# createns

Create nearest neighbor searcher object

## Syntax

``NS = createns(X)``
``NS = createns(X,Name,Value)``

## Description

example

````NS = createns(X)` creates either an `ExhaustiveSearcher` or `KDTreeSearcher` model object using the n-by-K numeric matrix of the training data `X`.```

example

````NS = createns(X,Name,Value)` specifies additional options using one or more name-value pair arguments. For example, you can specify `NSMethod` to determine which type of object to create.```

## Examples

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```load fisheriris X = meas; [n,k] = size(X)```
```n = 150 ```
```k = 4 ```

`X` has 150 observations and 4 predictors.

Prepare an exhaustive nearest neighbor searcher using the entire data set as training data.

`Mdl1 = ExhaustiveSearcher(X)`
```Mdl1 = ExhaustiveSearcher with properties: Distance: 'euclidean' DistParameter: [] X: [150x4 double] ```

`Mdl1` is an `ExhaustiveSearcher` model object, and its properties appear in the Command Window. The object contains information about the trained algorithm, such as the distance metric. You can alter property values using dot notation.

Alternatively, you can prepare an exhaustive nearest neighbor searcher by using `createns` and specifying `'exhaustive'` as the search method.

`Mdl2 = createns(X,'NSMethod','exhaustive')`
```Mdl2 = ExhaustiveSearcher with properties: Distance: 'euclidean' DistParameter: [] X: [150x4 double] ```

`Mdl2` is also an `ExhaustiveSearcher` model object, and it is equivalent to `Mdl1`.

To search `X` for the nearest neighbors to a batch of query data, pass the `ExhaustiveSearcher` model object and the query data to `knnsearch` or `rangesearch`.

Grow a four-dimensional Kd-tree that uses the Euclidean distance.

```load fisheriris X = meas; [n,k] = size(X)```
```n = 150 ```
```k = 4 ```

`X` has 150 observations and 4 predictors.

Grow a four-dimensional Kd-tree using the entire data set as training data.

`Mdl1 = KDTreeSearcher(X)`
```Mdl1 = KDTreeSearcher with properties: BucketSize: 50 Distance: 'euclidean' DistParameter: [] X: [150x4 double] ```

`Mdl1` is a `KDTreeSearcher` model object, and its properties appear in the Command Window. The object contains information about the grown four-dimensional Kd-tree, such as the distance metric. You can alter property values using dot notation.

Alternatively, you can grow a Kd-tree by using `createns`.

`Mdl2 = createns(X)`
```Mdl2 = KDTreeSearcher with properties: BucketSize: 50 Distance: 'euclidean' DistParameter: [] X: [150x4 double] ```

`Mdl2` is also a `KDTreeSearcher` model object, and it is equivalent to `Mdl1`. Because `X` has four columns and the default distance metric is Euclidean, `createns` creates a `KDTreeSearcher` model by default.

To find the nearest neighbors in `X` to a batch of query data, pass the `KDTreeSearcher` model object and the query data to `knnsearch` or `rangesearch`.

Grow a Kd-tree that uses the Minkowski distance with an exponent of five.

Load Fisher's iris data set. Create a variable for the petal dimensions.

```load fisheriris X = meas(:,3:4);```

Grow a Kd-tree. Specify the Minkowski distance with an exponent of five.

`Mdl = createns(X,'Distance','minkowski','P',5)`
```Mdl = KDTreeSearcher with properties: BucketSize: 50 Distance: 'minkowski' DistParameter: 5 X: [150x2 double] ```

Because `X` has two columns and the distance metric is Minkowski, `createns` creates a `KDTreeSearcher` model object by default.

Create an exhaustive searcher object by using the `createns` function. Pass the object and query data to the `knnsearch` function to find k-nearest neighbors.

`load fisheriris`

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

```rng('default'); % 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 an exhaustive nearest neighbor searcher using the training data. Specify the Mahalanobis distance for finding nearest neighbors.

`Mdl = createns(X,'Distance','mahalanobis')`
```Mdl = ExhaustiveSearcher with properties: Distance: 'mahalanobis' DistParameter: [4x4 double] X: [145x4 double] ```

Because the distance metric is Mahalanobis, `createns` creates an `ExhaustiveSearcher` model object by default.

The software uses the covariance matrix of the predictors (columns) in the training data for computing the Mahalanobis distance. To display this value, use `Mdl.DistParameter`.

`Mdl.DistParameter`
```ans = 4×4 0.6547 -0.0368 1.2320 0.5026 -0.0368 0.1914 -0.3227 -0.1193 1.2320 -0.3227 3.0671 1.2842 0.5026 -0.1193 1.2842 0.5800 ```

Find the indices of the training data (`Mdl.X`) that are the two nearest neighbors of each point in the query data (`Y`).

`IdxNN = knnsearch(Mdl,Y,'K',2)`
```IdxNN = 5×2 5 6 98 95 104 128 135 65 102 115 ```

Each row of `IdxNN` corresponds to a query data observation. The column order corresponds to the order of the nearest neighbors with respect to ascending distance. For example, based on the Mahalanobis metric, the second nearest neighbor of `Y(3,:)` is `X(128,:)`.

## Input Arguments

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Training data, specified as a numeric matrix. `X` has n rows, each corresponding to an observation (that is, an instance or example), and K columns, each corresponding to a predictor (that is, a feature).

Data Types: `single` | `double`

### Name-Value Arguments

Specify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose `Name` in quotes.

Example: `NS = createns(X,'Distance','mahalanobis')` creates an `ExhaustiveSearcher` model object that uses the Mahalanobis distance metric when searching for nearest neighbors.

For Exhaustive and Kd-Tree Nearest Neighbor Searchers

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Nearest neighbor search method used to define the type of object created, specified as the comma-separated pair consisting of `'NSMethod'` and `'kdtree'` or `'exhaustive'`.

The default value is `'kdtree'` when these three conditions are true:

• The number of columns of `X` (K) is less than or equal to 10 (that is, K ≤ 10).

• `X` is not sparse.

• `Distance` is `'euclidean'`, `'cityblock'`, `'chebychev'`, or `'minkowski'`.

Otherwise, the default value is `'exhaustive'`.

Example: `'NSMethod','exhaustive'`

Distance metric used when you call `knnsearch` or `rangesearch` to find nearest neighbors for future query points, specified as a character vector or string scalar of the distance metric name, or a function handle.

For both types of nearest neighbor searchers, `createns` 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 argument.

If `createns` uses the exhaustive search algorithm (`'NSMethod'` is `'exhaustive'`), then `createns` 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)
`'fasteuclidean'`Euclidean distance computed by using an alternative algorithm that saves time when the number of predictors is at least 10. In some cases, this faster algorithm can reduce accuracy. Algorithms starting with `'fast'` do not support sparse data. For details, see Algorithms.
`'fastseuclidean'`Standardized Euclidean distance computed by using an alternative algorithm that saves time when the number of predictors is at least 10. In some cases, this faster algorithm can reduce accuracy. Algorithms starting with `'fast'` do not support sparse data. For details, see Algorithms.
`'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
`'seuclidean'`Standardized Euclidean distance
`'spearman'`One minus the sample Spearman's rank correlation between observations (treated as sequences of values)

If `createns` uses the exhaustive search algorithm (`'NSMethod'` is `'exhaustive'`), then you can also specify a function handle for a custom distance metric by using `@` (for example, `@distfun`). A 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 `X` or from the query points `Y`, where K is the number of columns in `X`.

• An m-by-K matrix `ZJ` containing multiple rows of `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'`

Data Types: `char` | `string` | `function_handle`

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`

For Exhaustive Nearest Neighbor Searchers

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Covariance matrix for the Mahalanobis distance metric, specified as the comma-separated pair consisting of `'Cov'` and a K-by-K positive definite matrix, where K is the number of columns in `X`. This argument is valid only if `'Distance'` is `'mahalanobis'`.

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 of length K, where K is the number of columns in `X`. The software scales each difference between the training and query data using the corresponding element of `Scale`. This argument is valid only if `'Distance'` is `'seuclidean'`.

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

Data Types: `single` | `double`

For Nearest Neighbor Searchers Using Kd-Tree

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Maximum number of data points in each leaf node of the Kd-tree, specified as the comma-separated pair consisting of `'BucketSize'` and a positive integer.

This argument is valid only when you create a `KDTreeSearcher` model object.

Example: `'BucketSize',10`

Data Types: `single` | `double`

## Output Arguments

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Nearest neighbor searcher, returned as an `ExhaustiveSearcher` model object or a `KDTreeSearcher` model object.

Once you create a nearest neighbor searcher model object, you can find the neighboring points in the training data to the query data by performing a nearest neighbor search using `knnsearch` or a radius search using `rangesearch`.

## Algorithms

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### Fast Euclidean Distance Algorithm

The values of the `Distance` argument that begin `fast` (such as `'fasteuclidean'` and `'fastseuclidean'`) calculate Euclidean distances using an algorithm that uses extra memory to save computational time. This algorithm is named "Euclidean Distance Matrix Trick" in Albanie [1] and elsewhere. Internal testing shows that this algorithm saves time when the number of predictors is at least 10. Algorithms starting with `'fast'` do not support sparse data.

To find the matrix D of distances between all the points xi and xj, where each xi has n variables, the algorithm computes distance using the final line in the following equations:

`$\begin{array}{c}{D}_{i,j}^{2}=‖{x}_{i}-{x}_{j}{‖}^{2}\\ ={\left(}^{{x}_{i}}\left({x}_{i}-{x}_{j}\right)\\ =‖{x}_{i}{‖}^{2}-2{x}_{i}^{T}{x}_{j}+‖{x}_{j}{‖}^{2}.\end{array}$`

The matrix ${x}_{i}^{T}{x}_{j}$ in the last line of the equations is called the Gram matrix. Computing the set of squared distances is faster, but slightly less numerically stable, when you compute and use the Gram matrix instead of computing the squared distances by squaring and summing. For a discussion, see Albanie [1].

## References

[1] Albanie, Samuel. Euclidean Distance Matrix Trick. June, 2019. Available at https://www.robots.ox.ac.uk/%7Ealbanie/notes/Euclidean_distance_trick.pdf.

## Version History

Introduced in R2010a

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