Clustering is an unsupervised machine-learning technique. It is the process of division of the dataset into groups in which the members in the same group possess similarities in features. The commonly used clustering techniques are K-Means clustering, Hierarchical clustering, Density-based clustering, Model-based clustering, etc. It can even handle large datasets. We can implement the K-Means clustering machine learning algorithm in the elbow method using the scikit-learn library in Python.

The Elbow Method is a technique used in data analysis and machine learning for determining the optimal number of clusters in a dataset. It involves plotting the variance explained by different numbers of clusters and identifying the “elbow” point, where the rate of variance decreases sharply levels off, suggesting an appropriate cluster count for analysis or model training.

- Understand the K-Means algorithm.
- Understand and Implement K-Means Clustering Elbow Method.

*This article was published as a part of the Data Science Blogathon.*

Quiz Time

Are you up for a challenge in the realm of the Elbow Method for Finding the Optimal Number of Clusters in K-Means? Challenge yourself here!

The **elbow method is a graphical representation of finding the optimal ‘K’ **in a K-means clustering. It works by finding WCSS (Within-Cluster Sum of Square) i.e. the sum of the square distance between points in a cluster and the cluster centroid.

Let’s go through the steps involved in K-means clustering for a better understanding:

- Select the number of clusters for the dataset (K)
- Select the K number of centroids randomly from the dataset.
- Now we will use Euclidean distance or Manhattan distance as the metric to calculate the distance of the points from the nearest centroid and assign the points to that nearest cluster centroid, thus creating K clusters.
- Now we find the new centroid of the clusters thus formed.
- Again reassign the whole data point based on this new centroid, then repeat step 4. We will continue this for a given number of iterations until the position of the centroid doesn’t change, i.e., there is no more convergence.

Finding the optimal number of clusters is an important part of this algorithm. A commonly used method for finding the optimum K value is** Elbow Method. **

In the Elbow method, we are actually varying the number of clusters (K) from 1 – 10. For each value of K, we are calculating WCSS (Within-Cluster Sum of Square). WCSS is the sum of the squared distance between each point and the centroid in a cluster. When we plot the WCSS with the K value, the plot looks like an Elbow. As the number of clusters increases, the WCSS value will start to decrease. WCSS value is largest when K = 1. When we analyze the graph, we can see that the graph will rapidly change at a point and thus creating an elbow shape. From this point, the graph moves almost parallel to the X-axis. The K value corresponding to this point is the optimal value of K or an optimal number of clusters.

Now let’s implement K-Means clustering using Python.

The dataset we are using here is the Mall Customers data (Download here). It’s unlabeled data that contains the details of customers in a mall (features like genre, age, annual income(k$), and spending score). Our aim is to cluster the customers based on the relevant features of annual income and spending score.

First of all, we have to import the essential libraries.

```
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import sklearn
```

Now let’s import the given dataset and slice the important features.

```
dataset = pd.read_csv('Mall_Customers.csv')
X = dataset.iloc[:, [3, 4]].values
```

We have to find the optimal K value for clustering the data. Now we are using the Elbow Method to find the optimal K value.

```
from sklearn.cluster import KMeans
wcss = [] for i in range(1, 11):
kmeans = KMeans(n_clusters = i, init = 'k-means++', random_state = 42)
kmeans.fit(X)
wcss.append(kmeans.inertia_)
```

The “init” argument is the method for initializing the centroid. We calculated the WCSS value for each K value. Now we have to plot the WCSS with the K value.

**Python Code:**

The graph will be like this:

The point at which the elbow shape is created is 5; that is, our K value or an optimal number of clusters is 5. Now let’s train the model on the input data with a number of clusters 5.

```
kmeans = KMeans(n_clusters = 5, init = "k-means++", random_state = 42)
y_kmeans = kmeans.fit_predict(X)
```

y_kmeans will be:

```
array([3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0,
3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 1,
3, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 2, 1, 2, 4, 2, 4, 2,
1, 2, 4, 2, 4, 2, 4, 2, 4, 2, 1, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2,
4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2,
4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2,
4, 2])
```

y_kmeans gives us different clusters corresponding to X. Now, let’s plot all the clusters using matplotlib.

```
plt.scatter(X[y_kmeans == 0, 0], X[y_kmeans == 0, 1], s = 60, c = 'red', label = 'Cluster1')
plt.scatter(X[y_kmeans == 1, 0], X[y_kmeans == 1, 1], s = 60, c = 'blue', label = 'Cluster2')
plt.scatter(X[y_kmeans == 2, 0], X[y_kmeans == 2, 1], s = 60, c = 'green', label = 'Cluster3)
plt.scatter(X[y_kmeans == 3, 0], X[y_kmeans == 3, 1], s = 60, c = 'violet', label = 'Cluster4')
plt.scatter(X[y_kmeans == 4, 0], X[y_kmeans == 4, 1], s = 60, c = 'yellow', label = 'Cluster5')
plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s = 100, c = 'black', label = 'Centroids')
plt.xlabel('Annual Income (k$)') plt.ylabel('Spending Score (1-100)') plt.legend()
plt.show()
```

Graph:

Now we will visualize the clusters using the scatter plot. As you can see, there are 5 clusters in total that are visualized in different colors, and the centroid of each cluster is visualized in black color.

```
# Importing the libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd # Importing the dataset
X = dataset.iloc[:, [3, 4]].values
dataset = pd.read_csv('Mall_Customers.csv')
from sklearn.cluster import KMeans
# Using the elbow method to find the optimal number of clusters wcss = [] for i in range(1, 11):
wcss.append(kmeans.inertia_)
kmeans = KMeans(n_clusters = i, init = 'k-means++', random_state = 42) kmeans.fit(X) plt.plot(range(1, 11), wcss) plt.xlabel('Number of clusters')
y_kmeans = kmeans.fit_predict(X)
plt.ylabel('WCSS') plt.show() # Training the K-Means model on the dataset kmeans = KMeans(n_clusters = 5, init = 'k-means++', random_state = 42) y_kmeans = kmeans.fit_predict(X)
# Visualising the clusters
plt.scatter( X[y_kmeans == 1, 0], X[y_kmeans == 1, 1], s = 60, c = 'blue', label = 'Cluster2')
plt.scatter( X[y_kmeans == 0, 0], X[y_kmeans == 0, 1], s = 60, c = 'red', label = 'Cluster1') plt.scatter( X[y_kmeans == 2, 0], X[y_kmeans == 2, 1], s = 60, c = 'green', label = 'Cluster3')
plt.scatter( kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s = 100, c = 'black', label = 'Centroids')
plt.scatter( X[y_kmeans == 3, 0], X[y_kmeans == 3, 1], s = 60, c = 'violet', label = 'Cluster4') plt.scatter( X[y_kmeans == 4, 0], X[y_kmeans == 4, 1], s = 60, c = 'yellow', label = 'Cluster5') plt.xlabel('Annual Income (k$)') plt.ylabel('Spending Score (1-100)') plt.legend()
plt.show()
```

The elbow method, while a useful tool for determining the optimal number of clusters in K-means clustering, has some drawbacks:

- Subjectivity: The choice of the “elbow point” can be subjective and might vary between individuals analyzing the same data.
- Non-Gaussian Data: It assumes that clusters are spherical and equally sized, which may not hold for complex datasets with irregularly shaped or differently sized clusters.
- Sensitivity to Initialization: K-means itself is sensitive to initial cluster centroids, which can affect the WCSS values and, consequently, the choice of the optimal K.
- Inefficient for Large Datasets: For large datasets, calculating WCSS for a range of K values can be computationally expensive and time-consuming.
- Unsuitable for All Distributions: The elbow method is not suitable for all data distributions, especially when clusters have varying densities or are non-convex.
- Limited to K-means: It specifically applies to K-means clustering and may not be suitable for other clustering algorithms with different objectives.

Despite these drawbacks, the elbow method remains a valuable starting point for selecting the number of clusters, and it often provides useful insights into the data’s underlying structure. However, it’s essential to complement it with other validation techniques when working with more complex datasets or different clustering algorithms.

In this article, we covered the basic concepts of the K-Means Clustering algorithm in Machine Learning. We used the Elbow method to find the optimal K value for clustering the data in our sample data set. We then used the matplotlib Python library to visualize the clusters as a scatterplot graph. In the upcoming articles, we can learn more about different ML Algorithms.

**Key Takeaways**

- K-Means is a popular unsupervised machine-learning algorithm widely used by Data Scientists on unlabeled data.
- The k-Means Elbow method is used to find the optimal value of the K in the K-Means algorithm.

A. The elbow method is a technique used in clustering analysis to determine the optimal number of clusters. It involves plotting the within-cluster sum of squares (WCSS) for different cluster numbers and identifying the “elbow” point where WCSS starts to level off.

A. The elbow method is a clustering validation technique. It helps find the optimal number of clusters by plotting WCSS for a range of cluster counts and selecting the point where the plot forms an “elbow” or a significant change in the rate of decrease.

A. The elbow method calculates the WCSS for different numbers of clusters in a K-means clustering algorithm. It assesses the trade-off between reducing WCSS by increasing clusters and simplicity.

A. It’s a valuable technique in machine learning for selecting the appropriate number of clusters in various applications.

*The media shown in this article are not owned by Analytics Vidhya and is used at the Author’s discretion.*

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Understanding Cost Function
Understanding Gradient Descent
Math Behind Gradient Descent
Assumptions of Linear Regression
Implement Linear Regression from Scratch
Train Linear Regression in Python
Implementing Linear Regression in R
Diagnosing Residual Plots in Linear Regression Models
Generalized Linear Models
Introduction to Logistic Regression
Odds Ratio
Implementing Logistic Regression from Scratch
Introduction to Scikit-learn in Python
Train Logistic Regression in python
Multiclass using Logistic Regression
How to use Multinomial and Ordinal Logistic Regression in R ?
Challenges with Linear Regression
Introduction to Regularisation
Implementing Regularisation
Ridge Regression
Lasso Regression

Introduction to Stacking
Implementing Stacking
Variants of Stacking
Implementing Variants of Stacking
Introduction to Blending
Bootstrap Sampling
Introduction to Random Sampling
Hyper-parameters of Random Forest
Implementing Random Forest
Out-of-Bag (OOB) Score in the Random Forest
IPL Team Win Prediction Project Using Machine Learning
Introduction to Boosting
Gradient Boosting Algorithm
Math behind GBM
Implementing GBM in python
Regularized Greedy Forests
Extreme Gradient Boosting
Implementing XGBM in python
Tuning Hyperparameters of XGBoost in Python
Implement XGBM in R/H2O
Adaptive Boosting
Implementing Adaptive Boosing
LightGBM
Implementing LightGBM in Python
Catboost
Implementing Catboost in Python

Introduction to Clustering
Applications of Clustering
Evaluation Metrics for Clustering
Understanding K-Means
Implementation of K-Means in Python
Implementation of K-Means in R
Choosing Right Value for K
Profiling Market Segments using K-Means Clustering
Hierarchical Clustering
Implementation of Hierarchial Clustering
DBSCAN
Defining Similarity between clusters
Build Better and Accurate Clusters with Gaussian Mixture Models

Introduction to Machine Learning Interpretability
Framework and Interpretable Models
model Agnostic Methods for Interpretability
Implementing Interpretable Model
Understanding SHAP
Out-of-Core ML
Introduction to Interpretable Machine Learning Models
Model Agnostic Methods for Interpretability
Game Theory & Shapley Values

Deploying Machine Learning Model using Streamlit
Deploying ML Models in Docker
Deploy Using Streamlit
Deploy on Heroku
Deploy Using Netlify
Introduction to Amazon Sagemaker
Setting up Amazon SageMaker
Using SageMaker Endpoint to Generate Inference
Deploy on Microsoft Azure Cloud
Introduction to Flask for Model
Deploying ML model using Flask