Learn

The K-Means algorithm:

  1. Place k random centroids for the initial clusters.
  2. Assign data samples to the nearest centroid.
  3. Update centroids based on the above-assigned data samples.

Repeat Steps 2 and 3 until convergence.

In this exercise, we will implement Step 4.

This is the part of the algorithm where we repeatedly execute Step 2 and 3 until the centroids stabilize (convergence).

We can do this using a while loop. And everything from Step 2 and 3 goes inside the loop.

For the condition of the while loop, we need to create an array named errors. In each error index, we calculate the difference between the updated centroid (centroids) and the old centroid (centroids_old).

The loop ends when all three values in errors are 0.

Instructions

1.

On line 40 of script.py, initialize error:

error = np.zeros(3)

Then, use the distance() function to calculate the distance between the updated centroid and the old centroid and put them in error:

error[0] = distance(centroids[0], centroids_old[0])
# do the same for error[1]
# do the same for error[2]
2.

After that, add a while loop: 

while error.all() != 0:

And move everything below (from Step 2 and 3) inside.

And recalculate error again at the end of each iteration of the while loop:

error[0] = distance(centroids[0], centroids_old[0])
# do the same for error[1]
# do the same for error[2]
3.

Awesome, now you have everything, let’s visualize it.

After the while loop finishes, let’s create an array of colors:

colors = ['r', 'g', 'b']

Then, create a for loop that iterates k times.

Inside the for loop (similar to what we did in the last exercise), create an array named points where we get all the data points that have the cluster label i.

Then we are going to make a scatter plot of points[:, 0] vs points[:, 1] using the scatter() function:

plt.scatter(points[:, 0], points[:, 1], c=colors[i], alpha=0.5)
4.

Then, paste the following code at the very end. Here, we are visualizing all the points in each of the labels a different color.

plt.scatter(centroids[:, 0], centroids[:, 1], marker='D', s=150)

plt.xlabel('sepal length (cm)')
plt.ylabel('sepal width (cm)')

plt.show()

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