The Elbow Method involves plotting the explained variance as a function of the number of clusters and picking the elbow of the curve as the number of clusters to use. This elbow point is considered to be a point after which diminishing returns are observed, indicating that increasing the number of clusters does not provide much better modeling of the data.
**Implementation Steps:**
- Run k-means clustering on the dataset for a range of values of k (e.g., 1 to 10).
- For each value of k, calculate the sum of squared errors (SSE) within clusters.
- Plot k against the SSE. The “elbow” in this plot, where the rate of decrease sharply changes, can be considered as indicating the appropriate number of clusters.
**Implementing in Python**
Here's a simplistic implementation of the Elbow Method using scikit-learn, which is a common library for k-means in Python:
```python
from sklearn.cluster import KMeans
import matplotlib.pyplot as plt
# Assuming X is your matrix of features
sse = []
list_k = list(range(1, 10))
for k in list_k:
km = KMeans(n_clusters=k)
km.fit(X)
sse.append(km.inertia_)
# Plot sse against k
plt.figure(figsize=(6, 6))
plt.plot(list_k, sse, '-o')
plt.xlabel('Number of clusters k')
plt.ylabel('Sum of squared distances')
plt.title('Elbow Method For Optimal k')
plt.show()
```