kmeans instability

[cookiedan42]

I've been encountering sporadic test failures due to the test_kmeans_three_clusters test
Running it in a loop seems to show instability in the results of kmeans

@urschrei

 #[test]
    fn test_kmeans_three_clusters_loop() {
        let points = [
            // Cluster 1
            point!(x: 0.0, y: 0.0),
            point!(x: 1.0, y: 0.0),
            // Cluster 2
            point!(x: 10.0, y: 10.0),
            point!(x: 11.0, y: 10.0),
            // Cluster 3
            point!(x: 20.0, y: 20.0),
            point!(x: 21.0, y: 20.0),
        ];
        
        for i in 0..100_000 {
            
            let labels = points.kmeans(3).unwrap();
            // Each pair should be in the same cluster
            assert_eq!(labels[0], labels[1],"failed at loop {}",i);
            assert_eq!(labels[2], labels[3],"failed at loop {}",i);
            assert_eq!(labels[4], labels[5],"failed at loop {}",i);

            // All three pairs should be in different clusters
            assert_ne!(labels[0], labels[2],"failed at loop {}",i);
            assert_ne!(labels[2], labels[4],"failed at loop {}",i);
            assert_ne!(labels[0], labels[4],"failed at loop {}",i);
        }
    }

[urschrei]

Urg pretty sure this is a bug, but it has an easy fix. But I also think that the test (being run in a loop) is bad: because it uses a random seed, running it in a loop will always eventually result in a failure because the seed will place multiple centroids in the same cluster, which leads to incorrect local minima. I'm fairly sure this is an inherent limitation of k-means, we just need to document it and set up the test to use a fixed seed (which will always give the same result, which will be correct if the algorithm is correct. Which it will be when I fix the bug)