In K-means clustering, what happens if the initial centroids are poorly chosen?

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Question: In K-means clustering, what happens if the initial centroids are poorly chosen?

Options:

Correct Answer: The algorithm may converge to a local minimum

Solution:

Poorly chosen initial centroids can lead K-means to converge to a local minimum rather than the global minimum, resulting in suboptimal clustering.

In K-means clustering, what happens if the initial centroids are poorly chosen?

In K-means clustering, what happens if the initial centroids are poorly chosen?

Step 1: K-means clustering starts by selecting initial points called centroids, which represent the center of clusters.
Step 2: If these initial centroids are not chosen well, they may not represent the actual data distribution.
Step 3: Poor initial centroids can cause the algorithm to group data points incorrectly.
Step 4: As the algorithm runs, it will adjust the centroids based on the assigned data points.
Step 5: If the centroids start in a bad position, the algorithm may settle into a local minimum, meaning it finds a solution that is not the best possible one.
Step 6: This results in clusters that do not accurately reflect the true structure of the data.

K-means Clustering – A method of partitioning data into clusters based on distance to centroids.
Initial Centroids – The starting points for the clusters that can significantly affect the outcome of the clustering process.
Local vs Global Minimum – The difference between a suboptimal solution (local minimum) and the best possible solution (global minimum) in optimization problems.