ML | OPTICS Clustering Implementing using Sklearn

Prerequisites: OPTICS Clustering This article will demonstrate how to implement OPTICS Clustering technique using Sklearn in Python. The dataset used for the demonstration is the Mall Customer Segmentation Data which can be downloaded from Kaggle. 

Step 1: Importing the required libraries

OPTICS (Ordering Points To Identify the Clustering Structure) is a density-based clustering algorithm that is used to identify the structure of clusters in high-dimensional data. It is similar to DBSCAN, but it also produces a cluster ordering that can be used to identify the density-based clusters at multiple levels of granularity.

The implementation of OPTICS clustering using scikit-learn (sklearn) is straightforward. You can use the OPTICS class from the sklearn.cluster module. Here is an example of how to use it:

Python

from sklearn.cluster import OPTICS
import numpy as np

# Generate sample data
np.random.seed(0)
X = np.random.randn(100, 2)

# Initialize the OPTICS clustering model
optics = OPTICS(min_samples=5, xi=0.05, min_cluster_size=0.05)

# Fit the model to the data
optics.fit(X)

# Get the cluster labels
labels = optics.labels_

In this example, the min_samples parameter controls the minimum number of samples required to form a dense region, the xi parameter controls the maximum distance between two samples to be considered as a neighborhood, and the min_cluster_size parameter controls the minimum size of a dense region to be considered as a cluster.

The fit method is used to fit the model to the data, and the labels_ attribute is used to get the cluster labels for each sample in the data.

Note that the implementation of OPTICS clustering in scikit-learn is based on the original paper by Ankerst, Mihael, and Markus (1999). You might consider reading this paper to learn more about the algorithm.

Python3

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib import gridspec
from sklearn.cluster import OPTICS, cluster_optics_dbscan
from sklearn.preprocessing import normalize, StandardScaler

Step 2: Loading the Data

Python3

# Changing the working location to the location of the data
cd C:\Users\Dev\Desktop\Kaggle\Customer Segmentation

X = pd.read_csv('Mall_Customers.csv')

# Dropping irrelevant columns
drop_features = ['CustomerID', 'Gender']
X = X.drop(drop_features, axis = 1)

# Handling the missing values if any
X.fillna(method ='ffill', inplace = True)

X.head()

Step 3: Preprocessing the Data

Python3

# Scaling the data to bring all the attributes to a comparable level
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

# Normalizing the data so that the data
# approximately follows a Gaussian distribution
X_normalized = normalize(X_scaled)

# Converting the numpy array into a pandas DataFrame
X_normalized = pd.DataFrame(X_normalized)

# Renaming the columns
X_normalized.columns = X.columns

X_normalized.head()

Step 4: Building the Clustering Model

Python3

# Building the OPTICS Clustering model
optics_model = OPTICS(min_samples = 10, xi = 0.05, min_cluster_size = 0.05)

# Training the model
optics_model.fit(X_normalized)

Step 5: Storing the results of the training

Python3

# Producing the labels according to the DBSCAN technique with eps = 0.5
labels1 = cluster_optics_dbscan(reachability = optics_model.reachability_,
                                   core_distances = optics_model.core_distances_,
                                   ordering = optics_model.ordering_, eps = 0.5)

# Producing the labels according to the DBSCAN technique with eps = 2.0
labels2 = cluster_optics_dbscan(reachability = optics_model.reachability_,
                                   core_distances = optics_model.core_distances_,
                                   ordering = optics_model.ordering_, eps = 2)

# Creating a numpy array with numbers at equal spaces till
# the specified range
space = np.arange(len(X_normalized))

# Storing the reachability distance of each point
reachability = optics_model.reachability_[optics_model.ordering_]

# Storing the cluster labels of each point
labels = optics_model.labels_[optics_model.ordering_]

print(labels)

Step 6: Visualizing the results

Python3

# Defining the framework of the visualization
plt.figure(figsize =(10, 7))
G = gridspec.GridSpec(2, 3)
ax1 = plt.subplot(G[0, :])
ax2 = plt.subplot(G[1, 0])
ax3 = plt.subplot(G[1, 1])
ax4 = plt.subplot(G[1, 2])

# Plotting the Reachability-Distance Plot
colors = ['c.', 'b.', 'r.', 'y.', 'g.']
for Class, colour in zip(range(0, 5), colors):
    Xk = space[labels == Class]
    Rk = reachability[labels == Class]
    ax1.plot(Xk, Rk, colour, alpha = 0.3)
ax1.plot(space[labels == -1], reachability[labels == -1], 'k.', alpha = 0.3)
ax1.plot(space, np.full_like(space, 2., dtype = float), 'k-', alpha = 0.5)
ax1.plot(space, np.full_like(space, 0.5, dtype = float), 'k-.', alpha = 0.5)
ax1.set_ylabel('Reachability Distance')
ax1.set_title('Reachability Plot')

# Plotting the OPTICS Clustering
colors = ['c.', 'b.', 'r.', 'y.', 'g.']
for Class, colour in zip(range(0, 5), colors):
    Xk = X_normalized[optics_model.labels_ == Class]
    ax2.plot(Xk.iloc[:, 0], Xk.iloc[:, 1], colour, alpha = 0.3)

ax2.plot(X_normalized.iloc[optics_model.labels_ == -1, 0],
        X_normalized.iloc[optics_model.labels_ == -1, 1],
       'k+', alpha = 0.1)
ax2.set_title('OPTICS Clustering')

# Plotting the DBSCAN Clustering with eps = 0.5
colors = ['c', 'b', 'r', 'y', 'g', 'greenyellow']
for Class, colour in zip(range(0, 6), colors):
    Xk = X_normalized[labels1 == Class]
    ax3.plot(Xk.iloc[:, 0], Xk.iloc[:, 1], colour, alpha = 0.3, marker ='.')

ax3.plot(X_normalized.iloc[labels1 == -1, 0],
        X_normalized.iloc[labels1 == -1, 1],
       'k+', alpha = 0.1)
ax3.set_title('DBSCAN clustering with eps = 0.5')

# Plotting the DBSCAN Clustering with eps = 2.0
colors = ['c.', 'y.', 'm.', 'g.']
for Class, colour in zip(range(0, 4), colors):
    Xk = X_normalized.iloc[labels2 == Class]
    ax4.plot(Xk.iloc[:, 0], Xk.iloc[:, 1], colour, alpha = 0.3)

ax4.plot(X_normalized.iloc[labels2 == -1, 0],
        X_normalized.iloc[labels2 == -1, 1],
       'k+', alpha = 0.1)
ax4.set_title('DBSCAN Clustering with eps = 2.0')


plt.tight_layout()
plt.show()