Practical Machine Learning

About This Book

Clustering

Clustering

# Set up library imports and define a helper function to display numpy arrays.
import numpy as np
import matplotlib.pyplot as plt
from sklearn.neighbors import NearestNeighbors
from sklearn.cluster import KMeans
from collections import defaultdict

# Useful in beautifying numpy arrays.
from IPython.display import HTML, display
import tabulate
def pp(a, show_head=False): 
    '''
    args: show_head -> if True print only first 5 rows.
    return: None
    '''
    if a.ndim < 2:
        a = [a]
    if show_head:
        display(HTML(tabulate.tabulate(a[:5], tablefmt='html')))
        return
    display(HTML(tabulate.tabulate(a, tablefmt='html')))

Unsupervised Learning

Kmeans Clustering

So far, we dealt with datasets in which we're also given a label for each datapoint (supervised setting). Now, we'll deal with datasets in which we don't know the labels (unsupervised setting). In this tutorial, given a training set, we want to group the data into a few cohesive clusters- called clustering.

Algorithm:

• Initilaize k clusters randomly (we can pick any k training examples).

• Repeat Until Convergence:

  1. Assign each training example to a cluster based on how close it is to a cluster.

  2. Compute mean of all the points assigned to cluster i- that mean is your new guess for cluster i.

Demo

Play with this k-meas clustering demo.

K-means

Let's consider a randmom synthetic datset.

np.random.seed(0)
X = np.vstack([np.random.randn(50,2) + [-3,0], np.random.randn(50,2) + [3,0]])
plt.scatter(X[:,0], X[:,1])
plt.axis([-6,6,-3,3])

[-6, 6, -3, 3]

Even if you weren’t to look at the code that generated these points, it should be fairly apparent that there are two different clusters of points here. The goal of the k-means algorithm is to find a set of k “centers” (that is, points μ(i)∈Rn) such that every data point is close to at least one center. By doing so, we can also associate each point with it’s closest center, and use this as an indication of which cluster it belong to.

Train a Kmeans and Find Centroids Assigned

kmeans = KMeans(n_clusters=2, random_state=0).fit(X)
pp(kmeans.labels_) # label (either cluster assignment) of each datapoint

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Notes on k-means Clustering for a theoretical treatment.

Final Centroids Found:

kmeans.cluster_centers_

array([[ 2.98127847,  0.18274747],
       [-2.98319384,  0.10280987]])

Nearest Neighbour

We've already seen Nearest Neighbour in the context of classification in tutorial 4. Here, we'll use it for clustering (unsupervised learning/no labels given).

neigh = NearestNeighbors(n_neighbors=3, radius=0.4)
neigh.fit(X)

NearestNeighbors(n_neighbors=3, radius=0.0)

X.shape

(100, 2)

Closest points for each example in X

More in Docs

Indexes of Closest datapoints

For each example

Change radius to strict similarity criterion and run the subsequent cells.

# Print Closest indexes for each of the 100 examples
closes_points_indexes = neigh.radius_neighbors(radius=3)[1] # points within radius 1
pp(closes_points_indexes)

[ 1 2 3 4 5 6 7 8 9 11 12 13 14 15 17 18 19 22 25 26 27 28 29 30 32 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 70 95]

[ 0 3 4 5 6 7 8 11 13 14 15 17 18 19 21 23 25 27 28 32 34 35 37 39 40 42 43 44 45 46 47 48 49]

[ 0 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 22 26 27 28 29 30 31 32 34 35 36 37 38 39 41 42 43 46 47 49 70 74]

[ 0 1 2 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 1 2 3 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 1 2 3 4 6 7 8 9 10 11 13 14 15 17 18 19 21 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 38 39 40 42 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 7 8 9 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 8 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 9 11 12 13 14 15 16 17 18 19 20 22 23 25 26 27 28 29 30 31 32 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 4 5 13 15 17 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 38 39 40 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 2 3 6 7 8 9 11 13 15 18 19 22 26 27 28 32 35 36 37 39 41 43 47 49 70 74 95 79 83]

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 11 13 15 17 18 19 22 23 25 27 28 29 30 32 34 35 36 37 39 40 42 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 2 3 4 6 7 8 9 11 13 15 17 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 43 47 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 17 19 22 23 25 26 27 28 29 30 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 2 3 4 6 7 8 9 10 11 13 15 16 17 19 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 43 44 45 46 47 49]

[ 1 4 5 7 10 13 15 17 19 22 23 24 25 27 28 29 30 33 34 38 39 40 44 45 46 47 48 49]

[ 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 43 44 45 46 47 48 49]

[ 1 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 24 25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 3 4 5 6 7 9 10 11 13 15 16 17 19 20 21 22 23 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 43 44 45 46 47 48 49]

[ 0 1 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 2 3 4 5 6 7 8 9 10 11 12 13 15 16 17 18 19 20 22 23 24 25 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 43 44 45 46 47 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 31 32 33 34 35 36 37 38 39 40 41 43 44 45 46 47 48 49]

[ 0 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31 32 33 34 35 36 37 38 39 40 41 43 44 45 46 47 48 49]

[ 2 3 4 6 7 8 9 10 11 13 15 16 17 19 20 22 23 24 25 26 27 28 29 30 32 33 34 35 36 37 38 39 40 41 43 44 45 46 47 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 3 4 5 6 7 9 10 11 13 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 34 35 37 38 39 40 41 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36 37 38 39 40 41 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 36 37 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 22 24 25 26 27 28 29 30 31 32 34 35 37 38 39 41 43 45 46 47 49]

[ 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 38 39 40 41 42 43 44 45 46 47 48 49]

[ 0 2 3 4 5 6 7 8 9 10 11 13 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 39 40 41 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 40 41 42 43 44 45 46 47 48 49]

[ 0 1 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 38 39 41 42 43 44 45 46 47 48 49]

[ 0 2 3 4 6 7 8 9 11 12 13 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 43 45 46 47 49]

[ 0 1 2 3 4 5 6 7 8 9 11 13 14 15 17 18 19 23 25 27 28 32 35 37 39 40 43 44 45 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 44 45 46 47 48 49]

[ 0 1 3 4 5 6 7 8 9 10 11 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 42 43 45 46 47 48 49]

[ 0 1 3 4 5 6 7 8 9 10 11 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 46 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 47 48 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 48 49]

[ 0 1 3 4 5 6 7 8 9 10 11 13 14 15 17 18 19 21 22 23 24 25 27 28 29 30 32 33 34 35 37 38 39 40 42 43 44 45 46 47 49]

[ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48]

[62 66 76 77 83 88 89 90 91 53 96 71 60 69 97 64 59 92 68 98 81 55 84 85 86 78 54 58 99 72]

[70 74 95 56 57 62 63 65 66 67 73 52 75 76 77 79 80 82 83 87 88 89 90 93 94 53 96 61 71 60 69 97 64 59 68 98 81 84 85 86 58]

[70 74 95 56 57 62 63 65 66 67 51 73 75 76 77 79 80 82 87 88 89 93 94 53 61 71 97 64 59 68 98 81 84 85 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 96 61 71 60 69 97 64 59 92 68 98 81 55 50 84 85 86 78 58]

[56 57 63 65 66 67 73 75 77 80 89 94 61 71 69 97 64 59 68 98 81 55 50 84 85 86 78 58 99 72]

[56 57 62 63 65 66 67 73 75 77 80 87 89 94 53 96 61 71 60 69 97 64 59 92 68 98 81 50 84 85 86 78 54 58 99 72]

[70 74 95 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 87 88 89 93 94 53 61 71 97 64 59 68 98 81 55 84 85 54 58]

[70 74 95 56 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 84 85 86 78 54 58 99 72]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 50 84 85 86 78 54 99 72]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 93 94 53 96 61 71 60 69 97 64 92 68 98 81 55 50 84 85 86 78 54 58 99 72]

[70 74 95 57 62 65 66 67 51 73 75 76 77 79 82 83 87 88 89 90 91 93 94 53 96 61 71 69 97 64 59 92 68 98 81 55 50 84 85 86 78 58 72]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 87 88 89 90 93 94 53 96 71 60 69 97 64 59 92 68 98 81 55 84 85 86 78 54 58 99 72]

[70 74 95 56 57 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 50 84 85 86 78 58]

[70 74 95 56 57 62 65 66 67 51 73 52 75 76 77 79 80 82 87 88 89 93 94 53 61 71 97 64 59 68 98 81 55 84 85 86 54 58 99 72]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 59 92 68 98 81 55 50 84 85 86 78 54 58 99 72]

[70 74 95 56 57 62 63 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 84 85 86 78 54 58]

[70 74 95 56 57 62 63 65 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 50 84 85 86 78 54 58]

[70 74 95 56 57 62 63 65 66 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 84 85 86 78 54 58 99]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 98 81 55 50 84 85 86 78 54 58 99 72]

[70 74 95 57 62 65 66 67 51 73 75 76 77 79 82 83 87 88 89 90 91 93 94 53 96 61 71 60 97 64 59 92 68 98 81 55 50 84 85 86 78 54 58 72]

[ 0 2 12 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 84 85 86 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 60 69 97 64 59 92 68 98 81 55 50 84 85 86 78 54 58 99 72]

[57 63 75 77 89 61 71 60 69 97 64 59 68 98 81 55 50 84 85 86 78 54 58 99]

[70 74 95 56 57 62 63 65 66 67 51 52 75 76 77 79 80 82 83 87 88 89 90 93 94 53 96 61 71 60 69 97 64 59 68 98 81 55 84 85 86 78 54 58]

[ 2 12 70 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 84 85 86 78 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 76 77 79 80 82 87 88 89 93 94 53 96 61 71 60 69 97 64 59 68 98 81 55 84 85 86 54 58 99 72]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 50 84 85 86 78 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 50 84 85 86 78 54 58 72]

[74 95 57 62 65 66 67 73 76 77 79 83 87 88 89 90 91 93 53 96 61 71 60 69 97 64 59 92 68 98 81 55 50 84 85 86 54 58 99 72]

[12 70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 84 85 86 78 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 82 87 88 89 93 94 53 61 71 97 64 59 68 98 81 55 84 85 86 54 58 99]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 55 50 84 85 86 78 54 58 99 72]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 83 87 88 89 90 93 94 53 96 61 71 60 69 97 64 59 68 98 81 84 85 86 58]

[12 70 74 95 57 62 65 66 67 51 73 76 77 79 82 87 88 89 90 91 93 53 96 71 60 69 97 64 59 92 68 98 81 50 84 85 86 78 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 50 85 86 78 54 58 99 72]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 50 84 86 78 54 58 99 72]

[70 74 95 57 62 63 65 66 67 51 73 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 50 84 85 78 54 58 99 72]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 84 85 86 78 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 50 84 85 86 78 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 55 50 84 85 86 78 54 58 99 72]

[70 74 95 57 62 65 66 67 51 73 76 77 79 82 83 87 88 89 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 50 84 85 86 78 58]

[70 74 95 62 65 66 67 76 77 79 83 87 88 89 90 93 53 96 71 60 69 97 64 92 68 81 50 85 86 78 58]

[70 74 95 57 62 65 66 67 76 77 79 83 87 88 89 90 91 93 53 96 61 71 60 69 97 64 59 68 98 81 55 50 84 85 86 78 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 94 53 96 61 71 60 69 97 64 59 92 68 98 81 84 85 86 78 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 87 88 89 90 93 53 96 61 71 60 69 97 64 59 68 98 81 55 84 85 86 54 58 99]

[ 0 12 70 74 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 97 64 59 92 68 98 81 84 85 86 78 58]

[70 74 95 57 62 65 66 67 51 73 75 76 77 79 82 83 87 88 89 90 91 93 94 53 61 71 60 69 97 64 59 92 68 98 81 55 50 84 85 86 78 58]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 91 93 94 53 96 61 71 60 69 64 59 92 68 98 81 55 50 84 85 86 78 54 58 99 72]

[70 74 95 56 57 62 63 65 66 67 51 73 52 75 76 77 79 80 82 83 87 88 89 90 93 94 53 96 61 71 60 69 97 64 59 92 68 81 55 50 84 85 86 78 54 58 99 72]

[57 63 67 75 80 89 94 61 71 97 64 59 68 98 81 55 50 84 85 86 78 54 58 72]

Distances of Closest datapoints

For each example

# print correspondig distances
closes_points_distances = neigh.radius_neighbors(radius=2.5)[0] # points within radius 1
pp(closes_points_distances)

[2.00125651 1.38131852 0.98321179 1.86730039 1.93276734 1.04095661 1.32186205 0.66279136 1.9179434 1.45403208 1.92223566 1.81590286 1.09392835 1.60925523 2.12599071 0.96356768 2.26315759 2.42329617 1.79245602 1.70034347 1.777776 1.06989784 1.75024547 1.74109451 2.10391683 2.33140832 1.52094702 0.82403847 2.31798191 1.65914873 1.44064932 2.23498257 1.63714128]

[2.00125651 2.39242195 2.12617245 1.14694608 2.13037065 1.98080156 2.49974883 0.94985634 2.03676127 2.47089563 1.06854515 2.07346736 2.14234074 2.12661442 0.61533122 2.42906908 2.36813325 1.71666114 1.48052417 1.65574284 1.06982728 2.02661656]

[1.38131852 1.23446157 2.41042781 1.55951421 1.93533006 0.85770345 1.5593633 1.03030645 0.62399912 1.98574971 2.4694347 2.18409103 2.48865783 2.27090674 2.35374105 2.43759486 2.38704088 2.35999359 2.20941335 1.78542499 1.58742591 0.77236261 1.4941206 2.41174782 1.50922295 1.0536544 2.26253274 2.22086161]

[0.98321179 2.39242195 1.23446157 1.19383853 1.79659631 0.3320945 0.70108454 0.54664466 0.94849187 0.59698423 1.85454845 0.90503929 1.72228013 0.95532211 1.33397472 1.38243167 1.34590641 2.36729116 1.48763211 2.39070172 1.9224455 1.78706938 1.13712483 0.99330706 1.5984492 1.63585157 2.36418836 0.8122309 1.86848003 0.35697428 1.09988334 0.76459042 1.87039409 1.27859434 2.36248247 1.46716703 2.116799 0.23046855 2.35324748 1.9283827 1.35006026 1.04333617 2.15306236 0.99187282]

[1.86730039 2.12617245 2.41042781 1.19383853 1.07256525 0.91127175 0.5524637 1.7118753 1.33144509 2.46179539 1.50506479 0.61606655 1.94870803 0.26019593 0.35287056 1.55085956 0.76742787 2.06029443 2.22304261 0.9409748 1.20670451 1.63422834 0.792602 1.64260211 0.07710361 0.20125034 0.93814972 0.95768971 2.2517233 0.85948936 1.52787091 0.88044075 0.87866165 2.06192253 1.20644577 1.25227158 0.41112746 1.16962426 2.02825551 2.17689423 1.41146653 1.16218268 0.86548813 0.64608846 0.54664395 1.37996559 0.23029192]

[1.93276734 1.14694608 1.79659631 1.07256525 1.46850282 1.16001481 2.13923109 2.31454914 2.31155959 1.64439722 1.38881757 1.07616623 1.38803045 1.11507094 1.8351879 1.91577012 2.00207352 1.55215799 2.42266238 1.48992019 1.04029706 1.15440776 1.97671329 1.98913197 1.85635462 2.03248353 1.75266768 1.44868048 2.15462213 2.27233174 1.47046736 1.42136941 1.41489265 1.9342396 1.2789008 0.59430188 0.48193398 0.77726236 0.35747789 1.05242359]

[1.04095661 2.13037065 1.55951421 0.3320945 0.91127175 1.46850282 0.38150146 0.80260178 1.0736879 0.87000624 2.18177243 0.77911369 1.55300883 0.65812711 1.10949182 1.17818558 1.22413164 2.37727483 1.38851436 2.11792763 2.39836456 1.67760307 1.82032643 0.84670335 0.71766722 1.47705385 1.51211692 2.42755075 0.78396978 2.41544284 1.66979266 0.03277234 1.40828017 0.88265571 1.77584343 1.07458893 2.07780547 1.68402523 1.91746624 0.51523851 2.05560898 1.60221425 1.01809142 0.71124168 1.82561043 0.69331916]

[1.32186205 1.98080156 1.93533006 0.70108454 0.5524637 1.16001481 0.38150146 1.1803787 1.19494987 1.1551242 0.65557654 1.57337763 0.29232096 0.81138926 1.17180093 1.04658671 2.30276848 1.22669784 1.75374543 2.12907247 1.34038708 1.79011617 0.48144259 0.37863386 1.28354125 1.3140559 2.41319197 0.78222961 2.0780761 1.38022058 0.35107436 1.71579867 1.01933044 1.60032245 0.80477588 1.70604356 1.87004508 1.87916565 0.89659697 1.67737332 1.22775832 0.68476671 0.38302642 1.51547926 0.32422981]

[0.66279136 2.49974883 0.85770345 0.54664466 1.7118753 2.13923109 0.80260178 1.1803787 1.3475562 0.82754239 1.47043929 1.44843209 1.67496418 1.4606631 1.87713056 1.43204324 1.8839122 2.01722305 2.46180102 2.22959863 1.64881449 1.51513076 2.13422677 2.1720339 1.33125333 2.41510163 0.83478006 1.0890418 1.19245817 2.39421904 1.82444389 1.68209072 2.10105552 0.31630761 2.37436974 1.74640689 1.45795896 2.48298254 1.49591905]

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[2.4659081 2.33093589 2.24945093 1.41181125 1.66101048 2.24068673 1.77768117 1.62470924 1.69111004 2.38864673 2.12785042 1.91802886 1.92499568 1.28921832 2.16170312 2.34265111 2.30277312 2.07070251 1.91736816 1.40669965 1.95903129 2.05410897 2.22958289 1.59847195 1.59817977 1.39955354 0.95521093 1.31802076 1.30388405 0.49872877 0.42325127 0.89950184 1.7204293 0.47595107 0.75708599 1.23000372 1.7122988 0.33099041 0.23293415 0.7443579 1.18085612 1.69943844 0.24257103 1.74163429 1.67029651]

[0.48442038 1.30907763 0.58123568 1.12621912 0.95834883 1.12687689 1.27842525 0.54826306 0.98179595 0.61303841 0.1329018 0.41480947 1.10050223 1.44714324 1.73857172 1.88246539 1.28455133 1.30641002 2.39972618 0.25109403 1.59090985 1.12981746 2.3842748 0.80139325 0.8509913 1.78687715 2.33600927 1.59810125 1.40775964 2.02239116 1.94737331 1.84116123 2.08695847 1.99733499 2.30277312 2.47042244 2.20972213 2.39150945]

[2.04402165 1.12825283 1.83530322 2.45878248 1.42822491 2.09670654 1.60992929 2.2508918 0.76240524 1.26089381 1.11670236 2.39972618 2.22662564 0.87757392 1.65448036 0.66816234 0.7666178 1.60033 0.9898528 1.03212273 2.47248229 1.44689143 1.4674732 2.05104221 1.62645598 2.06699685 2.0609223 2.17705585 2.39250174]

[2.48138832 1.53484729 1.9395536 2.23220343 1.97052588 1.88406019 1.85896658 2.24804295 1.87833732 2.24565732 1.61748629 2.45442858 2.33307749 2.47042244 2.25199171 2.23133548 1.67062126 2.28917935 2.30765359 2.28448385 1.92307584 1.92655872 1.34562434 1.06974258 1.63240011 1.6172236 0.82493525 0.52361852 0.83412449 1.99982599 0.8060621 0.65563687 0.33099041 0.8993337 1.80400242 0.26717693 1.02306175 1.39822263 1.37622535 0.52982385 1.41087962 1.34985271]

[2.41513259 2.36896822 2.21431882 2.38917969 1.28350567 1.68195318 2.04482523 1.70509516 1.62078555 1.59727376 2.28590419 1.99991273 1.70975754 2.02130513 1.41552963 2.20234942 2.14661204 2.20972213 1.9884906 1.99742965 1.40897258 2.11985798 2.04270933 2.06297822 1.70809135 1.76988957 1.18449635 0.81782858 1.5190444 1.50619334 0.63122116 0.26392774 0.67697899 1.94340211 0.6295056 0.52632753 0.23293415 1.11408367 1.92436577 0.26717693 0.97186469 1.41371555 1.53424903 0.47447239 1.60605678 1.59054882]

[2.18098106 2.33752451 1.83789591 1.63040799 2.01570306 1.67653019 1.99755621 1.61116281 0.9553643 2.01560714 2.0609223 2.3134466 1.66068717 1.47281891 1.41073188 2.1734117 2.08346761 1.27410391 1.03459098 2.05479481 1.45954086 0.65713725 0.63855651 0.58408784 1.07445294 1.59185047 0.97882591 0.52396698 1.47697996 0.7443579 1.85635114 1.24047186 1.02306175 0.97186469 0.50671016 2.38328722 0.50418984 2.37845832 2.20800167]

[0.51722789 1.17736716 0.48859766 1.24059443 0.77571291 0.8979537 1.31238689 0.30021797 0.74278432 0.39843019 0.37234454 0.45203438 1.26964527 1.41338698 1.53556733 1.63857388 1.12512624 1.3582598 0.25109403 2.22662564 1.39043901 0.880883 2.16613002 0.63332544 0.91042889 1.55799742 2.10030741 1.48029105 1.20181869 2.27198802 2.27925817 1.77587058 1.72841526 1.6657912 1.84029756 1.81160011 2.07070251 2.25199171 1.9884906 2.3134466 2.15086702]

[1.32198473 0.56091181 1.07454335 1.58516318 0.55077673 1.22925535 0.73283727 1.37622212 1.72344504 1.80987626 0.1489259 0.70543908 0.42631496 1.59090985 0.87757392 1.39043901 0.78797743 0.81960341 1.54215415 0.80045367 2.23347713 0.39406823 0.9016063 2.29730812 1.64182116 1.24899517 1.26547278 1.42422757 1.83878711 2.14640025 1.69519499 1.4615074 2.18416756 1.91736816 2.23133548 1.99742965 1.66068717 1.96913023 1.83045044]

[1.11836338 0.98475737 0.87372662 1.93557949 0.80706656 0.29165886 1.83189793 0.60916418 0.21927032 0.68317899 1.25311396 1.19083827 2.0554707 1.73952507 0.89210237 0.76890126 0.82829524 1.91252517 1.12981746 1.65448036 0.880883 0.78797743 1.39612773 2.24876185 0.64977729 1.55175117 0.76608141 1.25652152 1.51043275 0.87664766 1.39268625 1.39943546 0.99689418 1.19334857 1.40092878 1.94703627 1.05652933 1.46833177 1.40669965 2.48722789 1.67062126 1.40897258 1.47281891 1.92550438 1.4133495 ]

[2.14131016 1.3264676 1.89146367 2.179105 1.27176718 1.95886568 1.44279316 2.07065675 0.67346888 0.75597304 1.22793206 2.3842748 0.66816234 2.16613002 0.81960341 1.39612773 0.89652267 1.61237261 0.63032292 0.37660751 2.07632491 0.78066679 0.8012258 1.48922368 2.0567608 2.49280978 1.0052162 1.49233578 2.46993867 1.95903129 2.23730986 2.28917935 2.11985798 1.41073188 1.50973553 1.78367524]

[1.88572986 2.07439439 2.25544285 1.40062083 1.65244408 1.85530917 0.7666178 1.54215415 2.24876185 0.89652267 2.32174829 1.49376144 1.21610031 1.51785076 1.53573846 2.36045769 1.4128164 2.35574962 2.1734117 2.10744579]

[2.2513771 1.9624992 2.08769193 1.57430855 1.1851792 2.12082882 1.62645598 1.69519499 1.94703627 1.0052162 1.4128164 2.39332826 1.34519747 0.79366498 2.28360308 0.5608639 0.55823029 1.43413996 2.01007053 1.39460739 2.42998553 1.7204293 1.28336612 1.99982599 1.94340211 0.97882591 0.72389375 1.48244523]

[0.54737203 0.55559083 0.28582895 1.87374427 1.12359624 0.4568061 1.91766318 0.59086317 0.43053116 0.78053698 0.93215 1.08194443 1.89270478 1.95783065 0.94935609 1.23452105 0.49187576 1.97285787 0.80139325 1.60033 0.63332544 0.80045367 0.64977729 1.61237261 2.32174829 1.5348375 1.05666805 1.61971297 1.89498966 1.3983271 1.87587283 1.88751536 1.64296192 1.81185564 1.92615847 2.39332826 1.70103366 2.02854441 2.05410897 2.30765359 2.04270933 2.08346761 2.0620691 ]

[1.33530081 2.085807 1.39076151 0.38668821 0.87794927 1.69324708 0.43180278 1.00422423 1.51259122 0.87276592 0.78161093 0.45988403 0.59030523 0.69259229 2.36945882 2.2977453 2.02239781 0.45577708 0.8509913 0.91042889 2.23347713 1.55175117 1.5348375 2.31354481 1.06016945 1.28284761 2.12943259 1.81185606 1.48921125 2.19074401 1.67388316 2.22958289 2.28448385 2.06297822 2.3934562 ]

[0.26280067 0.72899999 1.69876449 1.15628018 0.72909294 1.79973681 0.58954138 0.66174077 0.77411705 0.70270206 0.93105723 1.68084031 1.89511023 1.22316597 1.51409588 0.7197088 1.84271257 0.58123568 1.83530322 0.48859766 1.07454335 0.87372662 1.89146367 0.28582895 1.39076151 1.34249064 1.90554122 1.91148483 1.50520387 2.15724222 2.16844784 1.86834383 1.97016149 2.01634201 1.92893548 2.13831929 2.24945093 2.48138832 2.21431882 2.33752451 2.27952259]

[2.16615775 1.45908367 1.90554122 1.98377922 1.21105621 1.85710635 1.35761042 1.93859919 2.46672317 2.44638464 0.78384875 0.5080724 1.3271681 2.33600927 1.03212273 2.10030741 0.9016063 1.25652152 0.37660751 1.21610031 1.61971297 0.56308478 1.81484918 0.42134561 0.44170893 1.14436857 1.72879069 2.19003127 0.79366498 1.14039742 2.15041885 1.59817977 1.9308108 1.92655872 1.76988957 1.03459098 1.16924721 1.4140682 ]

[2.10513504 1.86191306 1.86834383 2.49999046 1.25491251 1.21804163 2.23657367 1.47566179 1.21475522 1.43618765 2.12587203 1.92944905 1.9755254 1.42716069 0.79280781 1.69183084 2.33615125 2.02239116 2.05104221 1.77587058 1.42422757 0.99689418 1.48922368 2.36045769 1.64296192 2.12943259 1.09974725 1.14436857 1.51474198 0.88189201 0.93940362 0.93026225 0.59787695 1.09751572 1.43413996 0.06475446 1.02561427 0.49872877 1.7228747 1.79798047 0.82493525 0.63122116 0.58408784 1.09050723 2.16526421 0.42429766 2.2279485 2.1690143 ]

[2.29541484 2.45151706 2.13831929 1.96146792 1.04000693 1.75988804 1.58394974 1.56769264 1.64864169 1.41529881 2.04747993 1.70999111 2.2444047 1.22371022 2.24103118 1.72291607 2.29662679 1.68396798 1.99733499 1.81160011 2.18416756 1.46833177 2.46993867 2.02854441 1.67388316 1.9680213 2.15041885 0.69075459 0.63378909 1.96312937 1.95305848 1.02561427 0.42777403 0.18605108 2.42998553 1.05010484 0.75708599 1.09887276 2.43916078 0.65563687 0.52632753 1.47697996 1.93622895 1.32544811 0.99412114 1.48300833 1.61588906]

[2.48920812 2.26306903 1.86502535 2.11621336 2.2279485 1.75672123 1.60360476 2.21448241 1.48300833 1.74163429 0.52224587 1.41087962 1.60605678 2.37845832 0.28013101 1.92439673 0.44951295]

Using these closest indexes we can cluster the closest examples.

In the code below, keeping track of datapoints already assigned to a cluster, we simply put the closest datapoints for each example in one cluster (a simple approach).

clusters = defaultdict(list)
already_assigned_datapoints = set()
cluster_id = 0
for idx, closest_datapoints in enumerate(closes_points_indexes):
    "Add these points to set- to keep track"
    # first add this element
    if idx not in already_assigned_datapoints:
        already_assigned_datapoints.add(idx)
        clusters[cluster_id].append(idx)
    # now add its closed neighbours
    for _datapoint in closest_datapoints:
        if _datapoint not in already_assigned_datapoints:
            already_assigned_datapoints.add(_datapoint)
            clusters[cluster_id].append(_datapoint)
    cluster_id = cluster_id + 1

Arbitrary Cluster id (on the left)- Elements in that cluster (on the right)

array = np.array(list(clusters.items()))
pp(array) # cluster id on the left is arbitrary.

0	[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 22, 25, 26, 27, 28, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 70, 95]
1	[21, 23]
2	[16, 20, 31, 74]
3	[24, 33]
4	[10]
12	[79, 83]
50	[50, 62, 66, 76, 77, 88, 89, 90, 91, 53, 96, 71, 60, 69, 97, 64, 59, 92, 68, 98, 81, 55, 84, 85, 86, 78, 54, 58, 99, 72]
51	[51, 56, 57, 63, 65, 67, 73, 52, 75, 80, 82, 87, 93, 94, 61]

Practical Machine Learning

Hamza