DBSCAN is one of the famous clustering algorithm. Spatial clustering of density-based applications (DBSCAN) is a well-known data clustering algorithm widely used in data mining and machine learning. Based on a set of points (let's think in a 2-dimensional space), DBSCAN groups together points that are close to each other based on a distance measurement (usually Euclidean distance) and a minimum number of points. It also marks the points in low-density regions as outliers. DBSCAN can find non-linearly separable clusters. 

DBSCAN Clustering in Machine Learning

DBSCAN(DB, distFunc, eps, minPts) {
   C = 0                                                  /* Cluster counter */
   for each point P in database DB {
      if label(P) ≠ undefined then continue               /* Previously processed in inner loop */
      Neighbors N = RangeQuery(DB, distFunc, P, eps)      /* Find neighbors */
      if |N| < minPts then {                              /* Density check */
         label(P) = Noise                                 /* Label as Noise */
         continue
      }
      C = C + 1                                           /* next cluster label */
      label(P) = C                                        /* Label initial point */
      Seed set S = N \ {P}                                /* Neighbors to expand */
      for each point Q in S {                             /* Process every seed point */
         if label(Q) = Noise then label(Q) = C            /* Change Noise to border point */
         if label(Q) ≠ undefined then continue            /* Previously processed */
         label(Q) = C                                     /* Label neighbor */
         Neighbors N = RangeQuery(DB, distFunc, Q, eps)   /* Find neighbors */
         if |N| ≥ minPts then {                           /* Density check */
            S = S ∪ N                                     /* Add new neighbors to seed set */
         }
      }
   }
}

/* credit: wikipedia */

# credit: geeksforgeeks
import numpy as np 
from sklearn.cluster import DBSCAN 
from sklearn import metrics 
from sklearn.datasets.samples_generator import make_blobs 
from sklearn.preprocessing import StandardScaler 
from sklearn import datasets 
  
# Load data in X 
db = DBSCAN(eps=0.3, min_samples=10).fit(X) 
core_samples_mask = np.zeros_like(db.labels_, dtype=bool) 
core_samples_mask[db.core_sample_indices_] = True
labels = db.labels_ 
  
# Number of clusters in labels, ignoring noise if present. 
n_clusters_ = len(set(labels)) - (1 if -1 in labels else 0) 
  
print(labels) 
  
# Plot result 
import matplotlib.pyplot as plt 
  
# Black removed and is used for noise instead. 
unique_labels = set(labels) 
colors = ['y', 'b', 'g', 'r'] 
print(colors) 
for k, col in zip(unique_labels, colors): 
    if k == -1: 
        # Black used for noise. 
        col = 'k'
  
    class_member_mask = (labels == k) 
  
    xy = X[class_member_mask & core_samples_mask] 
    plt.plot(xy[:, 0], xy[:, 1], 'o', markerfacecolor=col, 
                                      markeredgecolor='k',  
                                      markersize=6) 
  
    xy = X[class_member_mask & ~core_samples_mask] 
    plt.plot(xy[:, 0], xy[:, 1], 'o', markerfacecolor=col, 
                                      markeredgecolor='k', 
                                      markersize=6) 
  
plt.title('number of clusters: %d' %n_clusters_) 
plt.show()