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Class Definition: ExhaustiveSearcher

Class: ExhaustiveSearcher

Exhaustive nearest neighbor searcher class.

The ExhaustiveSearcher class implements an exhaustive search algorithm for nearest neighbor queries. It stores training data and supports various distance metrics along with their parameter values for performing an exhaustive search. The exhaustive search algorithm computes the distance from each query point to all the points in the training data and facilitates a nearest neighbor search using knnsearch or a radius search using rangesearch.

You can either use the ExhaustiveSearcher class constructor or the createns function to create an ExhaustiveSearcher object.

See also: createns, KDTreeSearcher, hnswSearcher, knnsearch, rangesearch

Source Code: ExhaustiveSearcher

Properties

  • For "minkowski", a positive scalar exponent (default 2).
  • For "seuclidean", a nonnegative vector of scaling factors matching the number of columns in X (default is standard deviation of X).
  • For "mahalanobis", a positive definite covariance matrix matching the dimensions of X (default is cov (X)).
  • Empty for other metrics or custom functions.

Methods

ExhaustiveSearcher: obj = ExhaustiveSearcher (X)
ExhaustiveSearcher: obj = ExhaustiveSearcher (X, name, value)

obj = ExhaustiveSearcher (X) constructs an ExhaustiveSearcher object with training data X using the default "euclidean" distance metric. X must be an N×P numeric matrix, where rows represent observations and columns represent features.

obj = ExhaustiveSearcher (X, name, value) allows customization through name-value pairs:

NameValue
"Distance"Distance metric, specified as a character vector (e.g., "euclidean", "minkowski") or a function handle. Default is "euclidean". See pdist2 for supported metrics.
"P"a positive scalar specifying the exponent for the Minkowski distance. Valid only when "Distance" is "minkowski". Default is 2.
"Scale"a nonnegative vector with the same number of elements as the columns in X specifying the scale parameter for the standardized Euclidean distance. Valid only when "Distance" is "seuclidean". Default is std (X).
"Cov"a positive definite matrix matching the number of columns in X specifying the covariance matrix for the Mahalanobis distance. Valid only when "Distance" is "mahalanobis". Default is cov (X).

See also: ExhaustiveSearcher, knnsearch, rangesearch, pdist2

ExhaustiveSearcher: [idx, D] = knnsearch (obj, Y)
ExhaustiveSearcher: [idx, D] = knnsearch (obj, Y, name, value)

[idx, D] = knnsearch (obj, Y) returns the indices idx and distances D of the nearest neighbor in obj.X to each point in Y, using the distance metric specified in obj.Distance.

  • obj is an ExhaustiveSearcher object.
  • Y is an M×P numeric matrix of query points, where P must match the number of columns in obj.X.

[idx, D] = knnsearch (obj, Y, name, value) allows additional options via name-value pairs:

NameValue
"K"A positive integer specifying the number of nearest neighbors to find. Default is 1.
"IncludeTies"Logical flag indicating whether to include all neighbors tied with the Kth smallest distance. Default is false. If true, idx and D are cell arrays.

idx contains the indices of the nearest neighbors in obj.X. D contains the corresponding distances.

See also: ExhaustiveSearcher, rangesearch, pdist2

ExhaustiveSearcher: [idx, D] = rangesearch (obj, Y, r)
ExhaustiveSearcher: [idx, D] = rangesearch (obj, Y, r, name, value)

[idx, D] = rangesearch (obj, Y, r) returns the indices idx and distances D of all points in obj.X within radius r of each point in Y, using the distance metric specified in obj.Distance.

  • obj is an ExhaustiveSearcher object.
  • Y is an M×P numeric matrix of query points, where P must match the number of columns in obj.X.
  • r is a nonnegative scalar specifying the search radius.

[idx, D] = rangesearch (…, name, value) allows additional options via name-value pairs:

NameValue
"SortIndices"Logical flag indicating whether to sort the indices by distance. Default is true.

idx and D are cell arrays where each cell contains the indices and distances for one query point in Y.

See also: ExhaustiveSearcher, knnsearch, pdist2

Example: 1

  

 ## Demo to verify implementation using fisheriris dataset
 load fisheriris
 rng('default');
 numSamples = size (meas, 1);
 queryIndices = [20, 95, 123, 136, 138];
 dataPoints = meas(~ismember (1:numSamples, queryIndices), :);
 queryPoints = meas(queryIndices, :);
 searchModel = ExhaustiveSearcher (dataPoints, 'Distance', 'mahalanobis')
 mahalanobisParam = searchModel.DistParameter
 searchRadius = 3;
 nearestNeighbors = knnsearch (searchModel, queryPoints, "K", 2)
 neighborsInRange = rangesearch (searchModel, queryPoints, searchRadius)

searchModel =

  ExhaustiveSearcher with properties:

                 Distance: 'mahalanobis'
            DistParameter: [4x4 double]
                        X: [145x4 double]
mahalanobisParam =

   0.654708  -0.036803   1.231971   0.502620
  -0.036803   0.191363  -0.322715  -0.119293
   1.231971  -0.322715   3.067148   1.284234
   0.502620  -0.119293   1.284234   0.579984

nearestNeighbors =

     5     6
    98    95
   104   128
   135    65
   102   115

neighborsInRange =
{
  [1,1] =

   Columns 1 through 16:

       5     6    21    46    48    44    37    22     1     8    11    27    26    33    18    12

   Columns 17 through 32:

      39     7    40    49    32    47    19     3    28    29    17    20    43    23    42    16

   Columns 33 through 48:

      30     4    56    34    85    24    10    51    38    61    13    88    14    35    25    78

   Columns 49 through 64:

      91    95     2   125    70     9    45    64   134    31    98    36    94   122    15    96

   Columns 65 through 80:

     109    63    66   115    86   145    82   143    77   103   139    74    71    55   124    59

   Columns 81 through 96:

     126    65   131    75    92   102    83    52   110   111    84   100   138    67   119    58

   Columns 97 and 98:

      79    89

  [2,1] =

   Columns 1 through 16:

      98    95    83    88    78    89    55    63    69    91    94    90    82    92    59    80

   Columns 17 through 32:

     100   138   131    57    66    67    81    61   125   102   115   145   134    96   110   118

   Columns 33 through 48:

     126    93     4    53    64    29    30    72     9    73    47    79    56    38   107   103

   Columns 49 through 64:

     124    42    70    51    14    84    10    12    13    34     3   121   130    71    85   112

   Columns 65 through 80:

       7     8    25    74   120    60   143    24    77    49    39    26   122    54     2    37

   Columns 81 through 96:

      58    45     5    97    86   109     1    27   139   105   101    23   111   142    20    22

   Columns 97 through 112:

      18    75    28    40    44    46    52    48    21    35    65    76   123    62    11    43

   Columns 113 through 121:

     132   135    87   119   106     6   127   128   104

  [3,1] =

   Columns 1 through 16:

     104   128   127   106   117   123    58    52    76    50   107    86    74   101    65    75

   Columns 17 through 32:

      77   131    96    72    54    73   115   129    51    63    67    91    71    87   110    92

   Columns 33 through 35:

      62   118    82

  [4,1] =

   Columns 1 through 16:

     135    65    75   101   111   117    77    54    50    86   137    52    76   119   141   128

   Columns 17 through 32:

      74    71   121   142   143   136    58   124    51   109   110   104    68    87    96    31

   Columns 33 and 34:

      36   139

  [5,1] =

   Columns 1 through 16:

     102   115    91    94    63    56   145    83    88    95    55   131    66    85   122    78

   Columns 17 through 32:

      70   103   125    73    98    84   134   123    51    90   126    67   100   138    61    96

   Columns 33 through 48:

     139   110   107    24    44   101    12   106   109    77    82   130   143    86    59    46

   Columns 49 through 64:

      37   104   127    29    69    92    58    72   132    89    99   116   124    52    74    64

   Columns 65 through 80:

       5     8   111     4    30   120    47     7   144   121   118    42   133    39    80    48

   Columns 81 through 96:

      32    81    71   119    27    10     6    54     1    26    75   108    57   128    21     3

   Columns 97 through 109:

      65    79    20    11   112    34    50    49   135    22    38   129     9

}

Example: 2

  

 ## Create an ExhaustiveSearcher with Euclidean distance
 X = [1, 2; 3, 4; 5, 6];
 obj = ExhaustiveSearcher (X);
 ## Find the nearest neighbor to [2, 3]
 Y = [2, 3];
 [idx, D] = knnsearch (obj, Y);
 disp ("Nearest neighbor index:"); disp (idx);
 disp ("Distance:"); disp (D);
 ## Find all points within radius 2
 [idx, D] = rangesearch (obj, Y, 2);
 disp ("Indices within radius:"); disp (idx);
 disp ("Distances:"); disp (D);

Nearest neighbor index:
1
Distance:
1.4142
Indices within radius:
{
  [1,1] =

     1   2

}
Distances:
{
  [1,1] =

     1.4142   1.4142

}

Example: 3

  

 ## Create an ExhaustiveSearcher with Minkowski distance (P=1)
 X = [0, 0; 1, 0; 0, 1];
 obj = ExhaustiveSearcher (X, "Distance", "minkowski", "P", 1);
 ## Find the 2 nearest neighbors to [0.5, 0.5]
 Y = [0.5, 0.5];
 [idx, D] = knnsearch (obj, Y, "K", 2);
 disp ("Nearest neighbor indices:"); disp (idx);
 disp ("Distances:"); disp (D);

Nearest neighbor indices:
   1   2
Distances:
   1   1

Example: 4

  

 rng(42);
 disp('Demonstrating ExhaustiveSearcher');

 n = 100;
 mu1 = [0.3, 0.3];
 mu2 = [0.7, 0.7];
 sigma = 0.1;
 X1 = mu1 + sigma * randn(n/2, 2);
 X2 = mu2 + sigma * randn(n/2, 2);
 X = [X1; X2];

 obj = ExhaustiveSearcher(X);

 Y = [0.3, 0.3; 0.7, 0.7; 0.5, 0.5];

 K = 5;
 [idx, D] = knnsearch(obj, Y, "K", K);

 disp('For the first query point:');
 disp(['Query point: ', num2str(Y(1,:))]);
 disp('Indices of nearest neighbors:');
 disp(idx(1,:));
 disp('Distances:');
 disp(D(1,:));

 figure;
 scatter(X(:,1), X(:,2), 36, 'b', 'filled'); % Training points
 hold on;
 scatter(Y(:,1), Y(:,2), 36, 'r', 'filled'); % Query points
 for i = 1:size(Y,1)
     query = Y(i,:);
     neighbors = X(idx(i,:), :);
     for j = 1:K
         plot([query(1), neighbors(j,1)], [query(2), neighbors(j,2)], 'k-');
     end
 end
 hold off;
 title('K Nearest Neighbors with ExhaustiveSearcher');
 xlabel('X1');
 ylabel('X2');

 r = 0.15;
 [idx, D] = rangesearch(obj, Y, r);

 disp('For the first query point in rangesearch:');
 disp(['Query point: ', num2str(Y(1,:))]);
 disp('Indices of points within radius:');
 disp(idx{1});
 disp('Distances:');
 disp(D{1});

 figure;
 scatter(X(:,1), X(:,2), 36, 'b', 'filled');
 hold on;
 scatter(Y(:,1), Y(:,2), 36, 'r', 'filled');
 theta = linspace(0, 2*pi, 100);
 for i = 1:size(Y,1)
     center = Y(i,:);
     x_circle = center(1) + r * cos(theta);
     y_circle = center(2) + r * sin(theta);
     plot(x_circle, y_circle, 'g-');
     % Highlight points within radius
     if ~isempty(idx{i})
         in_radius = X(idx{i}, :);
         scatter(in_radius(:,1), in_radius(:,2), 36, 'g', 'filled');
     end
 end
 hold off;
 title('Points within Radius with ExhaustiveSearcher');
 xlabel('X1');
 ylabel('X2');

Demonstrating ExhaustiveSearcher
For the first query point:
Query point: 0.3         0.3
Indices of nearest neighbors:
   49   19   14   46   34
Distances:
   0.029932   0.040026   0.046845   0.051107   0.054789
For the first query point in rangesearch:
Query point: 0.3         0.3
Indices of points within radius:
 Columns 1 through 19:

   49   19   14   46   34   23   12   41    1    3   42   48   24    2   11   37   10   27   32

 Columns 20 through 34:

   20   44   40   39   21    7   31   45   30    4   16   47    9   29    8
Distances:
 Columns 1 through 9:

   0.029932   0.040026   0.046845   0.051107   0.054789   0.063517   0.067855   0.071365   0.073769

 Columns 10 through 18:

   0.075991   0.082686   0.084066   0.090008   0.095171   0.096337   0.096836   0.097593   0.098255

 Columns 19 through 27:

   0.098948   0.101780   0.108652   0.108983   0.114272   0.116760   0.120198   0.121721   0.122560

 Columns 28 through 34:

   0.127342   0.128062   0.128687   0.130208   0.136007   0.142870   0.143009
plotted figure

plotted figure