k-means from Scratch

An interviewer asks: "Implement k-means with numpy only." The idea in one sentence: start from k centers, give every point to its nearest center, move each center to the mean of its points, and repeat until nothing changes.

The starting code gives you 9 points, 3 starting centers and distances(points, centers), which gives back a table with one row per point and one column per center. Four numpy tools do the rest. .argmin(axis=1) gives back, for each row, the position of its smallest number. points[labels == j] keeps only the rows whose label is j. .mean(axis=0) gives back the mean of each column. (a != b).any() gives back True when at least one number differs.

d = np.array([[4.0, 1.0], [0.5, 3.0], [2.0, 6.0]])
print(d.argmin(axis=1))            # [1 0 0]

pts = np.array([[0, 0], [4, 2], [2, 2]])
lab = np.array([1, 0, 1])
print(pts[lab == 1].mean(axis=0))  # [1. 1.]

Each round of the loop makes two moves: label every point with its nearest center, then put each center at the mean of its group. When a round moves no center, the loop stops. On this lesson's points the script must print:

Labels: [0 0 0 2 2 2 1 1 1]
Centers:
[[1.67 2.  ]
 [2.   8.33]
 [8.67 8.  ]]
Rounds until nothing changed: 3
Same groups as scikit-learn's KMeans on 60 random points: True

Your task: fill in mean_of_groups so each row of result is the mean of one group. Then write the while loop of kmeans: the labels from the nearest center, the new centers from the group means, a stop rule with .any(), and the move to the new centers.

Assignment
Follow the Coding Tutorial to write the group means and the k-means loop, one line at a time.

Hint
changed starts as True, so the first round always runs. In the finished loop the order is: labels, new centers, the stop rule, then centers = new_centers. The script runs only once all seven lines are in.