78 3.15 8.7 160
202 173 mpfi 3.58 2.87 8.8 134
203 145 idi 3.01 3.40 23.0 106
204 141 mpfi 3.78 3.15 9.5 114
peakrpm citympg highwaympg price
0 5000 21 27 13495.0
1 5000 21 27 16500.0
2 5000 19 26 16500.0
3 5500 24 30 13950.0
4 5500 18 22 17450.0
.. ... ... ... ...
200 5400 23 28 16845.0
201 5300 19 25 19045.0
202 5500 18 23 21485.0
203 4800 26 27 22470.0
204 5400 19 25 22625.0
[205 rows x 26 columns]
print(df.describe())
km=KMeans(n_clusters=3)
print(km)
car_ID symboling wheelbase carlength carwidth carheight \
count 205.000000 205.000000 205.000000 205.000000 205.000000 205.000000
mean 103.000000 0.834146 98.756585 174.049268 65.907805 53.724878
std 59.322565 1.245307 6.021776 12.337289 2.145204 2.443522
min 1.000000 -2.000000 86.600000 141.100000 60.300000 47.800000
25% 52.000000 0.000000 94.500000 166.300000 64.100000 52.000000
50% 103.000000 1.000000 97.000000 173.200000 65.500000 54.100000
75% 154.000000 2.000000 102.400000 183.100000 66.900000 55.500000
max 205.000000 3.000000 120.900000 208.100000 72.300000 59.800000
curbweight enginesize boreratio stroke compressionratio \
count 205.000000 205.000000 205.000000 205.000000 205.000000
mean 2555.565854 126.907317 3.329756 3.255415 10.142537
std 520.680204 41.642693 0.270844 0.313597 3.972040
min 1488.000000 61.000000 2.540000 2.070000 7.000000
25% 2145.000000 97.000000 3.150000 3.110000 8.600000
50% 2414.000000 120.000000 3.310000 3.290000 9.000000
75% 2935.000000 141.000000 3.580000 3.410000 9.400000
max 4066.000000 326.000000 3.940000 4.170000 23.000000
horsepower peakrpm citympg highwaympg price
count 205.000000 205.000000 205.000000 205.000000 205.000000
mean 104.117073 5125.121951 25.219512 30.751220 13276.710571
std 39.544167 476.985643 6.542142 6.886443 7988.852332
min 48.000000 4150.000000 13.000000 16.000000 5118.000000
25% 70.000000 4800.000000 19.000000 25.000000 7788.000000
50% 95.000000 5200.000000 24.000000 30.000000 10295.000000
75% 116.000000 5500.000000 30.000000 34.000000 16503.000000
max 288.000000 6600.000000 49.000000 54.000000 45400.000000
KMeans(n_clusters=3)
y=km.fit_predict(df[["citympg","price"]])
print(y)
[2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 2 1 1 1 1 1 1 1 2 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 2 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 1 1 1 1 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 2 2 0 2 2 2 2 2 2 2 2 2 2 2]
df["cluster"]=y
print(df)
df0=df[df.cluster==0]
df1=df[df.cluster==1]
df2=df[df.cluster==2]
print(df0,df1,df2)
car_ID symboling CarName fueltype aspiration \
0 1 3 alfa-romero giulia gas std
1 2 3 alfa-romero stelvio gas std
2 3 1 alfa-romero Quadrifoglio gas std
3 4 2 audi 100 ls gas std
4 5 2 audi 100ls gas std
.. ... ... ... ... ...
200 201 -1 volvo 145e (sw) gas std
201 202 -1 volvo 144ea gas turbo
202 203 -1 volvo 244dl gas std
203 204 -1 volvo 246 diesel turbo
204 205 -1 volvo 264gl gas turbo
doornumber carbody drivewheel enginelocation wheelbase ... \
0 two convertible rwd front 88.6 ...
1 two convertible rwd front 88.6 ...
2 two hatchback rwd front 94.5 ...
3 four sedan fwd front 99.8 ...
4 four sedan 4wd front 99.4 ...
.. ... ... ... ... ... ...
200 four sedan rwd front 109.1 ...
201 four sedan rwd front 109.1 ...
202 four sedan rwd front 109.1 ...
203 four sedan rwd front 109.1 ...
204 four sedan rwd front 109.1 ...
fuelsystem boreratio stroke compressionratio horsepower peakrpm \
0 mpfi 3.47 2.68 9.0 111 5000
1 mpfi 3.47 2.68 9.0 111 5000
2 mpfi 2.68 3.47 9.0 154 5000
3 mpfi 3.19 3.40 10.0 102 5500
4 mpfi 3.19 3.40 8.0 115 5500
.. ... ... ... ... ... ...
200 mpfi 3.78 3.15 9.5 114 5400
201 mpfi 3.78 3.15 8.7 160 5300
202 mpfi 3.58 2.87 8.8 134 5500
203 idi 3.01 3.40 23.0 106 4800
204 mpfi 3.78 3.15 9.5 114 5400
citympg highwaympg price cluster
0 21 27 13495.0 2
1 21 27 16500.0 2
2 19 26 16500.0 2
3 24 30 13950.0 2
4 18 22 17450.0 2
.. ... ... ... ...
200 23 28 16845.0 2
201 19 25 19045.0 2
202 18 23 21485.0 2
203 26 27 22470.0 2
204 19 25 22625.0 2
[205 rows x 27 columns]
car_ID symboling CarName fueltype aspiration \
18 19 2 chevrolet impala gas std
19 20 1 chevrolet monte carlo gas std
20 21 0 chevrolet vega 2300 gas std
21 22 1 dodge rampage gas std
22 23 1 dodge challenger se gas std
.. ... ... ... ... ...
187 188 2 volkswagen super beetle diesel turbo
188 189 2 volkswagen dasher gas std
189 190 3 vw dasher gas std
190 191 3 vw rabbit gas std
193 194 0 volkswagen dasher gas std
doornumber carbody drivewheel enginelocation wheelbase ... \
18 two hatchback fwd front 88.4 ...
19 two hatchback fwd front 94.5 ...
20 four sedan fwd front 94.5 ...
21 two hatchback fwd front 93.7 ...
22 two hatchback fwd front 93.7 ...
.. ... ... ... ... ... ...
187 four sedan fwd front 97.3 ...
188 four sedan fwd front 97.3 ...
189 two convertible fwd front 94.5 ...
190 two hatchback fwd front 94.5 ...
193 four wagon fwd front 100.4 ...
fuelsystem boreratio stroke compressionratio horsepower peakrpm \
18 2bbl 2.91 3.03 9.50 48 5100
19 2bbl 3.03 3.11 9.60 70 5400
20 2bbl 3.03 3.11 9.60 70 5400
21 2bbl 2.97 3.23 9.41 68 5500
22 2bbl 2.97 3.23 9.40 68 5500
.. ... ... ... ... ... ...
187 idi 3.01 3.40 23.00 68 4500
188 mpfi 3.19 3.40 10.00 100 5500
189 mpfi 3.19 3.40 8.50 90 5500
190 mpfi 3.19 3.40 8.50 90 5500
193 mpfi 3.19 3.40 9.00 88 5500
citympg highwaympg price cluster
18 47 53 5151.0 0
19 38 43 6295.0 0
20 38 43 6575.0 0
21 37 41 5572.0 0
22 31 38 6377.0 0
.. ... ... ... ...
187 37 42 9495.0 0
188 26 32 9995.0 0
189 24 29 11595.0 0
190 24 29 9980.0 0
193 25 31 12290.0 0
[124 rows x 27 columns] car_ID symboling CarName fueltype aspiration \
15 16 0 bmw x4 gas std
16 17 0 bmw x5 gas std
17 18 0 bmw x3 gas std
47 48 0 jaguar xj gas std
48 49 0 jaguar xf gas std
49 50 0 jaguar xk gas std
68 69 -1 buick century luxus (sw) diesel turbo
69 70 0 buick century diesel turbo
70 71 -1 buick skyhawk diesel turbo
71 72 -1 buick opel isuzu deluxe gas std
72 73 3 buick skylark gas std
73 74 0 buick century special gas std
74 75 1 buick regal sport coupe (turbo) gas std
126 127 3 porcshce panamera gas std
127 128 3 porsche cayenne gas std
128 129 3 porsche boxter gas std
129 130 1 porsche cayenne gas std
doornumber carbody drivewheel enginelocation wheelbase ... \
15 four sedan rwd front 103.5 ...
16 two sedan rwd front 103.5 ...
17 four sedan rwd front 110.0 ...
47 four sedan rwd front 113.0 ...
48 four sedan rwd front 113.0 ...
49 two sedan rwd front 102.0 ...
68 four wagon rwd front 110.0 ...
69 two hardtop rwd front 106.7 ...
70 four sedan rwd front 115.6 ...
71 four sedan rwd front 115.6 ...
72 two convertible rwd front 96.6 ...
73 four sedan rwd front 120.9 ...
74 two hardtop rwd front 112.0 ...
126 two hardtop rwd rear 89.5 ...
127 two hardtop rwd rear 89.5 ...
128 two convertible rwd rear 89.5 ...
129 two hatchback rwd front 98.4 ...
fuelsystem boreratio stroke compressionratio horsepower peakrpm \
15 mpfi 3.62 3.39 8.0 182 5400
16 mpfi 3.62 3.39 8.0 182 5400
17 mpfi 3.62 3.39 8.0 182 5400
47 mpfi 3.63 4.17 8.1 176 4750
48 mpfi 3.63 4.17 8.1 176 4750
49 mpfi 3.54 2.76 11.5 262 5000
68 idi 3.58 3.64 21.5 123 4350
69 idi 3.58 3.64 21.5 123 4350
70 idi 3.58 3.64 21.5 123 4350
71 mpfi 3.46 3.10 8.3 155 4750
72 mpfi 3.46 3.10 8.3 155 4750
73 mpfi 3.80 3.35 8.0 184 4500
74 mpfi 3.80 3.35 8.0 184 4500
126 mpfi 3.74 2.90 9.5 207 5900
127 mpfi 3.74 2.90 9.5 207 5900
128 mpfi 3.74 2.90 9.5 207 5900
129 mpfi 3.94 3.11 10.0 288 5750
citympg highwaympg price cluster
15 16 22 30760.0 1
16 16 22 41315.0 1
17 15 20 36880.0 1
47 15 19 32250.0 1
48 15 19 35550.0 1
49 13 17 36000.0 1
68 22 25 28248.0 1
69 22 25 28176.0 1
70 22 25 31600.0 1
71 16 18 34184.0 1
72 16 18 35056.0 1
73 14 16 40960.0 1
74 14 16 45400.0 1
126 17 25 32528.0 1
127 17 25 34028.0 1
128 17 25 37028.0 1
129 17 28 31400.5 1
[17 rows x 27 columns] car_ID symboling CarName fueltype aspiration \
0 1 3 alfa-romero giulia gas std
1 2 3 alfa-romero stelvio gas std
2 3 1 alfa-romero Quadrifoglio gas std
3 4 2 audi 100 ls gas std
4 5 2 audi 100ls gas std
.. ... ... ... ... ...
200 201 -1 volvo 145e (sw) gas std
201 202 -1 volvo 144ea gas turbo
202 203 -1 volvo 244dl gas std
203 204 -1 volvo 246 diesel turbo
204 205 -1 volvo 264gl gas turbo
doornumber carbody drivewheel enginelocation wheelbase ... \
0 two convertible rwd front 88.6 ...
1 two convertible rwd front 88.6 ...
2 two hatchback rwd front 94.5 ...
3 four sedan fwd front 99.8 ...
4 four sedan 4wd front 99.4 ...
.. ... ... ... ... ... ...
200 four sedan rwd front 109.1 ...
201 four sedan rwd front 109.1 ...
202 four sedan rwd front 109.1 ...
203 four sedan rwd front 109.1 ...
204 four sedan rwd front 109.1 ...
fuelsystem boreratio stroke compressionratio horsepower peakrpm \
0 mpfi 3.47 2.68 9.0 111 5000
1 mpfi 3.47 2.68 9.0 111 5000
2 mpfi 2.68 3.47 9.0 154 5000
3 mpfi 3.19 3.40 10.0 102 5500
4 mpfi 3.19 3.40 8.0 115 5500
.. ... ... ... ... ... ...
200 mpfi 3.78 3.15 9.5 114 5400
201 mpfi 3.78 3.15 8.7 160 5300
202 mpfi 3.58 2.87 8.8 134 5500
203 idi 3.01 3.40 23.0 106 4800
204 mpfi 3.78 3.15 9.5 114 5400
citympg highwaympg price cluster
0 21 27 13495.0 2
1 21 27 16500.0 2
2 19 26 16500.0 2
3 24 30 13950.0 2
4 18 22 17450.0 2
.. ... ... ... ...
200 23 28 16845.0 2
201 19 25 19045.0 2
202 18 23 21485.0 2
203 26 27 22470.0 2
204 19 25 22625.0 2
[64 rows x 27 columns]
plt.scatter(df1.citympg,df1["price"],color="red")
plt.show()
plt.scatter(df0.citympg,df0["price"],color="red")
plt.scatter(df1.citympg,df1["price"],color="blue")
plt.scatter(df2.citympg,df2["price"],color="green")
plt.scatter(km.cluster_centers_[:,0],km.cluster_centers_[:,1],color="purple",marker="")
plt.legend()
plt.show()
def minmax(col):
for i in range(0,len(col)):
new_value=(float(col[i])-float(min(col)))/(float(max(col))-float(min(col)))
ex.append(new_value)
ex=[]
minmax(df.citympg)
df["city_mpg1"]=ex
print(df)
car_ID symboling CarName fueltype aspiration \
0 1 3 alfa-romero giulia gas std
1 2 3 alfa-romero stelvio gas std
2 3 1 alfa-romero Quadrifoglio gas std
3 4 2 audi 100 ls gas std
4 5 2 audi 100ls gas std
.. ... ... ... ... ...
200 201 -1 volvo 145e (sw) gas std
201 202 -1 volvo 144ea gas turbo
202 203 -1 volvo 244dl gas std
203 204 -1 volvo 246 diesel turbo
204 205 -1 volvo 264gl gas turbo
doornumber carbody drivewheel enginelocation wheelbase ... \
0 two convertible rwd front 88.6 ...
1 two convertible rwd front 88.6 ...
2 two hatchback rwd front 94.5 ...
3 four sedan fwd front 99.8 ...
4 four sedan 4wd front 99.4 ...
.. ... ... ... ... ... ...
200 four sedan rwd front 109.1 ...
201 four sedan rwd front 109.1 ...
202 four sedan rwd front 109.1 ...
203 four sedan rwd front 109.1 ...
204 four sedan rwd front 109.1 ...
boreratio stroke compressionratio horsepower peakrpm citympg \
0 3.47 2.68 9.0 111 5000 21
1 3.47 2.68 9.0 111 5000 21
2 2.68 3.47 9.0 154 5000 19
3 3.19 3.40 10.0 102 5500 24
4 3.19 3.40 8.0 115 5500 18
.. ... ... ... ... ... ...
200 3.78 3.15 9.5 114 5400 23
201 3.78 3.15 8.7 160 5300 19
202 3.58 2.87 8.8 134 5500 18
203 3.01 3.40 23.0 106 4800 26
204 3.78 3.15 9.5 114 5400 19
highwaympg price cluster city_mpg1
0 27 13495.0 2 0.222222
1 27 16500.0 2 0.222222
2 26 16500.0 2 0.166667
3 30 13950.0 2 0.305556
4 22 17450.0 2 0.138889
.. ... ... ... ...
200 28 16845.0 2 0.277778
201 25 19045.0 2 0.166667
202 23 21485.0 2 0.138889
203 27 22470.0 2 0.361111
204 25 22625.0 2 0.166667
[205 rows x 28 columns]
ex=[]
minmax(df["price"])
df["new_price"]=ex
print(df)
car_ID symboling CarName fueltype aspiration \
0 1 3 alfa-romero giulia gas std
1 2 3 alfa-romero stelvio gas std
2 3 1 alfa-romero Quadrifoglio gas std
3 4 2 audi 100 ls gas std
4 5 2 audi 100ls gas std
.. ... ... ... ... ...
200 201 -1 volvo 145e (sw) gas std
201 202 -1 volvo 144ea gas turbo
202 203 -1 volvo 244dl gas std
203 204 -1 volvo 246 diesel turbo
204 205 -1 volvo 264gl gas turbo
doornumber carbody drivewheel enginelocation wheelbase ... stroke \
0 two convertible rwd front 88.6 ... 2.68
1 two convertible rwd front 88.6 ... 2.68
2 two hatchback rwd front 94.5 ... 3.47
3 four sedan fwd front 99.8 ... 3.40
4 four sedan 4wd front 99.4 ... 3.40
.. ... ... ... ... ... ... ...
200 four sedan rwd front 109.1 ... 3.15
201 four sedan rwd front 109.1 ... 3.15
202 four sedan rwd front 109.1 ... 2.87
203 four sedan rwd front 109.1 ... 3.40
204 four sedan rwd front 109.1 ... 3.15
compressionratio horsepower peakrpm citympg highwaympg price \
0 9.0 111 5000 21 27 13495.0
1 9.0 111 5000 21 27 16500.0
2 9.0 154 5000 19 26 16500.0
3 10.0 102 5500 24 30 13950.0
4 8.0 115 5500 18 22 17450.0
.. ... ... ... ... ... ...
200 9.5 114 5400 23 28 16845.0
201 8.7 160 5300 19 25 19045.0
202 8.8 134 5500 18 23 21485.0
203 23.0 106 4800 26 27 22470.0
204 9.5 114 5400 19 25 22625.0
cluster city_mpg1 new_price
0 2 0.222222 0.207959
1 2 0.222222 0.282558
2 2 0.166667 0.282558
3 2 0.305556 0.219254
4 2 0.138889 0.306142
.. ... ... ...
200 2 0.277778 0.291123
201 2 0.166667 0.345738
202 2 0.138889 0.406311
203 2 0.361111 0.430763
204 2 0.166667 0.434611
[205 rows x 29 columns]
km=KMeans(n_clusters=3)
print(km)
KMeans(n_clusters=3)
y_new=km.fit_predict(df[["city_mpg1","new_price"]])
df["cluster_minmax"]=y_new
print(df)
car_ID symboling CarName fueltype aspiration \
0 1 3 alfa-romero giulia gas std
1 2 3 alfa-romero stelvio gas std
2 3 1 alfa-romero Quadrifoglio gas std
3 4 2 audi 100 ls gas std
4 5 2 audi 100ls gas std
.. ... ... ... ... ...
200 201 -1 volvo 145e (sw) gas std
201 202 -1 volvo 144ea gas turbo
202 203 -1 volvo 244dl gas std
203 204 -1 volvo 246 diesel turbo
204 205 -1 volvo 264gl gas turbo
doornumber carbody drivewheel enginelocation wheelbase ... \
0 two convertible rwd front 88.6 ...
1 two convertible rwd front 88.6 ...
2 two hatchback rwd front 94.5 ...
3 four sedan fwd front 99.8 ...
4 four sedan 4wd front 99.4 ...
.. ... ... ... ... ... ...
200 four sedan rwd front 109.1 ...
201 four sedan rwd front 109.1 ...
202 four sedan rwd front 109.1 ...
203 four sedan rwd front 109.1 ...
204 four sedan rwd front 109.1 ...
compressionratio horsepower peakrpm citympg highwaympg price \
0 9.0 111 5000 21 27 13495.0
1 9.0 111 5000 21 27 16500.0
2 9.0 154 5000 19 26 16500.0
3 10.0 102 5500 24 30 13950.0
4 8.0 115 5500 18 22 17450.0
.. ... ... ... ... ... ...
200 9.5 114 5400 23 28 16845.0
201 8.7 160 5300 19 25 19045.0
202 8.8 134 5500 18 23 21485.0
203 23.0 106 4800 26 27 22470.0
204 9.5 114 5400 19 25 22625.0
cluster city_mpg1 new_price cluster_minmax
0 2 0.222222 0.207959 0
1 2 0.222222 0.282558 0
2 2 0.166667 0.282558 0
3 2 0.305556 0.219254 0
4 2 0.138889 0.306142 0
.. ... ... ... ...
200 2 0.277778 0.291123 0
201 2 0.166667 0.345738 0
202 2 0.138889 0.406311 0
203 2 0.361111 0.430763 0
204 2 0.166667 0.434611 0
[205 rows x 30 columns]
df0=df[df.cluster_minmax==0]
df1=df[df.cluster_minmax==1]
df2=df[df.cluster_minmax==2]
plt.scatter(df0.city_mpg1,df0["price"],color="red")
plt.scatter(df1.city_mpg1,df1["price"],color="blue")
plt.scatter(df2.city_mpg1,df2["price"],color="green")
print(km.cluster_centers_)
print(km.algorithm)
plt.scatter(km.cluster_centers_[:,0],km.cluster_centers_[:,1],color="purple",marker="*")
plt.legend()
plt.show()
[[4.25736961e-01 8.44108163e+03] [1.58730159e-01 3.07089286e+04] [2.09104938e-01 1.72513380e+04] [4.62962963e-02 4.25583333e+04] [2.30676329e-01 1.35170435e+04] [2.03703704e-01 2.27405556e+04] [7.14285714e-02 3.55322857e+04] [5.41343669e-01 6.49518605e+03] [3.22420635e-01 1.07446786e+04]] auto
# elbow curve
k_range =range(1,10)
sse=[]
for k in k_range:
km=KMeans(n_clusters=k)
km.fit(df[["city_mpg1","price"]])
sse.append(km.inertia_)
print(sse)
plt.plot(k_range,sse)
plt.show()
[13019639368.730158, 4066798748.743803, 1341589671.6069074, 874350217.9278326, 592651809.056312, 421922997.9901843, 297527096.07242996, 223270865.44694558, 174100038.8407037]
In [42]:
import seaborn as sns
sns.regplot(x="city_mpg1", y="price", data=df)
plt.show()
