Question

Implement the following update centers function in Python

def _update_centers(self, old_centers, cluster_idx, points): np.random.seed(1) Args: old_centers: old centers KxD numpy array, where K is the number of clusters, and D is the dimension cluster_idx: numpy array of length N, the cluster assignment for each point points: NxD numpy array, the observations Return: centers: new centers, KxD numpy array, where K is the number of clusters, and D is the dimension.

Answer 1

class KMeans(object):

    def __init__(self): 
        pass

    def _init_centers(self, points, K, **kwargs):
        
        return points[np.random.choice(points.shape[0], K, replace = False)]

    def _update_assignment(self, centers, points):
        
        return np.argmin(pairwise_dist(centers, points), axis = 0)

    def _update_centers(self, old_centers, cluster_idx, points):
        
        K = old_centers.shape[0]
        centers = np.empty(old_centers.shape)
        for i in range(K):
            centers[i] = np.mean(points[cluster_idx == i], axis = 0)
        return centers

    def _get_loss(self, centers, cluster_idx, points):
        
        return np.sum(pairwise_dist(centers, points)[cluster_idx, np.arange(len(cluster_idx))])
        
    def __call__(self, points, K, max_iters=100, abs_tol=1e-16, rel_tol=1e-16, verbose=False, **kwargs):
       
        centers = self._init_centers(points, K, **kwargs)
        for it in range(max_iters):
            cluster_idx = self._update_assignment(centers, points)
            centers = self._update_centers(centers, cluster_idx, points)
            loss = self._get_loss(centers, cluster_idx, points)
            K = centers.shape[0]
            if it:
                diff = np.abs(prev_loss - loss)
                if diff < abs_tol and diff / prev_loss < rel_tol: break
            prev_loss = loss
            if verbose: print('iter %d, loss: %.4f' % (it, loss))
        return cluster_idx, centers, loss