DBSCAN Clustering
A density-based clustering algorithm called DBSCAN (Density-Based Spatial Clustering of Applications with Noise) clusters together densely packed data points while classifying outliers as noise. The user does not need to predetermine the number of clusters while using DBSCAN. Clusters are described as continuous high-density areas divided by low-density areas. DBSCAN can detect clusters of any shape and is resistant to outliers. Its two parameters are min_samples, which is the bare minimum of data points needed to build a dense region, and epsilon (eps), which specifies the radius of the neighborhood around a data point.
Implementing DBSCAN using PyTorch
1. Importing necessary libraries
Python3
import torchimport matplotlib.pyplot as pltfrom sklearn.datasets import make_moons |
2. Generate Synthetic Data
Generate synthetic data using make_moons function with 200 samples, some noise (0.05), and a fixed random state.
Python3
# Generate synthetic dataX, _ = make_moons(n_samples=200, noise=0.05, random_state=0)X = torch.tensor(X, dtype=torch.float) |
3. DBSCAN Algorithm
Define Euclidean distance function to calculate the distance between two points.
Python3
def euclidean_distance(x1, x2): return torch.sqrt(torch.sum((x1 - x2) ** 2, dim=1)) |
DBSCAN Function performs clustering.
The dbscan function implements the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm, a density-based clustering method. It takes an input dataset X, maximum distance parameter eps, and minimum number of samples parameter min_samples. It iterates over each data point, finding its neighbors within the specified distance. If a point has fewer neighbors than min_samples, it is labeled as noise; otherwise, it is labeled with a new cluster label and its neighbors are recursively visited to expand the cluster. The function efficiently assigns cluster labels to each point in the dataset based on their density and proximity relationships, providing a flexible and effective clustering method without requiring the number of clusters to be specified beforehand.
Python3
def dbscan(X, eps, min_samples): n_samples = X.shape[0] labels = torch.zeros(n_samples, dtype=torch.int) # Initialize cluster label and visited flags cluster_label = 0 visited = torch.zeros(n_samples, dtype=torch.bool) # Iterate over each point for i in range(n_samples): if visited[i]: continue visited[i] = True # Find neighbors neighbors = torch.nonzero(euclidean_distance(X[i], X) < eps).squeeze() if neighbors.shape[0] < min_samples: # Label as noise labels[i] = 0 else: # Expand cluster cluster_label += 1 labels[i] = cluster_label expand_cluster(X, labels, visited, neighbors, cluster_label, eps, min_samples) return labels |
This function implements the core logic of the DBSCAN algorithm, which iteratively identifies core points, expands clusters, and labels noise points. It operates directly on the input data and efficiently finds clusters without requiring the user to specify the number of clusters in advance.
Expand Cluster Function expands the cluster by assigning the cluster label to all reachable points from the core point.
Python3
def expand_cluster(X, labels, visited, neighbors, cluster_label, eps, min_samples): i = 0 while i < neighbors.shape[0]: neighbor_index = neighbors[i].item() if not visited[neighbor_index]: visited[neighbor_index] = True neighbor_neighbors = torch.nonzero(euclidean_distance(X[neighbor_index], X) < eps).squeeze() if neighbor_neighbors.shape[0] >= min_samples: neighbors = torch.cat((neighbors, neighbor_neighbors)) if labels[neighbor_index] == 0: labels[neighbor_index] = cluster_label i += 1 |
4. Performing Clustering and Visualize Clusters
Python3
# DBSCAN parameterseps = 0.3min_samples = 5# Perform clusteringlabels = dbscan(X, eps, min_samples)# Visualize clustersplt.figure(figsize=(8, 6))plt.scatter(X[:, 0], X[:, 1], c=labels, cmap='viridis')plt.title('DBSCAN Clustering')plt.xlabel('Feature 1')plt.ylabel('Feature 2')plt.colorbar()plt.show() |
Output:
PyTorch for Unsupervised Clustering
The aim of unsupervised clustering, a fundamental machine learning problem, is to divide data into groups or clusters based on resemblance or some underlying structure. One well-liked deep learning framework for unsupervised clustering problems is PyTorch.
Table of Content
- What is Unsupervised Clustering?
- K-means Clustering
- Hierarchical Clustering
- DBSCAN Clustering
- Evaluating Clustering Performance
Contact Us