K-Means ++ Algorithm

 K-Means++ is an improvement over the traditional K-Means clustering algorithm for

initializing the centroids. The K-Means++ algorithm ensures a better initial set of centroids,

resulting in improved clustering performance.

Here are the steps of the K-Means++ algorithm:

1. Choose the first centroid randomly from the data points.

2. For each data point, compute its distance to the nearest centroid that has already been chosen.

3. Choose the next centroid from the data points with probability proportional to the square of the distance to the nearest centroid. This means that points that are further away from already selected centroids are more likely to be chosen as the next centroid.

4. Repeat step 3 until all K centroids have been chosen.

5. Once the centroids have been initialized using K-Means++, proceed with the regular K-Means algorithm, i.e., assigning data points to the nearest centroid and updating the centroids until convergence.

The K-Means++ algorithm helps to avoid the problem of initializing centroids close together, which can result in poor clustering performance. By selecting initial centroids that are more spread out, K-Means++ can often achieve better clustering results than traditional K-Means.

We have used the K-Means++ clustering algorithm in our assignment for a better initial set of centroids.