Estimate neighborhood clustering threshold
returns an estimate of the neighborhood clustering threshold,
epsilon = clusterDBSCAN.estimateEpsilon(
used in the density-based spatial clustering of applications with noise (DBSCAN)algorithm.
epsilon is computed from input data
X using a
k-nearest neighbor (k-NN) search.
MaxNumPoints set a range of
k-values for which epsilon is calculated. The range extends from
MinNumPoints – 1 through
MaxNumPoints – 1.
k is the number of neighbors of a point, which is one less than the
number of points in a neighborhood.
Estimate Epsilon from Data
Create simulated target data and use the
clusterDBSCAN.estimateEpsilon function to calculate an appropriate epsilon threshold.
Create the target data as xy Cartesian coordinates.
X = [randn(20,2) + [11.5,11.5]; randn(20,2) + [25,15]; ... randn(20,2) + [8,20]; 10*rand(10,2) + [20,20]];
Set the range of values for the k-NN search.
minNumPoints = 15; maxNumPoints = 20;
Estimate the clustering threshold epsilon and display its value on a plot.
Use the estimated Epsilon value, 3.62, in the
clusterDBSCAN clusterer. Then, plot the clusters.
clusterer = clusterDBSCAN('MinNumPoints',6,'Epsilon',3.62, ... 'EnableDisambiguation',false); [idx,cidx] = clusterer(X); plot(clusterer,X,idx)
X — Input feature data
real-valued N-by-P matrix
Input feature data, specified as a real-valued N-by-P matrix. The N rows correspond to feature points in a P-dimensional feature space. The P columns contain the values of the features over which clustering takes place. The DBSCAN algorithm can cluster any type of data with appropriate
Epsilon settings. For example, a two-column input can contain the xy Cartesian coordinates, or range and Doppler.
MinNumPoints — Starting value of k-NN search range
The starting value of the k-NN search range, specified as a
MinNumPoints is used to specify the starting
value of k in the k-NN search range. The starting
value of k is one less than
MaxNumPoints — Set end value of k-NN search range
The end value of k-NN search range, specified as a positive
MaxNumPoints is used to specify the ending value of
k in the k-NN search range. The ending value of
k is one less than
epsilon — Estimated epsilon
Estimated epsilon, returned as a positive scalar.
DBSCAN clustering requires a value for the neighborhood size parameter ε. The
clusterDBSCAN object and the
clusterDBSCAN.estimateEpsilon function use a
k-nearest-neighbor search to estimate a scalar epsilon. Let
D be the distance of any point P to its
kth nearest neighbor. Define a
Dk(P)-neighborhood as a
neighborhood surrounding P that contains its
k-nearest neighbors. There are k + 1 points in the
including the point P itself. An outline of the estimation algorithm
For each point, find all the points in its Dk(P)-neighborhood
Accumulate the distances in all Dk(P)-neighborhoods for all points into a single vector.
Sort the vector by increasing distance.
Plot the sorted k-dist graph, which is the sorted distance against point number.
Find the knee of the curve. The value of the distance at that point is an estimate of epsilon.
The figure here shows distance plotted against point index for k = 20. The knee occurs at approximately 1.5. Any points below this threshold belong to a cluster. Any points above this value are noise.
There are several methods to find the knee of the curve.
clusterDBSCAN.estimateEpsilon first define the line connecting the
first and last points of the curve. The ordinate of the point on the sorted
k-dist graph furthest from the line and perpendicular to the line
When you specify a range of k values, the algorithm averages the estimate epsilon values for all curves. This figure shows that epsilon is fairly insensitive to k for k ranging from 14 through 19.
To create a single k-NN distance graph, set the
MinNumPoints property equal to the
Choosing the Minimum and Maximum Number of Points
The purpose of
MinNumPoints is to smooth
the density estimates. Because a cluster is a maximal set of density-connected points, choose
smaller values when the expected number of detections in a cluster is unknown. However, smaller
values make the DBSCAN algorithm more susceptible to noise. A general guideline for choosing
MinNumPoints= 2P where P is the number of feature dimensions in
For data sets that have one or more of the following properties:
many noise points
large number of points,
MinNumPointscan often improve clustering results.
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