What is Elbow Point?

The Elbow method is a heuristic used in determining the optimal number of clusters (k) for k-means clustering. It involves plotting the within-cluster sum of squares (WCSS) against the number of clusters (k).   

How it Works:

Calculate WCSS for Different Values of k:

For various values of k (e.g., k = 1, 2, 3, ...), run the k-means algorithm.   

For each k, calculate the WCSS, which is the sum of the squared distances between each point and its assigned cluster's centroid.   

Plot WCSS vs. k:

Create a line plot with the number of clusters (k) on the x-axis and the WCSS on the y-axis.   

Identify the "Elbow" Point:

Look for the "elbow" point in the plot. This is the point where the rate of decrease in WCSS sharply changes.   

The elbow point represents a good trade-off between minimizing WCSS and not having too many clusters.

Why it Works:

As k increases:

The WCSS generally decreases because points are assigned to closer clusters.   

When k equals the number of data points, WCSS becomes zero because each point forms its own cluster.

The "Elbow":

The "elbow" point indicates a point of diminishing returns. After this point, increasing k doesn't significantly reduce WCSS.   

In summary:

The Elbow method plots the within-cluster sum of squares (WCSS) against different values of k to help determine the optimal number of clusters for k-means. The "elbow" in the plot is used as a visual indicator of the best k value.