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 OPTICSimport numpy as np# Generate sample datanp.random.seed(0)X = np.random.randn(100, 2)# Initialize the OPTICS clustering modeloptics = OPTICS(min_samples=5, xi=0.05, min_cluster_size=0.05)# Fit the model to the dataoptics.fit(X)# Get the cluster labelslabels = 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 npimport pandas as pdimport matplotlib.pyplot as pltfrom matplotlib import gridspecfrom sklearn.cluster import OPTICS, cluster_optics_dbscanfrom sklearn.preprocessing import normalize, StandardScaler |
Step 2: Loading the Data
Python3
# Changing the working location to the location of the datacd C:\Users\Dev\Desktop\Kaggle\Customer SegmentationX = pd.read_csv('Mall_Customers.csv')# Dropping irrelevant columnsdrop_features = ['CustomerID', 'Gender']X = X.drop(drop_features, axis = 1)# Handling the missing values if anyX.fillna(method ='ffill', inplace = True)X.head() |
Step 3: Preprocessing the Data
Python3
# Scaling the data to bring all the attributes to a comparable levelscaler = StandardScaler()X_scaled = scaler.fit_transform(X)# Normalizing the data so that the data# approximately follows a Gaussian distributionX_normalized = normalize(X_scaled)# Converting the numpy array into a pandas DataFrameX_normalized = pd.DataFrame(X_normalized)# Renaming the columnsX_normalized.columns = X.columnsX_normalized.head() |
Step 4: Building the Clustering Model
Python3
# Building the OPTICS Clustering modeloptics_model = OPTICS(min_samples = 10, xi = 0.05, min_cluster_size = 0.05)# Training the modeloptics_model.fit(X_normalized) |
Step 5: Storing the results of the training
Python3
# Producing the labels according to the DBSCAN technique with eps = 0.5labels1 = 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 = 2.0labels2 = 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 rangespace = np.arange(len(X_normalized))# Storing the reachability distance of each pointreachability = optics_model.reachability_[optics_model.ordering_]# Storing the cluster labels of each pointlabels = optics_model.labels_[optics_model.ordering_]print(labels) |
Step 6: Visualizing the results
Python3
# Defining the framework of the visualizationplt.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 Plotcolors = ['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 Clusteringcolors = ['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 = 0.5colors = ['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 = 2.0colors = ['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() |
