Lecture 53:- K-Means Algo 2 Elbow Method

The Elbow Method is a technique used to determine the optimal number of clusters (K) for a K-Means clustering algorithm. It involves running K-Means on the dataset for a range of K values and plotting the sum of squared distances (inertia) between data points and their assigned centroids. The "elbow" point on the plot is where the inertia starts to decrease at a slower rate, indicating a suitable number of clusters.

Here's how you can use the Elbow Method to find the optimal K value:

1. Run K-Means: Run K-Means clustering for a range of K values, typically from 1 to a certain upper limit. For each K value, calculate the sum of squared distances (inertia) between data points and their assigned centroids.

2. Plot Inertia: Plot the calculated inertia values against the corresponding K values. The plot will often resemble an "elbow," and the point where the inertia starts to decrease at a slower rate is the suggested optimal K value.

3. Select K: Based on the plot, choose the K value where the inertia flattens out. This point represents a good trade-off between minimizing the inertia (within-cluster sum of squares) and preventing overfitting (too many clusters).

Here's a Python code example using the Elbow Method to determine the optimal number of clusters for K-Means using the scikit-learn library:

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import numpy as np from sklearn.datasets import make_blobs from sklearn.cluster import KMeans import matplotlib.pyplot as plt # Generate synthetic data data, _ = make_blobs(n_samples=300, centers=4, random_state=42) # Calculate inertia for a range of K values inertia_values = [] for k in range(1, 11): model = KMeans(n_clusters=k, random_state=42) model.fit(data) inertia_values.append(model.inertia_) # Plot the Elbow Method graph plt.plot(range(1, 11), inertia_values, marker='o') plt.xlabel('Number of Clusters (K)') plt.ylabel('Inertia') plt.title('Elbow Method for Optimal K') plt.xticks(np.arange(1, 11)) plt.show()

In this code, we generate synthetic data using make_blobs, calculate the inertia values for K values ranging from 1 to 10, and then plot the Elbow Method graph. The optimal K value is often where the curve starts to flatten out, resembling an "elbow."

Remember that the Elbow Method is a heuristic, and there might not always be a clear elbow point. In some cases, domain knowledge and other evaluation methods (e.g., silhouette score) might be needed to confirm the optimal number of clusters.