DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a data clustering algorithm It is a density-based clustering algorithm because it finds a number of clusters starting from the estimated density distribution of corresponding nodes.
It starts with an arbitrary starting point that has not been visited.
This point’s epsilon-neighborhood is retrieved, and if it contains sufficiently many points, a cluster is started. Then, a new unvisited point is retrieved and processed, leading to the discovery of a further cluster or noise. DBSCAN requires two parameters: epsilon (eps) and the minimum number of points required to form a cluster (minPts). If a point is found to be part of a cluster, its epsilon-neighborhood is also part of that cluster.
I implemented the pseudo code from DBSCAN wiki page:
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DBSCAN(D, eps, MinPts) C = 0 for each unvisited point P in dataset D mark P as visited N = getNeighbors (P, eps) if sizeof(N) < MinPts mark P as NOISE else C = next cluster expandCluster(P, N, C, eps, MinPts) expandCluster(P, N, C, eps, MinPts) add P to cluster C for each point P' in N if P' is not visited mark P' as visited N' = getNeighbors(P', eps) if sizeof(N') >= MinPts N = N joined with N' if P' is not yet member of any cluster add P' to cluster C |
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import numpy as numpy import scipy as scipy from sklearn import cluster import matplotlib.pyplot as plt def set2List(NumpyArray): list = [] for item in NumpyArray: list.append(item.tolist()) return list def GenerateData(): x1=numpy.random.randn(50,2) x2x=numpy.random.randn(80,1)+12 x2y=numpy.random.randn(80,1) x2=numpy.column_stack((x2x,x2y)) x3=numpy.random.randn(100,2)+8 x4=numpy.random.randn(120,2)+15 z=numpy.concatenate((x1,x2,x3,x4)) return z def DBSCAN(Dataset, Epsilon,MinumumPoints,DistanceMethod = 'euclidean'): # Dataset is a mxn matrix, m is number of item and n is the dimension of data m,n=Dataset.shape Visited=numpy.zeros(m,'int') Type=numpy.zeros(m) # -1 noise, outlier # 0 border # 1 core ClustersList=[] Cluster=[] PointClusterNumber=numpy.zeros(m) PointClusterNumberIndex=1 PointNeighbors=[] DistanceMatrix = scipy.spatial.distance.squareform(scipy.spatial.distance.pdist(Dataset, DistanceMethod)) for i in xrange(m): if Visited[i]==0: Visited[i]=1 PointNeighbors=numpy.where(DistanceMatrix[i]<Epsilon)[0] if len(PointNeighbors)<MinumumPoints: Type[i]=-1 else: for k in xrange(len(Cluster)): Cluster.pop() Cluster.append(i) PointClusterNumber[i]=PointClusterNumberIndex PointNeighbors=set2List(PointNeighbors) ExpandClsuter(Dataset[i], PointNeighbors,Cluster,MinumumPoints,Epsilon,Visited,DistanceMatrix,PointClusterNumber,PointClusterNumberIndex ) Cluster.append(PointNeighbors[:]) ClustersList.append(Cluster[:]) PointClusterNumberIndex=PointClusterNumberIndex+1 return PointClusterNumber def ExpandClsuter(PointToExapnd, PointNeighbors,Cluster,MinumumPoints,Epsilon,Visited,DistanceMatrix,PointClusterNumber,PointClusterNumberIndex ): Neighbors=[] for i in PointNeighbors: if Visited[i]==0: Visited[i]=1 Neighbors=numpy.where(DistanceMatrix[i]<Epsilon)[0] if len(Neighbors)>=MinumumPoints: # Neighbors merge with PointNeighbors for j in Neighbors: try: PointNeighbors.index(j) except ValueError: PointNeighbors.append(j) if PointClusterNumber[i]==0: Cluster.append(i) PointClusterNumber[i]=PointClusterNumberIndex return #Generating some data with normal distribution at #(0,0) #(8,8) #(12,0) #(15,15) Data=GenerateData() #Adding some noise with uniform distribution #X between [-3,17], #Y between [-3,17] noise=scipy.rand(50,2)*20 -3 Noisy_Data=numpy.concatenate((Data,noise)) size=20 fig = plt.figure() ax1=fig.add_subplot(2,1,1) #row, column, figure number ax2 = fig.add_subplot(212) ax1.scatter(Data[:,0],Data[:,1], alpha = 0.5 ) ax1.scatter(noise[:,0],noise[:,1],color='red' ,alpha = 0.5) ax2.scatter(noise[:,0],noise[:,1],color='red' ,alpha = 0.5) Epsilon=1 MinumumPoints=20 result =DBSCAN(Data,Epsilon,MinumumPoints) #printed numbers are cluster numbers print result #print "Noisy_Data" #print Noisy_Data.shape #print Noisy_Data for i in xrange(len(result)): ax2.scatter(Noisy_Data[i][0],Noisy_Data[i][1],color='yellow' ,alpha = 0.5) plt.show() |
Blue dots are actual data, red are noise and yellow are discovered clusters.
