Final answer:
The correct answer is option 4) All of the above, indicating that the K-means algorithm can stop if centroids stabilize, a maximum number of iterations is reached, or the sum of squared distances falls below a threshold.
Step-by-step explanation:
The correct answer is option 4) All of the above. The K-means algorithm, a popular clustering method used in data mining and machine learning, may terminate for several reasons. Firstly, the algorithm stops when the centroids of the clusters do not change between subsequent iterations, indicating that the clusters have stabilized. Secondly, K-means may halt when a pre-specified maximum number of iterations is reached, which prevents the algorithm from running indefinitely. Finally, the algorithm can also terminate when the sum of squared distances between data points and their assigned centroids drops below a certain threshold, suggesting that further movement of the centroids will not significantly improve the clustering. These conditions ensure that the algorithm concludes in a reasonable timeframe and with a satisfactory solution.
The K-means algorithm may use various termination conditions to stop iterations and converge to a solution. These include:
When the centroids do not change between iterations: If the positions of the centroids remain unchanged after an iteration, it implies that the algorithm has found the optimal solution.
When a maximum number of iterations is reached: The algorithm may terminate after a predefined number of iterations to prevent it from running indefinitely.
When the sum of squared distances between data points and their assigned centroids is below a threshold: If the distance between each data point and its assigned centroid falls below a certain threshold, the algorithm may terminate as it indicates a good clustering solution.
By using these termination conditions, the K-means algorithm can efficiently find clusters in a given dataset.