What is the time complexity of the K-means algorithm?

What is the time complexity of the K-means algorithm?

Step 1: Understand that K-means is an algorithm used to group data points into clusters.
Step 2: Identify the two main factors that affect the time it takes to run K-means: the number of data points (n) and the number of clusters (k).
Step 3: Realize that for each iteration of the K-means algorithm, we need to assign each data point to the nearest cluster center.
Step 4: This assignment step requires checking each of the n data points against each of the k clusters.
Step 5: Therefore, the time taken for this assignment step is O(nk).
Step 6: Note that K-means typically runs for multiple iterations until convergence, but the dominant factor in time complexity remains O(nk).
Step 7: Conclude that the overall time complexity of the K-means algorithm is O(nk).

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