DBSCAN

This notebook demonstrates using DBSCan to cluster a couple of datasets. It shows how changing its parameters (epsilon and min_samples) changes the resulting cluster structure.

import pandas as pd
import matplotlib.pyplot as plt
from itertools import cycle, islice
import numpy as np
from sklearn import cluster

Helper Function to Plot Datasets

figsize = (10,10)
point_size=150
point_border=0.8

def plot_dataset(dataset, xlim=(-15, 15), ylim=(-15, 15)):
    plt.figure(figsize=figsize)
    plt.scatter(dataset[:,0], dataset[:,1], s=point_size, 
                color="#00B3E9", edgecolor='black', lw=point_border)
    plt.xlim(xlim)
    plt.ylim(ylim)
    plt.show()

Blobs Dataset

Open first several points in the blobs dataset.

blobs = pd.read_csv('dbscan/blobs.csv')[:80].values
blobs[:5]
array([[ 8.62218539,  1.93579579],
       [-4.73670958, -7.97095765],
       [ 9.62122205,  0.92542315],
       [ 6.16209503, -0.27325437],
       [ 8.69748809, -1.05745206]])
plot_dataset(blobs)

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Helper Function to Plot Clusters

def plot_clustered_dataset(dataset, y_pred, xlim=(-15, 15), ylim=(-15, 15), 
                           neighborhood=False, epsilon=0.5, min_samples=5):

    fig, ax = plt.subplots(figsize=figsize)
    
    colors = np.array(list(islice(cycle(['#df8efd', '#78c465', '#ff8e34',
                                         '#f65e97', '#a65628', '#984ea3',
                                         '#999999', '#e41a1c', '#dede00']),
                                  int(max(y_pred) + 1))))
    colors = np.append(colors, '#BECBD6')
    
    if neighborhood:
        for point in dataset:
            circle1 = plt.Circle(point, epsilon, color='#666666', 
                                 fill=False, zorder=0, alpha=0.3)
            ax.add_artist(circle1)

    ax.scatter(dataset[:, 0], dataset[:, 1], s=point_size, 
               color=colors[y_pred], zorder=10, 
               edgecolor='black', lw=point_border)
    plt.xlim(xlim)
    plt.ylim(ylim)
    plt.title('Epsilon: {}, Min_Samples: {}'.format(epsilon, min_samples))
    plt.show()

Create and fit DBSCAN

dbscan = cluster.DBSCAN()
clustering_labels_1 = dbscan.fit_predict(blobs)
plot_clustered_dataset(blobs, clustering_labels_1)

png

Plot Epsilon, the radius of each point’s neighborhood. The default value in sklearn is 0.5.

plot_clustered_dataset(blobs, clustering_labels_1, neighborhood=True)

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We can see that an Epsilon value of 0.5 is too small for this dataset. We need to increase it such that points in a blob overlap each others’ neighborhoods, but not to the degree where a single cluster would pan two blobs.

for epsilon in [1, 1.5, 2, 5, 6]:
    dbscan = cluster.DBSCAN(eps=epsilon)
    clustering_labels_2 = dbscan.fit_predict(blobs)

    plot_clustered_dataset(blobs, clustering_labels_2, neighborhood=True, 
                           epsilon=epsilon)

png

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Epsilon values from 2 through 5 all appear viable to correctly classify this dataset.

Varied Dataset

varied = pd.read_csv('dbscan/varied.csv')[:300].values
plot_dataset(varied, xlim=(-14, 5), ylim=(-12, 7))

png

dbscan = cluster.DBSCAN()
clustering_labels_3 = dbscan.fit_predict(varied)
plot_clustered_dataset(varied, clustering_labels_3, 
                       xlim=(-14, 5), ylim=(-12, 7), 
                       neighborhood=True, epsilon=0.5)

png

Try to plot two scenarios:

Scenario 1: 3 clusters: left blob, right blob, central area

Scenario 2: 2 clusters: left blob, right blob

Scenario 1

3 clusters: left blob, right blob, central area

epsilon = 1.3
min_samples=5

dbscan = cluster.DBSCAN(eps=epsilon, min_samples=min_samples)
clustering_labels_3 = dbscan.fit_predict(varied)

plot_clustered_dataset(varied, clustering_labels_3, 
                       xlim=(-14, 5), ylim=(-12, 7), 
                       neighborhood=True, epsilon=epsilon,
                       min_samples=min_samples)

png

Scenario 2

2 clusters: left blob, right blob

epsilon = 1.3
min_samples=20

dbscan = cluster.DBSCAN(eps=epsilon, min_samples=min_samples)
clustering_labels_3 = dbscan.fit_predict(varied)

plot_clustered_dataset(varied, clustering_labels_3, 
                       xlim=(-14, 5), ylim=(-12, 7), 
                       neighborhood=True, epsilon=epsilon,
                       min_samples=min_samples)

png

Helper function to plot grid

def plot_dbscan_grid(dataset, eps_values, min_samples_values):
    
    fig = plt.figure(figsize=(16, 20))
    plt.subplots_adjust(left=.02, right=.98, bottom=0.001, top=.96, wspace=.05,
                        hspace=0.25)
    
    plot_num = 1
    for i, min_samples in enumerate(min_samples_values):
        for j, eps in enumerate(eps_values):
            ax = fig.add_subplot( len(min_samples_values) , len(eps_values), plot_num)

            dbscan = cluster.DBSCAN(eps=eps, min_samples=min_samples)
            y_pred_2 = dbscan.fit_predict(dataset)

            colors = np.array(list(islice(cycle(['#df8efd', '#78c465', '#ff8e34',
                                                 '#f65e97', '#a65628', '#984ea3',
                                                 '#999999', '#e41a1c', '#dede00']),
                                          int(max(y_pred_2) + 1))))
            colors = np.append(colors, '#BECBD6')


            for point in dataset:
                circle1 = plt.Circle(point, eps, color='#666666', 
                                     fill=False, zorder=0, alpha=0.3)
                ax.add_artist(circle1)

            ax.text(0, -0.03, 'Epsilon: {} \nMin_samples: {}'.format(eps, min_samples), 
                    transform=ax.transAxes, fontsize=16, va='top')
            ax.scatter(dataset[:, 0], dataset[:, 1], s=50, color=colors[y_pred_2], 
                       zorder=10, edgecolor='black', lw=0.5)

            plt.xticks(())
            plt.yticks(())
            plt.xlim(-14, 5)
            plt.ylim(-12, 7)

            plot_num = plot_num + 1
    plt.show()

Show Grid

The following grid plots the DBSCAN clustering results of a range of parameter values.

Epsilon varies horizontally, while vertically each row shows a different value of min_samples.

eps_values = [0.3, 0.5, 1, 1.3, 1.5]
min_samples_values = [2, 5, 10, 20, 80]

plot_dbscan_grid(varied, eps_values, min_samples_values)

png

Heuristics

If most/all data points are labeled as noise excpt for extremely dense regions, decrease epsilon and decrease min_samples

1

If most points belong to one cluster, decrease epsilon and increase min_samples

2

If most or all data points are labeled as noise, increase epsilon and decrease min_samples

3

If there are many small clusters (more than expected for the dataset), increase epsilon and increase min_samples

4