rangesearch

Find all neighbors within specified distance using searcher object

Description

example

Idx = rangesearch(Mdl,Y,r) searches for all neighbors (i.e., points, rows, or observations) in Mdl.X within radius r of each point (i.e., row or observation) in the query data Y using an exhaustive search or a Kd-tree. rangesearch returns Idx, which is a column vector of the indices of Mdl.X within r units.

example

Idx = rangesearch(Mdl,Y,r,Name,Value) returns the indices of the observation in Mdl.X within radius r of each observation in Y with additional options specified by one or more Name,Value pair arguments. For example, you can specify to use a different distance metric than is stored in Mdl.Distance or a different distance metric parameter than is stored in Mdl.DistParameter.

example

[Idx,D] = rangesearch(___) additionally returns the matrix D using any of the input arguments in the previous syntaxes. D contains the distances between the observations in Mdl.X within radius r of each observation in Y. By default, the function arranges the columns of D in ascending order by closeness, with respect to the distance metric.

Examples

collapse all

rangesearch accepts ExhaustiveSearcher or KDTreeSearcher model objects to search the training data for the nearest neighbors to the query data. An ExhaustiveSearcher model invokes the exhaustive searcher algorithm, and a KDTreeSearcher model defines a Kd-tree, which rangesearch uses to search for nearest neighbors.

Load Fisher's iris data set. Randomly reserve five observations from the data for query data. Focus on the petal dimensions.

load fisheriris
rng(1); % For reproducibility
n = size(meas,1);
idx = randsample(n,5);
X = meas(~ismember(1:n,idx),3:4); % Training data
Y = meas(idx,3:4);                % Query data

Grow a default two-dimensional Kd-tree.

MdlKDT = KDTreeSearcher(X)
MdlKDT = 
  KDTreeSearcher with properties:

       BucketSize: 50
         Distance: 'euclidean'
    DistParameter: []
                X: [145x2 double]

MdlKDT is a KDTreeSearcher model object. You can alter its writable properties using dot notation.

Prepare an exhaustive nearest neighbor searcher.

MdlES = ExhaustiveSearcher(X)
MdlES = 
  ExhaustiveSearcher with properties:

         Distance: 'euclidean'
    DistParameter: []
                X: [145x2 double]

MdlES is an ExhaustiveSearcher model object. It contains the options, such as the distance metric, to use to find nearest neighbors.

Alternatively, you can grow a Kd-tree or prepare an exhaustive nearest neighbor searcher using createns.

Search training data for the nearest neighbor indices that correspond to each query observation that are within a 0.5 cm radius. Conduct both types of searches and use the default settings.

r = 0.15; % Search radius
IdxKDT = rangesearch(MdlKDT,Y,r);
IdxES = rangesearch(MdlES,Y,r);
[IdxKDT IdxES]
ans=5×2 cell
    {1x27 double}    {1x27 double}
    {[       13]}    {[       13]}
    {1x27 double}    {1x27 double}
    {1x2  double}    {1x2  double}
    {1x0  double}    {1x0  double}

IdxKDT and IdxES are cell arrays of vectors corresponding to the indices of X that are within 0.15 cm of the observations in Y. Each row of the index matrices corresponds to a query observation.

Compare the results between the methods.

cellfun(@isequal,IdxKDT,IdxES)
ans = 5x1 logical array

   1
   1
   1
   1
   1

In this case, the results are the same.

Plot the results for the setosa irises.

setosaIdx = strcmp(species(~ismember(1:n,idx)),'setosa');
XSetosa = X(setosaIdx,:);
ySetosaIdx = strcmp(species(idx),'setosa');
YSetosa = Y(ySetosaIdx,:);

figure;
plot(XSetosa(:,1),XSetosa(:,2),'.k');
hold on;
plot(YSetosa(:,1),YSetosa(:,2),'*r');
for j = 1:sum(ySetosaIdx)
    c = YSetosa(j,:);
    circleFun = @(x1,x2)r^2 - (x1 - c(1)).^2 - (x2 - c(2)).^2;
    fimplicit(circleFun,[c(1) + [-1 1]*r, c(2) + [-1 1]*r],'b-')
end
xlabel 'Petal length (cm)';
ylabel 'Petal width (cm)';
title 'Setosa Petal Measurements';
legend('Observations','Query Data','Search Radius');
axis equal
hold off

Load Fisher's iris data set.

load fisheriris

Remove five irises randomly from the predictor data to use as a query set.

rng(1);                     % For reproducibility
n = size(meas,1);           % Sample size
qIdx = randsample(n,5);     % Indices of query data
X = meas(~ismember(1:n,qIdx),:);
Y = meas(qIdx,:);

Prepare a default exhaustive nearest neighbor searcher.

Mdl = ExhaustiveSearcher(X)
Mdl = 
  ExhaustiveSearcher with properties:

         Distance: 'euclidean'
    DistParameter: []
                X: [145x4 double]

Mdl is an ExhaustiveSearcher model.

Find the indices of the training data (X) that are within 0.15 cm of each point in the query data (Y). Specify that the distances are with respect to the Mahalanobis metric.

r = 1;
Idx = rangesearch(Mdl,Y,r,'Distance','mahalanobis')
Idx=5×1 cell
    {1x15 double}
    {1x5  double}
    {1x6  double}
    {[       84]}
    {[       69]}

Idx{3}
ans = 1×6

     1    34    33    22    24     2

Each cell of Idx corresponds to a query data observation and contains in X a vector of indices of the neighbors within 0.15cm of the query data. rangesearch arranges the indices in ascending order by distance. For example, using the Mahalanobis distance, the second nearest neighbor of Y(3,:) is X(34,:).

Load Fisher's iris data set.

load fisheriris

Remove five irises randomly from the predictor data to use as a query set.

rng(4);                     % For reproducibility
n = size(meas,1);           % Sample size
qIdx = randsample(n,5);     % Indices of query data
X = meas(~ismember(1:n,qIdx),:);
Y = meas(qIdx,:);

Grow a four-dimensional Kd-tree using the training data. Specify to use the Minkowski distance for finding nearest neighbors.

Mdl = KDTreeSearcher(X);

Mdl is a KDTreeSearcher model. By default, the distance metric for finding nearest neighbors is the Euclidean metric.

Find the indices of the training data (X) that are within 0.5 cm from each point in the query data (Y).

r = 0.5;
[Idx,D] = rangesearch(Mdl,Y,r);

Idx and D are five-element cell arrays of vectors. The vector values in Idx are the indices in X. The X indices represent the observations that are within 0.5 cm of the query data, Y. D contains the distances that correspond to the observations.

Display the results for query observation 3.

Idx{3}
ans = 1×2

   127   122

D{3}
ans = 1×2

    0.2646    0.4359

The closest observation to Y(3,:) is X(127,:), which is 0.2646 cm away. The next closest is X(122,:), which is 0.4359 cm away. All other observations are greater than 0.5 cm away from Y(5,:).

Input Arguments

collapse all

Nearest neighbor searcher, specified as an ExhaustiveSearcher or KDTreeSearcher model object, respectively.

If Mdl is an ExhaustiveSearcher model, then rangesearch searches for nearest neighbors using an exhaustive search. Otherwise, rangesearch uses the grown Kd-tree to search for nearest neighbors.

Query data, specified as a numeric matrix.

Y is an m-by-K matrix. Rows of Y correspond to observations (i.e., examples), and columns correspond to predictors (i.e., variables or features). Y must have the same number of columns as the training data stored in Mdl.X.

Data Types: single | double

Search radius around each point in the query data, specified as a nonnegative scalar.

rangesearch finds all observations in Mdl.X that are within distance r of each observation in Y. The property Mdl.Distance stores the distance.

Data Types: single | double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'Distance','minkowski','P',3 specifies to find all observations in Mdl.X within distance r of each observation in Y, using the Minkowski distance metric with exponent 3.

For Both Nearest Neighbor Searchers

collapse all

Distance metric used to find neighbors of the training data to the query observations, specified as the comma-separated pair consisting of 'Distance' and a character vector, string scalar, or function handle.

For both types of nearest neighbor searchers, rangesearch supports these distance metrics.

ValueDescription
'chebychev'Chebychev distance (maximum coordinate difference).
'cityblock'City block distance.
'euclidean'Euclidean distance.
'minkowski'Minkowski distance. The default exponent is 2. To specify a different exponent, use the 'P' name-value pair argument.

If Mdl is an ExhaustiveSearcher model object, then rangesearch also supports these distance metrics.

ValueDescription
'correlation'One minus the sample linear correlation between observations (treated as sequences of values).
'cosine'One minus the cosine of the included angle between observations (treated as row vectors).
'hamming'Hamming distance, which is the percentage of coordinates that differ.
'jaccard'One minus the Jaccard coefficient, which is the percentage of nonzero coordinates that differ.
'mahalanobis'Mahalanobis distance, computed using a positive definite covariance matrix. To change the value of the covariance matrix, use the 'Cov' name-value pair argument.
'seuclidean'Standardized Euclidean distance. Each coordinate difference between rows in Mdl.X and the query matrix is scaled by dividing by the corresponding element of the standard deviation computed from Mdl.X. To specify another scaling, use the 'Scale' name-value pair argument.
'spearman'One minus the sample Spearman's rank correlation between observations (treated as sequences of values).

If Mdl is an ExhaustiveSearcher model object, then you can also specify a function handle for a custom distance metric by using @ (for example, @distfun). The custom distance function must:

  • Have the form function D2 = distfun(ZI,ZJ).

  • Take as arguments:

    • A 1-by-K vector ZI containing a single row from Mdl.X or Y, where K is the number of columns of Mdl.X.

    • An m-by-K matrix ZJ containing multiple rows of Mdl.X or Y, where m is a positive integer.

  • Return an m-by-1 vector of distances D2, where D2(j) is the distance between the observations ZI and ZJ(j,:).

For more details, see Distance Metrics.

Example: 'Distance','minkowski'

Exponent for the Minkowski distance metric, specified as the comma-separated pair consisting of 'P' and a positive scalar. This argument is valid only if 'Distance' is 'minkowski'.

Example: 'P',3

Data Types: single | double

Flag to sort returned indices according to distance, specified as the comma-separated pair consisting of 'SortIndices' and either true (1) or false (0).

For faster performance when Y contains many observations that have many nearest points, you can set SortIndices to false. In this case, rangesearch returns the indices of the nearest points in no particular order. When SortIndices is true, the function arranges the indices of the nearest points in ascending order by distance.

Example: 'SortIndices',false

Data Types: logical

For Exhaustive Nearest Neighbor Searchers

collapse all

Covariance matrix for the Mahalanobis distance metric, specified as the comma-separated pair consisting of 'Cov' and a positive definite matrix. Cov is a K-by-K matrix, where K is the number of columns of Mdl.X. If you specify Cov and do not specify 'Distance','mahalanobis', then rangesearch returns an error message.

Example: 'Cov',eye(3)

Data Types: single | double

Scale parameter value for the standardized Euclidean distance metric, specified as the comma-separated pair consisting of 'Scale' and a nonnegative numeric vector. Scale has length K, where K is the number of columns of Mdl.X.

The software scales each difference between the training and query data using the corresponding element of Scale. If you specify Scale and do not specify 'Distance','seuclidean', then rangesearch returns an error message.

Example: 'Scale',quantile(Mdl.X,0.75) - quantile(Mdl.X,0.25)

Data Types: single | double

Note

If you specify 'Distance', 'Cov', 'P', or 'Scale', then Mdl.Distance and Mdl.DistParameter do not change value.

Output Arguments

collapse all

Training data indices of nearest neighbors, returned as a cell array of numeric vectors.

Idx is an m-by-1 cell array such that cell j (Idx{j}) contains an mj-dimensional vector of indices of the observations in Mdl.X that are within r units to the query observation Y(j,:). If SortIndices is true, then rangesearch arranges the elements of the vectors in ascending order by distance.

Distances of the neighbors to the query data, returned as a numeric matrix or cell array of numeric vectors.

D is an m-by-1 cell array such that cell j (D{j}) contains an mj-dimensional vector of the distances that the observations in Mdl.X are from the query observation Y(j,:). All elements of the vector are less than r. If SortIndices is true, then rangesearch arranges the elements of the vectors in ascending order.

Tips

knnsearch finds the k (positive integer) points in Mdl.X that are k-nearest for each Y point. In contrast, rangesearch finds all the points in Mdl.X that are within distance r (positive scalar) of each Y point.

Alternative Functionality

rangesearch is an object function that requires an ExhaustiveSearcher or a KDTreeSearcher model object, query data, and a distance. Under equivalent conditions, rangesearch returns the same results as rangesearch when you specify the name-value pair argument 'NSMethod','exhaustive' or 'NSMethod','kdtree', respectively.

Extended Capabilities

Introduced in R2011b