K Means Clustering Algorithm | K Means Solved Numerical Example Euclidean Distance by Mahesh Huddar

Summary

This video explains how to apply the K-means clustering algorithm to divide a dataset into clusters using the Euclidean distance. The provided data points are assigned to clusters based on the distance from given initial centroids. The video walks through the process of calculating distances, assigning points to clusters, updating centroids, and repeating the steps until convergence is achieved. The example involves recalculating centroids and reassigning points until a stable clustering result is reached. It's a practical demonstration of K-means with detailed step-by-step explanations.

Takeaways

• 📊 The video explains how to use the k-means clustering algorithm to divide a given dataset into clusters.
• 📌 Eight data points (A1, A2, A3, B1, B2, B3, C1, and C2) are provided, with A1, B1, and C1 as initial centroids.
• 🔍 The Euclidean distance formula is used to calculate the distance between data points and centroids.
• 📏 Step-by-step calculations show how to measure distances between data points (like A1 and centroid A1) and other centroids.
• 🧮 Data points are assigned to clusters based on the smallest calculated distance to the centroids.
• 🔄 After the first iteration, new centroids are calculated based on the average positions of assigned data points.
• 🚨 The process repeats by recalculating distances to the updated centroids and reassigning data points.
• 🔁 Iterations continue until data points converge and no longer change clusters, indicating a stable solution.
• 📝 The final clusters are listed, with each data point assigned to its respective cluster after convergence.
• ✅ The process demonstrates how k-means clustering works, including centroid updates and cluster reassignment based on the smallest distances.

Q & A

What is the main topic discussed in the video?

The video discusses how to use the K-means clustering algorithm to divide a given dataset into different clusters using the Euclidean distance.

What data points are provided in the example for clustering?

The data points provided are A1, A2, A3, B1, B2, B3, C1, and C2.

What are the initial centroids in the clustering example?

The initial centroids given in the example are A1, B1, and C1.

What is the formula used to calculate the distance between data points and centroids?

The Euclidean distance formula is used: √((x2 - x1)^2 + (y2 - y1)^2).

How is the assignment of data points to clusters determined?

Data points are assigned to clusters based on the smallest distance between the data point and the centroids of the clusters.

What happens after the initial cluster assignments are made?

After the initial cluster assignments, new centroids are calculated by averaging the coordinates of the data points in each cluster.

How are new centroids calculated after the first iteration?

The new centroids are calculated by taking the average of the x and y coordinates of all data points in each cluster.

What does it mean when a data point moves from one cluster to another during the iterations?

It means the data point is now closer to the centroid of a different cluster, indicating the clusters have not yet converged.

How is convergence determined in K-means clustering?

Convergence is determined when the cluster assignments stop changing after multiple iterations.

What is the final result after applying the K-means algorithm in the example?

The final result is that the data points are grouped into stable clusters, with A1, B1, and C2 in the first cluster; A2 and C1 in the third cluster; and A3, B2, and B3 in the second cluster.