fitcknn

Fit k-nearest neighbor classifier

Syntax

Mdl = fitcknn(Tbl,ResponseVarName)

Mdl = fitcknn(Tbl,formula)

Mdl = fitcknn(Tbl,Y)

Mdl = fitcknn(X,Y)

Mdl = fitcknn(___,Name=Value)

[Mdl,AggregateOptimizationResults] = fitcknn(___)

Description

Mdl = fitcknn(Tbl,ResponseVarName) returns a k-nearest neighbor classification model based on the input variables (also known as predictors, features, or attributes) in the table Tbl and output (response) Tbl.ResponseVarName.

Mdl = fitcknn(Tbl,formula) returns a k-nearest neighbor classification model based on the input variables in the table Tbl. formula is an explanatory model of the response and a subset of predictor variables in Tbl.

Mdl = fitcknn(Tbl,Y) returns a k-nearest neighbor classification model based on the predictor variables in the table Tbl and response array Y.

Mdl = fitcknn(X,Y) returns a k-nearest neighbor classification model based on the predictor data X and response Y.

Mdl = fitcknn(___,Name=Value) fits a model with additional options specified by one or more name-value arguments, using any of the previous syntaxes. For example, you can specify the tie-breaking algorithm, distance metric, or observation weights.

[Mdl,AggregateOptimizationResults] = fitcknn(___) also returns AggregateOptimizationResults, which contains hyperparameter optimization results when you specify the OptimizeHyperparameters and HyperparameterOptimizationOptions name-value arguments. You must also specify the ConstraintType and ConstraintBounds options of HyperparameterOptimizationOptions. You can use this syntax to optimize on compact model size instead of cross-validation loss, and to perform a set of multiple optimization problems that have the same options but different constraint bounds.

Examples

Train k-Nearest Neighbor Classifier

Train a k-nearest neighbor classifier using Fisher's iris data, where k, the number of nearest neighbors in the predictors, is 5.

Load Fisher's iris data.

load fisheriris
X = meas;
Y = species;

X is a numeric matrix that contains four measurements for 150 irises. Y is a cell array of character vectors that contains the corresponding iris species.

Train a 5-nearest neighbor classifier. Standardize the noncategorical predictor data.

Mdl = fitcknn(X,Y,NumNeighbors=5,Standardize=true)

Mdl = 
  ClassificationKNN
             ResponseName: 'Y'
    CategoricalPredictors: []
               ClassNames: {'setosa'  'versicolor'  'virginica'}
           ScoreTransform: 'none'
          NumObservations: 150
                 Distance: 'euclidean'
             NumNeighbors: 5


  Properties, Methods

Mdl is a trained ClassificationKNN classifier.

To access the properties of Mdl, use dot notation.

Mdl.ClassNames

ans = 3×1 cell
    {'setosa'    }
    {'versicolor'}
    {'virginica' }

Mdl.Prior

ans = 1×3

    0.3333    0.3333    0.3333

Mdl.Prior contains the class prior probabilities, which you can specify using the Prior name-value argument in fitcknn. The order of the class prior probabilities corresponds to the order of the classes in Mdl.ClassNames. By default, the prior probabilities are the respective relative frequencies of the classes in the data.

You can also reset the prior probabilities after training. For example, set the prior probabilities to 0.5, 0.2, and 0.3, respectively.

Mdl.Prior = [0.5 0.2 0.3];

You can pass Mdl to predict to label new measurements or crossval to cross-validate the classifier.

Train k-Nearest Neighbor Classifier Using Minkowski Metric

Train a k-nearest neighbor classifier using the Minkowski distance metric.

Load Fisher's iris data set.

load fisheriris
X = meas;
Y = species;

X is a numeric matrix that contains four measurements for 150 irises. Y is a cell array of character vectors that contains the corresponding iris species.

Train a 3-nearest neighbors classifier using the Minkowski metric. To use the Minkowski metric, you must use an exhaustive searcher. Standardize the noncategorical predictor data.

Mdl = fitcknn(X,Y,NumNeighbors=3, ...
    NSMethod="exhaustive",Distance="minkowski", ...
    Standardize=true);

Mdl is a ClassificationKNN classifier.

Find the Minkowski distance exponent used to train Mdl.

Mdl.DistParameter

ans = 
2

You can modify a distance parameter after creating a ClassificationKNN object. For example, set the Minkowski distance exponent to 4.

Mdl.DistParameter = 4;
Mdl.DistParameter

ans = 
4

Train k-Nearest Neighbor Classifier Using Custom Distance Metric

Train a k-nearest neighbor classifier using the chi-square distance.

Load Fisher's iris data set.

load fisheriris
X = meas;
Y = species;

The chi-square distance between j-dimensional points x and z is

$$\chi (x,z)=\sqrt{{\displaystyle \sum _{j=1}^J{w}_j{(x_j-z_j)}^2}},$$

where $$w_j$$ is a weight associated with dimension j.

Specify the chi-square distance function. The distance function must:

• Take one row of X, for example, x, and the matrix Z.

• Compare x to each row of Z.

• Return a vector D of length $$n_z$$, where $$n_z$$ is the number of rows of Z. Each element of D is the distance between the observation corresponding to x and the observations corresponding to each row of Z.

chiSqrDist = @(x,Z,wt)sqrt(((x-Z).^2)*wt);

This example uses arbitrary weights for illustration.

Train a 3-nearest neighbor classifier. It is good practice to standardize noncategorical predictor data.

k = 3;
w = [0.3; 0.3; 0.2; 0.2];
KNNMdl = fitcknn(X,Y,Distance=@(x,Z)chiSqrDist(x,Z,w), ...
    NumNeighbors=k,Standardize=true);

KNNMdl is a ClassificationKNN classifier.

Cross validate the KNN classifier using the default 10-fold cross validation. Examine the classification error.

rng(1); % For reproducibility
CVKNNMdl = crossval(KNNMdl);
classError = kfoldLoss(CVKNNMdl)

classError = 
0.0600

CVKNNMdl is a ClassificationPartitionedModel classifier.

Compare the classifier with one that uses a different weighting scheme.

w2 = [0.2; 0.2; 0.3; 0.3];
CVKNNMdl2 = fitcknn(X,Y,Distance=@(x,Z)chiSqrDist(x,Z,w2), ...
    NumNeighbors=k,KFold=10,Standardize=true);
classError2 = kfoldLoss(CVKNNMdl2)

classError2 = 
0.0400

The second weighting scheme yields a classifier that has better out-of-sample performance.

Optimize Fitted KNN Classifier

Automatically optimize hyperparameters of a k-nearest neighbor classifier by using fitcknn.

Load the fisheriris data set.

load fisheriris
X = meas;
Y = species;

Find hyperparameters that minimize the 5-fold cross-validation loss by using automatic hyperparameter optimization.

For reproducibility, set the random seed and use the "expected-improvement-plus" acquisition function.

rng(1)
Mdl = fitcknn(X,Y,OptimizeHyperparameters="auto", ...
    HyperparameterOptimizationOptions= ...
    struct(AcquisitionFunctionName="expected-improvement-plus"))

|====================================================================================================================|
| Iter | Eval   | Objective   | Objective   | BestSoFar   | BestSoFar   | NumNeighbors |     Distance |  Standardize |
|      | result |             | runtime     | (observed)  | (estim.)    |              |              |              |
|====================================================================================================================|
|    1 | Best   |        0.04 |     0.41715 |        0.04 |        0.04 |           13 |    minkowski |         true |
|    2 | Accept |     0.19333 |     0.19157 |        0.04 |    0.046097 |            1 |  correlation |         true |
|    3 | Accept |    0.053333 |    0.081495 |        0.04 |    0.047573 |           14 |    chebychev |         true |
|    4 | Accept |    0.046667 |    0.068536 |        0.04 |    0.041053 |            2 |    minkowski |        false |
|    5 | Accept |    0.053333 |    0.053916 |        0.04 |    0.046782 |            7 |    minkowski |         true |
|    6 | Accept |     0.10667 |     0.12176 |        0.04 |    0.046422 |            2 |  mahalanobis |        false |
|    7 | Accept |    0.093333 |    0.044255 |        0.04 |    0.040581 |           75 |    minkowski |        false |
|    8 | Accept |     0.15333 |     0.04828 |        0.04 |    0.040008 |           75 |    minkowski |         true |
|    9 | Best   |        0.02 |    0.056142 |        0.02 |     0.02001 |            4 |    minkowski |        false |
|   10 | Accept |    0.026667 |    0.046662 |        0.02 |    0.020012 |            8 |    minkowski |        false |
|   11 | Accept |     0.21333 |    0.050638 |        0.02 |    0.020008 |           69 |    chebychev |         true |
|   12 | Accept |    0.053333 |    0.045234 |        0.02 |    0.020009 |            5 |    chebychev |         true |
|   13 | Accept |    0.053333 |    0.059507 |        0.02 |    0.020009 |            1 |    chebychev |         true |
|   14 | Accept |    0.053333 |    0.074969 |        0.02 |    0.020008 |            5 |   seuclidean |        false |
|   15 | Accept |    0.053333 |    0.048708 |        0.02 |    0.020008 |           21 |   seuclidean |        false |
|   16 | Accept |    0.053333 |    0.046055 |        0.02 |    0.020009 |            1 |   seuclidean |        false |
|   17 | Accept |     0.15333 |    0.046417 |        0.02 |    0.020007 |           75 |   seuclidean |        false |
|   18 | Accept |        0.02 |    0.046131 |        0.02 |    0.019969 |            5 |    minkowski |        false |
|   19 | Accept |     0.33333 |    0.091216 |        0.02 |    0.019898 |            2 |     spearman |        false |
|   20 | Accept |     0.23333 |    0.045818 |        0.02 |    0.019888 |           71 |  mahalanobis |        false |
|====================================================================================================================|
| Iter | Eval   | Objective   | Objective   | BestSoFar   | BestSoFar   | NumNeighbors |     Distance |  Standardize |
|      | result |             | runtime     | (observed)  | (estim.)    |              |              |              |
|====================================================================================================================|
|   21 | Accept |    0.046667 |    0.043897 |        0.02 |    0.019895 |            1 |    cityblock |         true |
|   22 | Accept |    0.053333 |    0.041483 |        0.02 |    0.019892 |            6 |    cityblock |         true |
|   23 | Accept |        0.12 |    0.052464 |        0.02 |    0.019895 |           75 |    cityblock |         true |
|   24 | Accept |        0.06 |    0.052353 |        0.02 |    0.019903 |            2 |    cityblock |        false |
|   25 | Accept |    0.033333 |    0.044571 |        0.02 |    0.019899 |           17 |    cityblock |        false |
|   26 | Accept |        0.12 |    0.041868 |        0.02 |    0.019907 |           74 |    cityblock |        false |
|   27 | Accept |    0.033333 |    0.048068 |        0.02 |    0.019894 |            7 |    cityblock |        false |
|   28 | Accept |        0.02 |    0.048772 |        0.02 |    0.019897 |            1 |    chebychev |        false |
|   29 | Accept |        0.02 |    0.051426 |        0.02 |    0.019891 |            4 |    chebychev |        false |
|   30 | Accept |        0.08 |    0.044348 |        0.02 |    0.019891 |           28 |    chebychev |        false |

__________________________________________________________
Optimization completed.
MaxObjectiveEvaluations of 30 reached.
Total function evaluations: 30
Total elapsed time: 11.3991 seconds
Total objective function evaluation time: 2.1537

Best observed feasible point:
    NumNeighbors    Distance     Standardize
    ____________    _________    ___________

         4          minkowski       false   

Observed objective function value = 0.02
Estimated objective function value = 0.020124
Function evaluation time = 0.056142

Best estimated feasible point (according to models):
    NumNeighbors    Distance     Standardize
    ____________    _________    ___________

         5          minkowski       false   

Estimated objective function value = 0.019891
Estimated function evaluation time = 0.059452

Mdl = 
  ClassificationKNN
                         ResponseName: 'Y'
                CategoricalPredictors: []
                           ClassNames: {'setosa'  'versicolor'  'virginica'}
                       ScoreTransform: 'none'
                      NumObservations: 150
    HyperparameterOptimizationResults: [1×1 BayesianOptimization]
                             Distance: 'minkowski'
                         NumNeighbors: 5


  Properties, Methods

The trained classifier Mdl corresponds to the best estimated feasible point and uses the same hyperparameter values for NumNeighbors, Distance, and Standardize.

Verify the results. Note that the Mu and Sigma properties of a ClassificationKNN object are empty when the k-nearest neighbor classifier does not use standardization.

bestEstimatedPoint = bestPoint(Mdl.HyperparameterOptimizationResults, ...
    Criterion="min-visited-upper-confidence-interval")

bestEstimatedPoint=1×3 table
    NumNeighbors    Distance     Standardize
    ____________    _________    ___________

         5          minkowski       false   

classifierProperties = table(Mdl.NumNeighbors,string(Mdl.Distance), ...
    struct(Means=Mdl.Mu,StandardDeviations=Mdl.Sigma), ...
    VariableNames=["NumNeighbors","Distance","Standardize"])

classifierProperties=1×3 table
    NumNeighbors     Distance      Standardize
    ____________    ___________    ___________

         5          "minkowski"    1×1 struct 

classifierProperties.Standardize

ans = struct with fields:
                 Means: []
    StandardDeviations: []

Input Arguments

Tbl — Sample data

table

Sample data used to train the model, specified as a table. Each row of Tbl corresponds to one observation, and each column corresponds to one predictor variable. Optionally, Tbl can contain one additional column for the response variable. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

• If Tbl contains the response variable, and you want to use all remaining variables in Tbl as predictors, then specify the response variable by using ResponseVarName.

• If Tbl contains the response variable, and you want to use only a subset of the remaining variables in Tbl as predictors, then specify a formula by using formula.

• If Tbl does not contain the response variable, then specify a response variable by using Y. The length of the response variable and the number of rows in Tbl must be equal.

ResponseVarName — Response variable name

name of variable in Tbl

Response variable name, specified as the name of a variable in Tbl.

You must specify ResponseVarName as a character vector or string scalar. For example, if the response variable Y is stored as Tbl.Y, then specify it as "Y". Otherwise, the software treats all columns of Tbl, including Y, as predictors when training the model.

The response variable must be a categorical, character, or string array; a logical or numeric vector; or a cell array of character vectors. If Y is a character array, then each element of the response variable must correspond to one row of the array.

A good practice is to specify the order of the classes by using the ClassNames name-value argument.

Data Types: char | string

formula — Explanatory model of response variable and subset of predictor variables

character vector | string scalar

Explanatory model of the response variable and a subset of the predictor variables, specified as a character vector or string scalar in the form "Y~x1+x2+x3". In this form, Y represents the response variable, and x1, x2, and x3 represent the predictor variables.

To specify a subset of variables in Tbl as predictors for training the model, use a formula. If you specify a formula, then the software does not use any variables in Tbl that do not appear in formula.

The variable names in the formula must be both variable names in Tbl (Tbl.Properties.VariableNames) and valid MATLAB^® identifiers. You can verify the variable names in Tbl by using the isvarname function. If the variable names are not valid, then you can convert them by using the matlab.lang.makeValidName function.

Data Types: char | string

Y — Class labels

categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors

Class labels, specified as a categorical, character, or string array, a logical or numeric vector, or a cell array of character vectors. Each row of Y represents the classification of the corresponding row of X.

The software considers NaN, '' (empty character vector), "" (empty string), <missing>, and <undefined> values in Y to be missing values. Consequently, the software does not train using observations with a missing response.

Data Types: categorical | char | string | logical | single | double | cell

X — Predictor data

numeric matrix

Predictor data, specified as numeric matrix.

Each row corresponds to one observation (also known as an instance or example), and each column corresponds to one predictor variable (also known as a feature).

The length of Y and the number of rows of X must be equal.

To specify the names of the predictors in the order of their appearance in X, use the PredictorNames name-value pair argument.

Data Types: double | single

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.

Example: fitcknn(Tbl,Y,NumNeighbors=3,NSMethod="exhaustive",Distance="minkowski") specifies a classifier for three-nearest neighbors using the nearest neighbor search method and the Minkowski metric.

Note

You cannot use any cross-validation name-value argument together with the OptimizeHyperparameters name-value argument. You can modify the cross-validation for OptimizeHyperparameters only by using the HyperparameterOptimizationOptions name-value argument.

Model Parameters

BreakTies — Tie-breaking algorithm

"smallest" (default) | "nearest" | "random"

Tie-breaking algorithm used by the predict method if multiple classes have the same smallest cost, specified as one of the following:

• "smallest" — Use the smallest index among tied groups.

• "nearest" — Use the class with the nearest neighbor among tied groups.

• "random" — Use a random tiebreaker among tied groups.

By default, ties occur when multiple classes have the same number of nearest points among the k nearest neighbors.

Example: BreakTies="nearest"

BucketSize — Maximum data points in node

50 (default) | positive integer value

Maximum number of data points in the leaf node of the Kd-tree, specified as a positive integer value. This argument is meaningful only when NSMethod is "kdtree".

Example: BucketSize=40

Data Types: single | double

CacheSize — Size in megabytes of cache allocated for Gram matrix

1e3 (default) | "maximal" | positive scalar

Since R2025a

Size in megabytes of the cache allocated for the Gram matrix, specified as "maximal" or a positive scalar. The software can use CacheSize only when the Distance value begins with fast.

If the CacheSize value is "maximal", then during prediction, the software attempts to allocate enough memory for the Gram matrix, whose size is n-by-m, where n is the number of rows in the training predictor data (X or Tbl), and m is the number of rows in the test predictor data. The cache size does not have to be large enough for the Gram matrix, but must be at least large enough to hold an n-by-1 vector. Otherwise, the software uses the regular algorithm for computing the Euclidean distance.

If the Distance value begins with fast and CacheSize is too large or is "maximal", then the software might attempt to allocate a Gram matrix that exceeds the available memory. In this case, the software issues an error.

Example: CacheSize="maximal"

Data Types: single | double | char | string

CategoricalPredictors — Categorical predictor flag

[] | "all"

Categorical predictor flag, specified as one of the following:

• "all" — All predictors are categorical.

• [] — No predictors are categorical.

The predictor data for fitcknn must be either all continuous or all categorical.

• If the predictor data is in a table (Tbl), fitcknn assumes that a variable is categorical if it is a logical vector, categorical vector, character array, string array, or cell array of character vectors. If Tbl includes both continuous and categorical values, then you must specify the value of CategoricalPredictors so that fitcknn can determine how to treat all predictors, as either continuous or categorical variables.

• If the predictor data is a matrix (X), fitcknn assumes that all predictors are continuous. To identify all predictors in X as categorical, specify CategoricalPredictors as "all".

When you set CategoricalPredictors to "all", the default Distance is "hamming".

Example: CategoricalPredictors="all"

ClassNames — Names of classes to use for training

categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors

Names of classes to use for training, specified as a categorical, character, or string array; a logical or numeric vector; or a cell array of character vectors. ClassNames must have the same data type as the response variable in Tbl or Y.

If ClassNames is a character array, then each element must correspond to one row of the array.

Use ClassNames to:

• Specify the order of the classes during training.

• Specify the order of any input or output argument dimension that corresponds to the class order. For example, use ClassNames to specify the order of the dimensions of Cost or the column order of classification scores returned by predict.

• Select a subset of classes for training. For example, suppose that the set of all distinct class names in Y is ["a","b","c"]. To train the model using observations from classes "a" and "c" only, specify ClassNames=["a","c"].

The default value for ClassNames is the set of all distinct class names in the response variable in Tbl or Y.

Example: ClassNames=["b","g"]

Data Types: categorical | char | string | logical | single | double | cell

Cost — Cost of misclassification

square matrix | structure

Cost of misclassification of a point, specified as one of the following:

• Square matrix, where Cost(i,j) is the cost of classifying a point into class j if its true class is i (that is, the rows correspond to the true class and the columns correspond to the predicted class). To specify the class order for the corresponding rows and columns of Cost, additionally specify the ClassNames name-value pair argument.

• Structure S having two fields: S.ClassNames containing the group names as a variable of the same type as Y, and S.ClassificationCosts containing the cost matrix.

The default is Cost(i,j)=1 if i~=j, and Cost(i,j)=0 if i=j.

Data Types: single | double | struct

Cov — Covariance matrix

cov(X,"omitrows") (default) | positive definite matrix of scalar values

Covariance matrix, specified as a positive definite matrix of scalar values representing the covariance matrix when computing the Mahalanobis distance. This argument is only valid when Distance is "mahalanobis".

You cannot simultaneously specify Standardize and either of Scale or Cov.

Data Types: single | double

Distance — Distance metric

"cityblock" | "chebychev" | "correlation" | "cosine" | "euclidean" | "hamming" | function handle | ...

Distance metric, specified as a valid distance metric name or function handle. The allowable distance metric names depend on your choice of a neighbor-searcher method (see NSMethod).

NSMethod Value	Distance Metric Names
"exhaustive"	Any distance metric of ExhaustiveSearcher
"kdtree"	"cityblock", "chebychev", "euclidean", or "minkowski"

This table includes valid distance metrics of ExhaustiveSearcher.

Distance Metric Names	Description
"cityblock"	City block distance.
"chebychev"	Chebychev distance (maximum coordinate difference).
"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 vectors).
"euclidean"	Euclidean distance.
"fasteuclidean" (since R2025a)	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 Fast Euclidean Distance Algorithm.
"fastseuclidean" (since R2025a)	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 Fast Euclidean Distance Algorithm.
"hamming"	Hamming distance, percentage of coordinates that differ.
"jaccard"	One minus the Jaccard coefficient, the percentage of nonzero coordinates that differ.
"mahalanobis"	Mahalanobis distance, computed using a positive definite covariance matrix C. The default value of C is the sample covariance matrix of X, as computed by cov(X,"omitrows"). To specify a different value for C, use the Cov name-value argument.
"minkowski"	Minkowski distance. The default exponent is 2. To specify a different exponent, use the Exponent name-value argument.
"seuclidean"	Standardized Euclidean distance. Each coordinate difference between X and a query point is scaled, meaning divided by a scale value S. The default value of S is the standard deviation computed from X, S = std(X,"omitnan"). To specify another value for S, use the Scale name-value argument.
"spearman"	One minus the sample Spearman's rank correlation between observations (treated as sequences of values).
@distfun	Distance function handle. distfun has the form function D2 = distfun(ZI,ZJ) % calculation of distance ... where ZI is a 1-by-N vector containing one row of X or Y. ZJ is an M2-by-N matrix containing multiple rows of X or Y. D2 is an M2-by-1 vector of distances, and D2(k) is the distance between observations ZI and ZJ(k,:).

If you specify CategoricalPredictors as "all", then the default distance metric is "hamming". Otherwise, the default distance metric is "euclidean".

For more information, see Distance Metrics.

Example: Distance="minkowski"

Data Types: char | string | function_handle

DistanceWeight — Distance weighting function

"equal" (default) | "inverse" | "squaredinverse" | function handle

Distance weighting function, specified as a function handle or one of the values in this table.

Value	Description
"equal"	No weighting
"inverse"	Weight is 1/distance
"squaredinverse"	Weight is 1/distance2
@fcn	fcn is a function that accepts a matrix of nonnegative distances, and returns a matrix the same size containing nonnegative distance weights. For example, "squaredinverse" is equivalent to @(d)d.^(-2).

Example: DistanceWeight="inverse"

Data Types: char | string | function_handle

Exponent — Minkowski distance exponent

2 (default) | positive scalar value

Minkowski distance exponent, specified as a positive scalar value. This argument is only valid when Distance is "minkowski".

Example: Exponent=3

Data Types: single | double

IncludeTies — Tie inclusion flag

false (default) | true

Tie inclusion flag, specified as a logical value indicating whether predict includes all the neighbors whose distance values are equal to the kth smallest distance. If IncludeTies is true, predict includes all these neighbors. Otherwise, predict uses exactly k neighbors.

Example: IncludeTies=true

Data Types: logical

NSMethod — Nearest neighbor search method

"kdtree" | "exhaustive"

Nearest neighbor search method, specified as "kdtree" or "exhaustive".

• "kdtree" — Creates and uses a Kd-tree to find nearest neighbors. "kdtree" is valid when the distance metric is one of the following:

  • "euclidean"

  • "cityblock"

  • "minkowski"

  • "chebychev"

• "exhaustive" — Uses the exhaustive search algorithm. When predicting the class of a new point xnew, the software computes the distance values from all points in X to xnew to find nearest neighbors.

The default is "kdtree" when X has 10 or fewer columns, X is not sparse or a gpuArray, and the distance metric is a "kdtree" type; otherwise, "exhaustive".

Example: NSMethod="exhaustive"

NumNeighbors — Number of nearest neighbors to find

1 (default) | positive integer value

Number of nearest neighbors in X to find for classifying each point when predicting, specified as a positive integer value.

Example: NumNeighbors=3

Data Types: single | double

PredictorNames — Predictor variable names

string array of unique names | cell array of unique character vectors

Predictor variable names, specified as a string array of unique names or cell array of unique character vectors. The functionality of PredictorNames depends on the way you supply the training data.

• If you supply X and Y, then you can use PredictorNames to assign names to the predictor variables in X.

  • The order of the names in PredictorNames must correspond to the column order of X. That is, PredictorNames{1} is the name of X(:,1), PredictorNames{2} is the name of X(:,2), and so on. Also, size(X,2) and numel(PredictorNames) must be equal.

  • By default, PredictorNames is {'x1','x2',...}.

• If you supply Tbl, then you can use PredictorNames to choose which predictor variables to use in training. That is, fitcknn uses only the predictor variables in PredictorNames and the response variable during training.

  • PredictorNames must be a subset of Tbl.Properties.VariableNames and cannot include the name of the response variable.

  • By default, PredictorNames contains the names of all predictor variables.

  • A good practice is to specify the predictors for training using either PredictorNames or formula, but not both.

Example: "PredictorNames",["SepalLength","SepalWidth","PetalLength","PetalWidth"]

Data Types: string | cell

Prior — Prior probabilities

"empirical" (default) | "uniform" | vector of scalar values | structure

Prior probabilities for each class, specified as a value in this table.

Value	Description
"empirical"	The class prior probabilities are the class relative frequencies in Y.
"uniform"	All class prior probabilities are equal to 1/K, where K is the number of classes.
numeric vector	Each element is a class prior probability. Order the elements according to Mdl.ClassNames or specify the order using the ClassNames name-value pair argument. The software normalizes the elements such that they sum to 1.
structure	A structure S with two fields: S.ClassNames contains the class names as a variable of the same type as Y. S.ClassProbs contains a vector of corresponding prior probabilities. The software normalizes the elements such that they sum to 1.

If you set values for both Weights and Prior, the weights are renormalized to add up to the value of the prior probability in the respective class.

Example: Prior="uniform"

Data Types: char | string | single | double | struct

ResponseName — Response variable name

"Y" (default) | character vector | string scalar

Response variable name, specified as a character vector or string scalar.

• If you supply Y, then you can use ResponseName to specify a name for the response variable.

• If you supply ResponseVarName or formula, then you cannot use ResponseName.

Example: ResponseName="response"

Data Types: char | string

Scale — Distance scale

std(X,"omitnan") (default) | vector of nonnegative scalar values

Distance scale, specified as a vector containing nonnegative scalar values with length equal to the number of columns in X. Each coordinate difference between X and a query point is scaled by the corresponding element of Scale. This argument is only valid when Distance is "seuclidean".

You cannot simultaneously specify Standardize and either of Scale or Cov.

Data Types: single | double

ScoreTransform — Score transformation

"none" (default) | "doublelogit" | "invlogit" | "ismax" | "logit" | function handle | ...

Score transformation, specified as a character vector, string scalar, or function handle.

This table summarizes the available character vectors and string scalars.

Value	Description
"doublelogit"	1/(1 + e–2x)
"invlogit"	log(x / (1 – x))
"ismax"	Sets the score for the class with the largest score to 1, and sets the scores for all other classes to 0
"logit"	1/(1 + e–x)
"none" or "identity"	x (no transformation)
"sign"	–1 for x < 0 0 for x = 0 1 for x > 0
"symmetric"	2x – 1
"symmetricismax"	Sets the score for the class with the largest score to 1, and sets the scores for all other classes to –1
"symmetriclogit"	2/(1 + e–x) – 1

For a MATLAB function or a function you define, use its function handle for the score transform. The function handle must accept a matrix (the original scores) and return a matrix of the same size (the transformed scores).

Example: ScoreTransform="logit"

Data Types: char | string | function_handle

Standardize — Flag to standardize predictors

false (default) | true

Flag to standardize the predictors, specified as true (1) or false (0).

If you set Standardize=true, then the software centers and scales each column of the predictor data (X) by the column mean and standard deviation, respectively.

The software does not standardize categorical predictors, and throws an error if all predictors are categorical.

You cannot simultaneously specify Standardize=true and either of Scale or Cov.

It is good practice to standardize the predictor data.

Example: Standardize=true

Data Types: logical

Weights — Observation weights

numeric vector of positive values | name of variable in Tbl

Observation weights, specified as a numeric vector of positive values or name of a variable in Tbl. The software weighs the observations in each row of X or Tbl with the corresponding value in Weights. The size of Weights must equal the number of rows of X or Tbl.

If you specify the input data as a table Tbl, then Weights can be the name of a variable in Tbl that contains a numeric vector. In this case, you must specify Weights as a character vector or string scalar. For example, if the weights vector W is stored as Tbl.W, then specify it as "W". Otherwise, the software treats all columns of Tbl, including W, as predictors or the response when training the model.

By default, Weights is ones(n,1), where n is the number of observations in X or Tbl.

The software normalizes Weights to sum up to the value of the prior probability in the respective class. Inf weights are not supported.

Data Types: double | single | char | string

Cross-Validation Options

CrossVal — Cross-validation flag

"off" (default) | "on"

Cross-validation flag, specified as "on" or "off".

If you specify "on", then the software implements 10-fold cross-validation.

To override this cross-validation setting, use one of these name-value arguments: CVPartition, Holdout, KFold, or Leaveout. To create a cross-validated model, you can use one cross-validation name-value argument at a time only.

Alternatively, cross validate Mdl later using the crossval method.

Example: Crossval="on"

CVPartition — Cross-validation partition

[] (default) | cvpartition object

Cross-validation partition, specified as a cvpartition object that specifies the type of cross-validation and the indexing for the training and validation sets.

To create a cross-validated model, you can specify only one of these four name-value arguments: CVPartition, Holdout, KFold, or Leaveout.

Example: Suppose you create a random partition for 5-fold cross-validation on 500 observations by using cvp = cvpartition(500,KFold=5). Then, you can specify the cross-validation partition by setting CVPartition=cvp.

Holdout — Fraction of data for holdout validation

scalar value in the range (0,1)

Fraction of the data used for holdout validation, specified as a scalar value in the range (0,1). If you specify Holdout=p, then the software completes these steps:

1. Randomly select and reserve p*100% of the data as validation data, and train the model using the rest of the data.

2. Store the compact trained model in the Trained property of the cross-validated model.

To create a cross-validated model, you can specify only one of these four name-value arguments: CVPartition, Holdout, KFold, or Leaveout.

Example: Holdout=0.1

Data Types: double | single

KFold — Number of folds

10 (default) | positive integer value greater than 1

Number of folds to use in the cross-validated model, specified as a positive integer value greater than 1. If you specify KFold=k, then the software completes these steps:

1. Randomly partition the data into k sets.

2. For each set, reserve the set as validation data, and train the model using the other k – 1 sets.

3. Store the k compact trained models in a k-by-1 cell vector in the Trained property of the cross-validated model.

To create a cross-validated model, you can specify only one of these four name-value arguments: CVPartition, Holdout, KFold, or Leaveout.

Example: KFold=5

Data Types: single | double

Leaveout — Leave-one-out cross-validation flag

"off" (default) | "on"

Leave-one-out cross-validation flag, specified as "on" or "off". If you specify Leaveout="on", then for each of the n observations (where n is the number of observations, excluding missing observations, specified in the NumObservations property of the model), the software completes these steps:

1. Reserve the one observation as validation data, and train the model using the other n – 1 observations.

2. Store the n compact trained models in an n-by-1 cell vector in the Trained property of the cross-validated model.

To create a cross-validated model, you can specify only one of these four name-value arguments: CVPartition, Holdout, KFold, or Leaveout.

Example: Leaveout="on"

Data Types: char | string

Hyperparameter Optimization Options

OptimizeHyperparameters — Parameters to optimize

"none" (default) | "auto" | "all" | string array or cell array of eligible parameter names | vector of optimizableVariable objects

Parameters to optimize, specified as one of the following:

• "none" — Do not optimize.

• "auto" — Use ["Distance","NumNeighbors","Standardize"].

• "all" — Optimize all eligible parameters.

• String array or cell array of eligible parameter names.

• Vector of optimizableVariable objects, typically the output of hyperparameters.

The optimization attempts to minimize the cross-validation loss (error) for fitcknn by varying the parameters. To control the cross-validation type and other aspects of the optimization, use the HyperparameterOptimizationOptions name-value argument. When you use HyperparameterOptimizationOptions, you can use the (compact) model size instead of the cross-validation loss as the optimization objective by setting the ConstraintType and ConstraintBounds options.

Note

The values of OptimizeHyperparameters override any values you specify using other name-value arguments. For example, setting OptimizeHyperparameters to "auto" causes fitcknn to optimize hyperparameters corresponding to the "auto" option and to ignore any specified values for the hyperparameters.

The eligible parameters for fitcknn are:

• Distance — fitcknn searches among "cityblock", "chebychev", "correlation", "cosine", "euclidean", "hamming", "jaccard", "mahalanobis", "minkowski", "seuclidean", and "spearman".

• DistanceWeight — fitcknn searches among "equal", "inverse", and "squaredinverse".

• Exponent — fitcknn searches among positive real values, by default in the range [0.5,3].

• NumNeighbors — fitcknn searches among positive integer values, by default log-scaled in the range [1,max(2,round(NumObservations/2))].

• Standardize — fitcknn searches among the values "true" and "false".

Set nondefault parameters by passing a vector of optimizableVariable objects that have nondefault values. For example,

load fisheriris
params = hyperparameters("fitcknn",meas,species);
params(1).Range = [1,20];

Pass params as the value of OptimizeHyperparameters.

By default, the iterative display appears at the command line, and plots appear according to the number of hyperparameters in the optimization. For the optimization and plots, the objective function is the misclassification rate. To control the iterative display, set the Verbose option of the HyperparameterOptimizationOptions name-value argument. To control the plots, set the ShowPlots field of the HyperparameterOptimizationOptions name-value argument.

For an example, see Optimize Fitted KNN Classifier.

Example: OptimizeHyperparameters="auto"

HyperparameterOptimizationOptions — Options for optimization

HyperparameterOptimizationOptions object | structure

Options for optimization, specified as a HyperparameterOptimizationOptions object or a structure. This argument modifies the effect of the OptimizeHyperparameters name-value argument. If you specify HyperparameterOptimizationOptions, you must also specify OptimizeHyperparameters. All the options are optional. However, you must set ConstraintBounds and ConstraintType to return AggregateOptimizationResults. The options that you can set in a structure are the same as those in the HyperparameterOptimizationOptions object.

Option	Values	Default
Optimizer	"bayesopt" — Use Bayesian optimization. Internally, this setting calls bayesopt. "gridsearch" — Use grid search with NumGridDivisions values per dimension. "gridsearch" searches in a random order, using uniform sampling without replacement from the grid. After optimization, you can get a table in grid order by using the command sortrows(Mdl.HyperparameterOptimizationResults). "randomsearch" — Search at random among MaxObjectiveEvaluations points.	"bayesopt"
ConstraintBounds	Constraint bounds for N optimization problems, specified as an N-by-2 numeric matrix or []. The columns of ConstraintBounds contain the lower and upper bound values of the optimization problems. If you specify ConstraintBounds as a numeric vector, the software assigns the values to the second column of ConstraintBounds, and zeros to the first column. If you specify ConstraintBounds, you must also specify ConstraintType.	[]
ConstraintTarget	Constraint target for the optimization problems, specified as "matlab" or "coder". If ConstraintBounds and ConstraintType are [] and you set ConstraintTarget, then the software sets ConstraintTarget to []. The values of ConstraintTarget and ConstraintType determine the objective and constraint functions. For more information, see HyperparameterOptimizationOptions.	If you specify ConstraintBounds and ConstraintType, then the default value is "matlab". Otherwise, the default value is [].
ConstraintType	Constraint type for the optimization problems, specified as "size" or "loss". If you specify ConstraintType, you must also specify ConstraintBounds. The values of ConstraintTarget and ConstraintType determine the objective and constraint functions. For more information, see HyperparameterOptimizationOptions.	[]
AcquisitionFunctionName	Type of acquisition function: "expected-improvement-per-second-plus" "expected-improvement" "expected-improvement-plus" "expected-improvement-per-second" "lower-confidence-bound" "probability-of-improvement" Acquisition functions whose names include per-second do not yield reproducible results, because the optimization depends on the run time of the objective function. Acquisition functions whose names include plus modify their behavior when they overexploit an area. For more details, see Acquisition Function Types.	"expected-improvement-per-second-plus"
MaxObjectiveEvaluations	Maximum number of objective function evaluations. If you specify multiple optimization problems using ConstraintBounds, the value of MaxObjectiveEvaluations applies to each optimization problem individually.	30 for "bayesopt" and "randomsearch", and the entire grid for "gridsearch"
MaxTime	Time limit for the optimization, specified as a nonnegative real scalar. The time limit is in seconds, as measured by tic and toc. The software performs at least one optimization iteration, regardless of the value of MaxTime. The run time can exceed MaxTime because MaxTime does not interrupt function evaluations. If you specify multiple optimization problems using ConstraintBounds, the time limit applies to each optimization problem individually.	Inf
NumGridDivisions	For Optimizer="gridsearch", the number of values in each dimension. The value can be a vector of positive integers giving the number of values for each dimension, or a scalar that applies to all dimensions. The software ignores this option for categorical variables.	10
ShowPlots	Logical value indicating whether to show plots of the optimization progress. If this option is true, the software plots the best observed objective function value against the iteration number. If you use Bayesian optimization (Optimizer="bayesopt"), the software also plots the best estimated objective function value. The best observed objective function values and best estimated objective function values correspond to the values in the BestSoFar (observed) and BestSoFar (estim.) columns of the iterative display, respectively. You can find these values in the properties ObjectiveMinimumTrace and EstimatedObjectiveMinimumTrace of Mdl.HyperparameterOptimizationResults. If the problem includes one or two optimization parameters for Bayesian optimization, then ShowPlots also plots a model of the objective function against the parameters.	true
SaveIntermediateResults	Logical value indicating whether to save the optimization results. If this option is true, the software overwrites a workspace variable named "BayesoptResults" at each iteration. The variable is a BayesianOptimization object. If you specify multiple optimization problems using ConstraintBounds, the workspace variable is an AggregateBayesianOptimization object named "AggregateBayesoptResults".	false
Verbose	Display level at the command line: 0 — No iterative display 1 — Iterative display 2 — Iterative display with additional information For details, see the bayesopt Verbose name-value argument and the example Optimize Classifier Fit Using Bayesian Optimization.	1
UseParallel	Logical value indicating whether to run the Bayesian optimization in parallel, which requires Parallel Computing Toolbox™. Due to the nonreproducibility of parallel timing, parallel Bayesian optimization does not necessarily yield reproducible results. For details, see Parallel Bayesian Optimization.	false
Repartition	Logical value indicating whether to repartition the cross-validation at every iteration. If this option is false, the optimizer uses a single partition for the optimization. A value of true usually gives the most robust results because this setting takes partitioning noise into account. However, for optimal results, true requires at least twice as many function evaluations.	false
Specify only one of the following three options.
CVPartition	cvpartition object created by cvpartition	KFold=5 if you do not specify a cross-validation option
Holdout	Scalar in the range (0,1) representing the holdout fraction
KFold	Integer greater than 1

Example: HyperparameterOptimizationOptions=struct(UseParallel=true)

Output Arguments

Mdl — Trained k-nearest neighbor classification model

ClassificationKNN model object | ClassificationPartitionedModel cross-validated model object

Trained k-nearest neighbor classification model, returned as a ClassificationKNN model object or a ClassificationPartitionedModel cross-validated model object.

If you set any of the name-value pair arguments KFold, Holdout, CrossVal, or CVPartition, then Mdl is a ClassificationPartitionedModel cross-validated model object. Otherwise, Mdl is a ClassificationKNN model object.

To reference properties of Mdl, use dot notation. For example, to display the distance metric at the Command Window, enter Mdl.Distance.

If you specify OptimizeHyperparameters and set the ConstraintType and ConstraintBounds options of HyperparameterOptimizationOptions, then Mdl is an N-by-1 cell array of model objects, where N is equal to the number of rows in ConstraintBounds. If none of the optimization problems yields a feasible model, then each cell array value is [].

AggregateOptimizationResults — Aggregate optimization results

AggregateBayesianOptimization object

Aggregate optimization results for multiple optimization problems, returned as an AggregateBayesianOptimization object. To return AggregateOptimizationResults, you must specify OptimizeHyperparameters and HyperparameterOptimizationOptions. You must also specify the ConstraintType and ConstraintBounds options of HyperparameterOptimizationOptions. For an example that shows how to produce this output, see Hyperparameter Optimization with Multiple Constraint Bounds.

Tips

After training a model, you can generate C/C++ code that predicts labels for new data. Generating C/C++ code requires MATLAB Coder™. For details, see Introduction to Code Generation.

Algorithms

Missing Observations

NaNs or <undefined>s indicate missing observations. The following describes the behavior of fitcknn when the data set or weights contain missing observations.

• If any value of Y or any weight is missing, then fitcknn removes those values from Y, the weights, and the corresponding rows of X from the data. The software renormalizes the weights to sum to 1.

• If you specify to standardize predictors (Standardize=true) or the standardized Euclidean distance (Distance="seuclidean") without a scale, then fitcknn removes missing observations from individual predictors before computing the mean and standard deviation. In other words, the software implements mean and std with the "omitnan" option on each predictor.

• If you specify the Mahalanobis distance (Distance="mahalanobis") without its covariance matrix, then fitcknn removes rows of X that contain at least one missing value. In other words, the software implements cov with the "omitrows" option on the predictor matrix X.

Misclassification Costs, Prior Probabilities, and Observation Weights

• If you specify the Cost, Prior, and Weights name-value arguments, the output model object stores the specified values in the Cost, Prior, and W properties, respectively. The Cost property stores the user-specified cost matrix as is. The Prior and W properties store the prior probabilities and observation weights, respectively, after normalization. For details, see Misclassification Cost Matrix, Prior Probabilities, and Observation Weights.

• The software uses the Cost property for prediction, but not training. Therefore, Cost is not read-only; you can change the property value by using dot notation after creating the trained model.

• Suppose that you set Standardize=true.

  • If you also specify the Prior or Weights name-value argument, then fitcknn standardizes the predictors using their corresponding weighted means and weighted standard deviations. Specifically, fitcknn standardizes the predictor j using

    • $$x_j^{\ast }=\frac{x_j-{\mu }_j^{\ast }}{{\sigma }_j^{\ast }}.$$

      $${\mu }_j^{\ast }=\frac{1}{{\displaystyle \sum _k{w}_k}}{\displaystyle \sum _k{w}_k{x}_{jk}}.$$

      x_jk is observation k (row) of predictor j (column).

      $${\left({\sigma }_j^{\ast }\right)}^2=\frac{{\displaystyle \sum _k{w}_k}}{{\left({\displaystyle \sum _k{w}_k}\right)}^2-{\displaystyle \sum _k{w}_k^2}}{\displaystyle \sum _k{w}_k{\left(x_{jk}-{\mu }_j^{\ast }\right)}^2}.$$

  • If you also set Distance="mahalanobis" or Distance="seuclidean", then you cannot specify Scale or Cov. Instead, the software:

    1. Computes the means and standard deviations of each predictor.

    2. Standardizes the data using the results of step 1.

    3. Computes the distance parameter values using their respective default.

• If you specify Scale and either of Prior or Weights, then the software scales observed distances by the weighted standard deviations.

• If you specify Cov and either of Prior or Weights, then the software applies the weighted covariance matrix to the distances. In other words,

  $$Cov=\frac{{\displaystyle \sum _k{w}_k}}{{\left({\displaystyle \sum _k{w}_k}\right)}^2-{\displaystyle \sum _k{w}_k^2}}{\displaystyle \sum _j{\displaystyle \sum }_k^{}{w}_k{\left(x_{jk}-{\mu }_j^{*}\right)}^{\prime }\left(x_j-{\mu }_j^{*}\right)}.$$

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 x_i and x_j, where each x_i has n variables, the algorithm computes distance using the final line in the following equations:

$$\begin{array}{c}{D}_{i,j}^2=\Vert x_i-x_j{\Vert }^2\\ ={(}^{x_i}(x_i-x_j)\\ =\Vert x_i{\Vert }^2-2x_i^T{x}_j+\Vert x_j{\Vert }^2.\end{array}$$

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 more details, see Albanie [1].

To store the Gram matrix, the software uses a cache with the default size of 1e3 megabytes. You can set the cache size using the CacheSize name-value argument. If the value of CacheSize is too large or "maximal", then the software might try to allocate a Gram matrix that exceeds the available memory. In this case, the software issues an error.

References

[1] Albanie, Samuel. Euclidean Distance Matrix Trick. June, 2019. Available at https://samuelalbanie.com/files/Euclidean_distance_trick.pdf.

Prediction

ClassificationKNN predicts the classification of a point xnew using a procedure equivalent to this:

1. Find the NumNeighbors points in the training set X that are nearest to xnew.

2. Find the NumNeighbors response values Y to those nearest points.

3. Assign the classification label ynew that has the largest posterior probability among the values in Y.

For details, see Posterior Probability in the predict documentation.

Alternatives

Although fitcknn can train a multiclass KNN classifier, you can reduce a multiclass learning problem to a series of KNN binary learners using fitcecoc.

Extended Capabilities

Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

To perform parallel hyperparameter optimization, use the UseParallel=true option in the HyperparameterOptimizationOptions name-value argument in the call to the fitcknn function.

For more information on parallel hyperparameter optimization, see Parallel Bayesian Optimization.

For general information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• By default, fitcknn uses the exhaustive nearest neighbor search algorithm for gpuArray input arguments.

• You cannot specify the name-value argument NSMethod as "kdtree".

• You cannot specify the name-value argument Distance as "fasteuclidean", "fastseuclidean", or a function handle.

• You cannot specify the name-value argument IncludeTies as true.

• fitcknn fits the model on a GPU if one of the following applies:

  • The input argument X is a gpuArray object.

  • The input argument Tbl contains gpuArray predictor variables.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2014a

R2025a: Use fast Euclidean distances

The "fasteuclidean" and "fastseuclidean" distance metrics (Distance) accelerate the computation of Euclidean distances by using a cache and an alternative algorithm. You can set the size of the cache by using the CacheSize name-value argument.

R2025a: Compute serially when parallel hyperparameter optimization is not available

fitcknn defaults to serial hyperparameter optimization when HyperparameterOptimizationOptions includes UseParallel=true and the software cannot open a parallel pool.

In previous releases, the software issues an error under these circumstances.

R2023b: "auto" option of OptimizeHyperparameters includes Standardize

Starting in R2023b, when you specify "auto" as the OptimizeHyperparameters value, fitcknn includes Standardize as an optimizable hyperparameter.