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I will assume that the plot shows the sum of within distances of k-means. That is the sum of distances of every point to their closest cluster center. The optimization of K-Means does not guarantee a global minimum. You are much more likely to find local minima. As you increase k you might be unlucky and find a bad one. You could use a smart initialization strategy like k-means++, or run k-means several times with random initalizations for the cluster centers for each k and pick the solution with lowest within cost.

The results of K-Means is dependent on the cluster initialization.

I will assume that the plot shows the sum of within distances of k-means. That is the sum of distances of every point to their closest cluster center. The optimization of K-Means does not guarantee a global minimum. You are much more likely to find local minima. As you increase k you might be unlucky and find a bad one. You could use a smart initialization strategy like k-means++, or run k-means several times with random initalizations for the cluster centers for each k and pick the solution with lowest within cost. Using a smart initialization strategy will also speed up the computations and make you converge to the solution faster.

The results of K-Means is dependent on the cluster initialization.

I will assume that the plot shows the sum of within distances of k-means. That is the sum of distances of every point to their closest cluster center. The optimization of K-Means does not guarantee a global minima. You are much more likely to find local minimas. As you increase k you might be unlucky and find a bad one. You could use a smart initialization strategy like k-means++, or run k-means several times with random initalizations for the cluster centers for each k and pick the solution with lowest within cost.

The results of K-Means is dependent on the cluster initialization.

I will assume that the plot shows the sum of within distances of k-means. That is the sum of distances of every point to their closest cluster center. The optimization of K-Means does not guarantee a global minimum. You are much more likely to find local minima. As you increase k you might be unlucky and find a bad one. You could use a smart initialization strategy like k-means++, or run k-means several times with random initalizations for the cluster centers for each k and pick the solution with lowest within cost.

The results of K-Means is dependent on the cluster initialization.

I will assume that the plot shows the sum of within distances of k-means. That is the sum of distances of every point to their closest cluster center. The optimization of K-Means does not guarantee a global minima. You are much more likely to find local minimas. As you increase k you might be unlucky and find a bad one. You could use a smart initialization strategy like k-means++, or run k-means several times with random initalizations for the cluster centers for each k and pick the solution with lowest within cost.

I will assume that the plot shows the sum of within distances of k-means. That is the sum of distances of every point to their closest cluster center. The optimization of K-Means does not guarantee a global minima. You are much more likely to find local minimas. As you increase k you might be unlucky and find a bad one. You could use a smart initialization strategy like k-means++, or run k-means several times with random initalizations for the cluster centers for each k and pick the solution with lowest within cost.

The results of K-Means is dependent on the cluster initialization.