Understanding K – Means Clustering WIth Customer Segmentation Usecase

6. Euclidean Distance Formula

#Modelling
# Creating a variable X1 and assigning the values to it.
X1 = df.values

Importing KMeans from Sklearn.
To find the best value for “K” Clusters, we run it in a “for” loop

from sklearn.cluster import KMeans   #Importing KMeans from sklearn and
k_inertia = []                       # Creating a list to store the kmeans.inertia_
for k in range(1,11):
    kmeans = KMeans(n_clusters=k, init='k-means++')
    kmeans.fit(X1)
    k_inertia.append(kmeans.inertia_)

Visualizing from the Graph to find the “K Value” where the change in the  K-Means Inertia is negligible and that is the point where the curve shoots up.

K_means inertia is the measurement of how well the clusters have formed by calculating the distance between the Cluster Centroid and the data points in that cluster.

plt.figure(figsize=(12,6))

plt.grid()

plt.plot(range(1,11),k_inertia,linewidth = 2, color = "red", marker = "8")

plt.xlabel('K Values')

plt.ylabel("K_Inertia")

plt.show()

Taking the value of K as 2 that is k = 2 we will fit “kmeans” to the data stored in the Variable X1

kmeans = kmeans(n_clusters=2)

label = kmeans.fit_predict(X1)
print(label)  # To read the cordinates or values of the Cluster Centroids

The below code gives the coordinates of the Cluster centres.

print(kmeans.cluster_centers_)  # To plot the visualize the Data Points and the Cluster Centroids.

The scatter plot from matplotlib plots the points. Along the x-axis is the distance and the y-axis has the cost.

plt.scatter(X1[:,0], X1[:,1], c=kmeans.labels_, cmap='rainbow')
plt.scatter(kmeans.cluster_centers_[:,0] ,kmeans.cluster_centers_[:,1], color = 'black')
plt.title('K-Means')
plt.xlabel('Distance')
plt.ylabel('Cost') 
plt.show()

In the above Scatter plot, the Black Dots represents the Centroid and the Purple coloured and Red Colored represents Data Points.

Using the above understanding we will implement K-means for customer segmentation to identify the clusters based on “Age” and “Spending Score”

Steps 

Importing Libraries

# Importing Libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline

Reading its head that is the top 5 rows and its shape that is, it has 200 rows and 5 Columns. The Data has the following columns: “Customer ID”, “Gender”, “Age”, “Annual Income(k$)”, “Spending Score(1-100)”

df = pd.read_csv("Clustering.csv")

df.head()

To check the number of columns and rows

df.shape

The data frame has 200 rows and 5 columns.

To check for the missing Values

df.isnull().sum()

To check the data types

df.dtypes

The data type for the following column’s “Customer ID”, “Age”, “Annual Income (k$)” and “Spending Score (1-100)” is an int and for the column “Age” it is an Object.

Dropping the customer ID column as it is not required and checking the Head.

df.drop(['CustomerID'],axis=1, inplace=True) 

df.head()

The “Customer ID” column has been dropped.

Categorizing the customers based on Age and have divided into 5 groups.

age_18_25 = df['Age'][(df.Age >=18) & (df.Age <= 25)]
age_26_35 = df.Age[(df.Age >=26) & (df.Age <= 35)]
age_36_45 = df.Age[(df.Age >=36) & (df.Age <= 45)]
age_46_55 = df.Age[(df.Age >=46) & (df.Age <= 55)]
age_55above = df.Age[df.Age >=56]

On the x-axis, the customer Age is presented and on the Y-axis number of customer’s are marked

agex = ["18-25","26-35","36-45","46-55","56+"]
agey = [len(age_18_25.values),len(age_26_35.values),len(age_36_45.values),len(age_46_55.values),len(age_55above.values)]

plt.figure(1, figsize=(15,6))                        # Plotting the Graph

sns.barplot(x=agex, y=agey, palette = 'mako')

plt.title('Number of Customer and Ages')

plt.xlabel('Age')

plt.ylabel('Number of Customer')

plt.show()

The same can be repeated for the “Spending score (1 – 100)” Column.

Modelling following the previous example (Segmentation based on ‘Age’ and ‘Spending Score’)
To start with modeling we will create a variable and assign the values from “Age” and “Spending Score (1-100)”  to it

X1 = df.loc[:,['Age','Spending Score (1-100)']].values

Importing KMeans from Sklearn.
To find the best value for “K” Clusters we are running it in a “for” loop

from sklearn.cluster import KMeans

age_ss = []

for k in range(1,8):

    kmeans = KMeans(n_clusters=k, init='k-means++')

    kmeans.fit(X1)

    age_ss.append(kmeans.inertia_)

Visualizing from the Graph to find the K Value where the change in the K-Means Inertia is negligible and that is the point where the curve shoots up.


plt.figure(figsize=(12,6))

plt.grid()

plt.plot(range(1,8),age_ss,linewidth = 2, color = "red", marker = "8")

plt.xlabel('K Values')

plt.ylabel("K_Inertia")

plt.show()

Assigning the value of clusters as 3 that is k = 3

kmeans = KMeans(n_clusters=3)

label = kmeans.fit_predict(X1)

Custer based on Age and Spending Score (Scatter Plot)


plt.scatter(X1[:,0], X1[:,1], c=kmeans.labels_, cmap='rainbow')

plt.scatter(kmeans.cluster_centers_[:,0] ,kmeans.cluster_centers_[:,1], color = 'black')

plt.title('Clusters Of Customers')

plt.xlabel('Age')

plt.ylabel('Spending Score(1-100)')

plt.show()

9. Conclusion