Elbow method is a technique used to find the best number of clusters in a K-means clustering algorithm. K-means is a method that groups data points into clusters. The elbow method helps you find the suitable value of k by examining how the within-cluster sum of squares changes as k increases.
To apply the elbow method in K-means clustering, follow these steps:
1. Select a range of possible values for the number of clusters you want to find, such as k values from 1 to a certain maximum number.
2. Run the K-means algorithm for each value of k in the chosen range.
3. Calculate the WCSS for each k, which is the sum of squared distances between data points and their assigned cluster centroids using the formula: WCSS(k) = Σ(Σ(||x – μ||^2)).
4. Create a plot with k on the x-axis and the corresponding WCSS on the y-axis.
5. Look for a point on the plot where the rate of decrease in WCSS starts to slow down. This point is called the “elbow” point.
6. Based on the elbow point in the plot, choose the best value of k for your K-means clustering. The elbow point is where the WCSS starts to level off, indicating that it’s a good compromise between having too few or too many clusters. Remember, the optimal k value is subjective and may require some domain knowledge or interpretation. The elbow method provides a useful heuristic, but it’s not always clear-cut, especially if the data doesn’t have a clear elbow in the WCSS plot. In those cases, we may need to use other evaluation metrics or techniques, such as silhouette analysis, to find the best value of k for your specific problem.
Silhouette analysis is a method of examining how well a clustering algorithm, like K-means, groups data points. It measures the distance between each data point and its own cluster, as well as the distance to neighboring clusters. A higher score means that the clusters are well-defined and separate from each other, while a lower or negative score indicates that the clustering may not be optimal. Silhouette analysis can be used to evaluate the quality of clustering without relying on a specific example. It is a useful tool to assess whether the clusters created are meaningful and distinct.