In this plot, you will quickly learn about how to **find** **elbow point **using** SSE or Inertia plot **with **Python **code and ** **You may want to check out my blog on K-means clustering explained with Python example. The following topics get covered in this post:

- What is Elbow Method?
- How to create SSE / Inertia plot?
- How to find Elbow point using SSE Plot

Table of Contents

## What is Elbow Method?

Elbow method is one of the most popular method used to **select the optimal number of clusters** by fitting the model with a range of values for K in K-means algorithm. Elbow method requires drawing a line plot between SSE (Sum of Squared errors) vs number of clusters and finding the point representing the “**elbow point**” (the point after which the SSE or inertia starts decreasing in a linear fashion). Here is the sample elbow point. In the later sections, it is illustrated as to how to draw the line plot and find elbow point.

## How to Draw SSE / Inertia Plot

In order to find elbow point, you will need to draw SSE or inertia plot. In this section, you will see a custom Python function, **drawSSEPlotForKMeans,** which can be used to create the SSE (**Sum of Squared Error**) or Inertia plot representing SSE value on Y-axis and Number of clusters on X-axis. SSE is also called within-cluster SSE plot. Pay attention to some of the following function parameters which need to be passed to the method, **drawSSEPlotForKMeans**

**df**: Pandas dataframe consisting of the data**column_indice**s: Column indices representing the features in the dataframe.**n_clusters**(default as 8): Number of clusters**init**(default as k-means++): Represents method for initialization. The default value of**k-means++**represents the selection of the initial cluster centers (centroids) in a smart manner to speed up the convergence. The other values of init can be**random**, which represents the selection of n_clusters observations at random from data for the initial centroids.**n_init**(default as 10): Represents the number of time the k-means algorithm will be run independently, with different random centroids in order to choose the final model as the one with the lowest SSE.**max_iter**(default as 300): Represents the maximum number of iterations for each run. The iteration stops after the maximum number of**iterations**is reached even if the convergence criterion is not satisfied. This number must be between 1 and 999. In this paper (Scalable K-Means by ranked retrieval), the authors stated that K-means converges after 20-50 iterations in all practical situations, even on high dimensional datasets as they tested.**tol**(default as 1e-04): Tolerance value is used to check if the error is greater than the**tolerance**value. For error greater than tolerance value, K-means algorithm is run until the error falls below the**tolerance**value which implies that the algorithm has converged.**algorithm**(default as auto): Represents the type of K-means algorithm to use. The different values that algorithm can take is**auto**,**full**and**elkan.**The classical EM-style algorithm is**full**. The**elkan**variation is more efficient on data with well-defined clusters

```
def drawSSEPlot(df, column_indices, n_clusters=8, max_iter=300, tol=1e-04, init='k-means++', n_init=10, algorithm='auto'):
import matplotlib.pyplot as plt
inertia_values = []
for i in range(1, n_clusters+1):
km = KMeans(n_clusters=i, max_iter=max_iter, tol=tol, init=init, n_init=n_init, random_state=1, algorithm=algorithm)
km.fit_predict(df.iloc[:, column_indices])
inertia_values.append(km.inertia_)
fig, ax = plt.subplots(figsize=(8, 6))
plt.plot(range(1, n_clusters+1), inertia_values, color='red')
plt.xlabel('No. of Clusters', fontsize=15)
plt.ylabel('SSE / Inertia', fontsize=15)
plt.title('SSE / Inertia vs No. Of Clusters', fontsize=15)
plt.grid()
plt.show()
```

The following illustrates how the above function can be invoked to draw **SSE or inertia plot**. The Sklearn IRIS dataset is used for illustration purpose.

```
import pandas as pd
from sklearn.cluster import KMeans
from sklearn import datasets
iris = datasets.load_iris()
X = iris.data
y = iris.target
df = pd.DataFrame(X)
df.columns = ['sepal_length', 'sepal_width', 'petal_length', 'petal_width']
df['target'] = y
```

Here is the code representing how SSE / inertia plot will be invoked:

```
drawSSEPlotForKMeans(df, [0, 1, 2, 3])
```

Here is how the inertia / SSE plot would look like:

## How to find Elbow point using SSE Plot

The elbow point represents the point in the SSE / Inertia plot where SSE or inertia starts decreasing in a linear manner. In the fig 2, you may note that it is no. of clusters = 3 where the SSE starts decreasing in the linear manner.

## Conclusions

Here is the summary of what you learned in this post related to **finding elbow point **using **elbow method **which includes drawing **SSE / Inertia **plot:

**Elbow method**is used to**determine the most optimal value of K**representing number of clusters in K-means clustering algorithm.- Elbow method requires drawing a
**line plot**between**SSE**(Within-clusters Sum of Squared errors) vs number of clusters. - In the line plot, the point at this the SSE or inertia values start decreasing in a linear manner is called as
**elbow point.**

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