fitcknn
Fit knearest neighbor classifier
Syntax
Description
returns a knearest neighbor classification model based on
the input variables (also known as predictors, features, or attributes) in the
table Mdl
= fitcknn(Tbl
,ResponseVarName
)Tbl
and output (response)
Tbl.ResponseVarName
.
fits a model with additional options specified by one or more namevalue pair
arguments, using any of the previous syntaxes. For example, you can specify the
tiebreaking algorithm, distance metric, or observation weights.Mdl
= fitcknn(___,Name,Value
)
Examples
Train kNearest Neighbor Classifier
Train a knearest neighbor classifier for 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 petal measurements for 150 irises. Y
is a cell array of character vectors that contains the corresponding iris species.
Train a 5nearest neighbor classifier. Standardize the noncategorical predictor data.
Mdl = fitcknn(X,Y,'NumNeighbors',5,'Standardize',1)
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, and some of its properties appear in the Command Window.
To access the properties of Mdl
, use dot notation.
Mdl.ClassNames
ans = 3x1 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'
namevalue pair 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 crossvalidate the classifier.
Train a kNearest Neighbor Classifier Using the Minkowski Metric
Load Fisher's iris data set.
load fisheriris
X = meas;
Y = species;
X
is a numeric matrix that contains four petal measurements for 150 irises. Y
is a cell array of character vectors that contains the corresponding iris species.
Train a 3nearest neighbors classifier using the Minkowski metric. To use the Minkowski metric, you must use an exhaustive searcher. It is good practice to standardize noncategorical predictor data.
Mdl = fitcknn(X,Y,'NumNeighbors',3,... 'NSMethod','exhaustive','Distance','minkowski',... 'Standardize',1);
Mdl
is a ClassificationKNN
classifier.
You can examine the properties of Mdl
by doubleclicking Mdl
in the Workspace window. This opens the Variable Editor.
Train kNearest Neighbor Classifier Using Custom Distance Metric
Train a knearest neighbor classifier using the chisquare distance.
Load Fisher's iris data set.
load fisheriris X = meas; % Predictors Y = species; % Response
The chisquare distance between jdimensional 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 chisquare distance function. The distance function must:
Take one row of
X
, e.g.,x
, and the matrixZ
.Compare
x
to each row ofZ
.Return a vector
D
of length $${n}_{z}$$, where $${n}_{z}$$ is the number of rows ofZ
. Each element ofD
is the distance between the observation corresponding tox
and the observations corresponding to each row ofZ
.
chiSqrDist = @(x,Z,wt)sqrt((bsxfun(@minus,x,Z).^2)*wt);
This example uses arbitrary weights for illustration.
Train a 3nearest 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',1);
KNNMdl
is a ClassificationKNN
classifier.
Cross validate the KNN classifier using the default 10fold 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',1); classError2 = kfoldLoss(CVKNNMdl2)
classError2 = 0.0400
The second weighting scheme yields a classifier that has better outofsample performance.
Optimize Fitted KNN Classifier
This example shows how to optimize hyperparameters automatically using fitcknn
. The example uses the Fisher iris data.
Load the data.
load fisheriris
X = meas;
Y = species;
Find hyperparameters that minimize fivefold crossvalidation loss by using automatic hyperparameter optimization.
For reproducibility, set the random seed and use the 'expectedimprovementplus'
acquisition function.
rng(1) Mdl = fitcknn(X,Y,'OptimizeHyperparameters','auto',... 'HyperparameterOptimizationOptions',... struct('AcquisitionFunctionName','expectedimprovementplus'))
=====================================================================================================  Iter  Eval  Objective  Objective  BestSoFar  BestSoFar  NumNeighbors  Distance    result   runtime  (observed)  (estim.)    =====================================================================================================  1  Best  0.026667  0.61415  0.026667  0.026667  30  cosine   2  Accept  0.04  0.13781  0.026667  0.027197  2  chebychev   3  Accept  0.19333  0.27607  0.026667  0.030324  1  hamming   4  Accept  0.33333  0.24145  0.026667  0.033313  31  spearman   5  Best  0.02  0.22493  0.02  0.020648  6  cosine   6  Accept  0.073333  0.15893  0.02  0.023082  1  correlation   7  Accept  0.06  0.35923  0.02  0.020875  2  cityblock   8  Accept  0.04  0.11315  0.02  0.020622  1  euclidean   9  Accept  0.24  0.15714  0.02  0.020562  74  mahalanobis   10  Accept  0.04  0.38623  0.02  0.020649  1  minkowski   11  Accept  0.053333  0.11961  0.02  0.020722  1  seuclidean   12  Accept  0.19333  0.19365  0.02  0.020701  1  jaccard   13  Accept  0.04  0.28902  0.02  0.029203  1  cosine   14  Accept  0.04  0.4531  0.02  0.031888  75  cosine   15  Accept  0.04  0.13397  0.02  0.020076  1  cosine   16  Accept  0.093333  0.24705  0.02  0.020073  75  euclidean   17  Accept  0.093333  0.067164  0.02  0.02007  75  minkowski   18  Accept  0.1  0.21713  0.02  0.020061  75  chebychev   19  Accept  0.15333  0.074026  0.02  0.020044  75  seuclidean   20  Accept  0.1  0.25964  0.02  0.020044  75  cityblock  =====================================================================================================  Iter  Eval  Objective  Objective  BestSoFar  BestSoFar  NumNeighbors  Distance    result   runtime  (observed)  (estim.)    =====================================================================================================  21  Accept  0.033333  0.27342  0.02  0.020046  75  correlation   22  Accept  0.033333  0.17378  0.02  0.02656  9  cosine   23  Accept  0.033333  0.21921  0.02  0.02854  9  cosine   24  Accept  0.02  0.13948  0.02  0.028607  1  chebychev   25  Accept  0.02  0.19371  0.02  0.022264  1  chebychev   26  Accept  0.02  0.34487  0.02  0.021439  1  chebychev   27  Accept  0.02  0.34256  0.02  0.020999  1  chebychev   28  Accept  0.66667  0.12239  0.02  0.020008  75  hamming   29  Accept  0.04  0.22085  0.02  0.020008  12  correlation   30  Best  0.013333  0.081657  0.013333  0.013351  6  euclidean 
__________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 44.404 seconds Total objective function evaluation time: 6.8354 Best observed feasible point: NumNeighbors Distance ____________ _________ 6 euclidean Observed objective function value = 0.013333 Estimated objective function value = 0.013351 Function evaluation time = 0.081657 Best estimated feasible point (according to models): NumNeighbors Distance ____________ _________ 6 euclidean Estimated objective function value = 0.013351 Estimated function evaluation time = 0.13399
Mdl = ClassificationKNN ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' NumObservations: 150 HyperparameterOptimizationResults: [1x1 BayesianOptimization] Distance: 'euclidean' NumNeighbors: 6 Properties, Methods
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 inTbl
as predictors, then specify the response variable by usingResponseVarName
.If
Tbl
contains the response variable, and you want to use only a subset of the remaining variables inTbl
as predictors, then specify a formula by usingformula
.If
Tbl
does not contain the response variable, then specify a response variable by usingY
. The length of the response variable and the number of rows inTbl
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
namevalue
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
namevalue pair argument.
Data Types: double
 single
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue 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: 'NumNeighbors',3,'NSMethod','exhaustive','Distance','minkowski'
specifies a classifier for threenearest neighbors using the nearest neighbor search
method and the Minkowski metric.
Note
You cannot use any crossvalidation namevalue argument together with the
'OptimizeHyperparameters'
namevalue argument. You can modify the
crossvalidation for 'OptimizeHyperparameters'
only by using the
'HyperparameterOptimizationOptions'
namevalue argument.
BreakTies
— Tiebreaking algorithm
'smallest'
(default)  'nearest'
 'random'
Tiebreaking algorithm used by the predict
method
if multiple classes have the same smallest cost, specified as the
commaseparated pair consisting of 'BreakTies'
and
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 Kdtree, specified
as the commaseparated pair consisting of 'BucketSize'
and a positive
integer value. This argument is meaningful only when NSMethod
is
'kdtree'
.
Example: 'BucketSize',40
Data Types: single
 double
CategoricalPredictors
— Categorical predictor flag
[]
 'all'
Categorical predictor flag, specified as the commaseparated
pair consisting of 'CategoricalPredictors'
and
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. IfTbl
includes both continuous and categorical values, then you must specify the value of'CategoricalPredictors'
so thatfitcknn
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 inX
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 ofCost
or the column order of classification scores returned bypredict
.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 the commaseparated
pair consisting of 'Cost'
and one of the following:
Square matrix, where
Cost(i,j)
is the cost of classifying a point into classj
if its true class isi
(i.e., 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 ofCost
, additionally specify theClassNames
namevalue pair argument.Structure
S
having two fields:S.ClassNames
containing the group names as a variable of the same type asY
, andS.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 the commaseparated pair consisting
of 'Cov'
and 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 the commaseparated pair consisting
of 'Distance'
and a valid distance metric name
or function handle. The allowable distance metric names depend on
your choice of a neighborsearcher method (see NSMethod
).
NSMethod  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. 
'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' namevalue pair
argument. 
'minkowski'  Minkowski distance. The default exponent is 2 .
To specify a different exponent, use the 'Exponent' namevalue
pair 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
namevalue pair argument. 
'spearman'  One minus the sample Spearman's rank correlation between observations (treated as sequences of values). 
@ 
Distance function handle. function D2 = distfun(ZI,ZJ) % calculation of distance ...

If you specify CategoricalPredictors
as 'all'
,
then the default distance metric is 'hamming'
.
Otherwise, the default distance metric is 'euclidean'
.
For definitions, 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 the commaseparated
pair consisting of 'DistanceWeight'
and either
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/distance^{2} 
@  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 the commaseparated
pair consisting of 'Exponent'
and 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 the commaseparated pair consisting of
'IncludeTies'
and 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 the commaseparated
pair consisting of 'NSMethod'
and 'kdtree'
or 'exhaustive'
.
'kdtree'
— Creates and uses a Kdtree 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 pointxnew
, the software computes the distance values from all points inX
toxnew
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 the commaseparated
pair consisting of 'NumNeighbors'
and 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
andY
, then you can usePredictorNames
to assign names to the predictor variables inX
.The order of the names in
PredictorNames
must correspond to the column order ofX
. That is,PredictorNames{1}
is the name ofX(:,1)
,PredictorNames{2}
is the name ofX(:,2)
, and so on. Also,size(X,2)
andnumel(PredictorNames)
must be equal.By default,
PredictorNames
is{'x1','x2',...}
.
If you supply
Tbl
, then you can usePredictorNames
to choose which predictor variables to use in training. That is,fitcknn
uses only the predictor variables inPredictorNames
and the response variable during training.PredictorNames
must be a subset ofTbl.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
orformula
, 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 the commaseparated
pair consisting of 'Prior'
and 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 namevalue
pair argument. The software normalizes the elements such that they
sum to 1 . 
structure  A structure

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 useResponseName
to specify a name for the response variable.If you supply
ResponseVarName
orformula
, then you cannot useResponseName
.
Example: "ResponseName","response"
Data Types: char
 string
Scale
— Distance scale
std(X,'omitnan')
(default)  vector of nonnegative scalar values
Distance scale, specified as the commaseparated pair consisting
of 'Scale'
and 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 the commaseparated
pair consisting of 'Standardize'
and 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',1
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 the commaseparated pair consisting
of 'Weights'
and 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.
The software normalizes Weights
to sum up
to the value of the prior probability in the respective class.
By default, Weights
is ones(
,
where n
,1)n
is the number of observations in X
or Tbl
.
Data Types: double
 single
 char
 string
CrossVal
— Crossvalidation flag
'off'
(default)  'on'
Crossvalidation flag, specified as the commaseparated pair consisting of
'Crossval'
and 'on'
or
'off'
.
If you specify 'on'
, then the software implements 10fold
crossvalidation.
To override this crossvalidation setting, use one of these namevalue pair arguments:
CVPartition
, Holdout
,
KFold
, or Leaveout
. To create a
crossvalidated model, you can use one crossvalidation namevalue pair argument at a
time only.
Alternatively, cross validate Mdl
later using the crossval
method.
Example: 'Crossval','on'
CVPartition
— Crossvalidation partition
[]
(default)  cvpartition
partition object
Crossvalidation partition, specified as a cvpartition
partition object
created by cvpartition
. The partition object
specifies the type of crossvalidation and the indexing for the training and validation
sets.
To create a crossvalidated model, you can specify only one of these four namevalue
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: Suppose you create a random partition for 5fold crossvalidation on 500
observations by using cvp = cvpartition(500,'KFold',5)
. Then, you can
specify the crossvalidated model by using
'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:
Randomly select and reserve
p*100
% of the data as validation data, and train the model using the rest of the data.Store the compact, trained model in the
Trained
property of the crossvalidated model.
To create a crossvalidated model, you can specify only one of these four namevalue
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 a crossvalidated model, specified as a positive integer value
greater than 1. If you specify 'KFold',k
, then the software completes
these steps:
Randomly partition the data into
k
sets.For each set, reserve the set as validation data, and train the model using the other
k
– 1 sets.Store the
k
compact, trained models in ak
by1 cell vector in theTrained
property of the crossvalidated model.
To create a crossvalidated model, you can specify only one of these four namevalue
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: 'KFold',5
Data Types: single
 double
Leaveout
— Leaveoneout crossvalidation flag
'off'
(default)  'on'
Leaveoneout crossvalidation 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:
Reserve the one observation as validation data, and train the model using the other n – 1 observations.
Store the n compact, trained models in an nby1 cell vector in the
Trained
property of the crossvalidated model.
To create a crossvalidated model, you can specify only one of these four namevalue
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: 'Leaveout','on'
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 the commaseparated pair
consisting of 'OptimizeHyperparameters'
and one of
the following:
'none'
— Do not optimize.'auto'
— Use{'Distance','NumNeighbors'}
.'all'
— Optimize all eligible parameters.String array or cell array of eligible parameter names.
Vector of
optimizableVariable
objects, typically the output ofhyperparameters
.
The optimization attempts to minimize the crossvalidation loss
(error) for fitcknn
by varying the parameters. For
information about crossvalidation loss (albeit in a different context),
see Classification Loss. To control the
crossvalidation type and other aspects of the optimization, use the
HyperparameterOptimizationOptions
namevalue
pair.
Note
The values of 'OptimizeHyperparameters'
override any values you specify
using other namevalue 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 logscaled 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
field of the
'HyperparameterOptimizationOptions'
namevalue argument. To control the
plots, set the ShowPlots
field of the
'HyperparameterOptimizationOptions'
namevalue argument.
For an example, see Optimize Fitted KNN Classifier.
Example: 'auto'
HyperparameterOptimizationOptions
— Options for optimization
structure
Options for optimization, specified as a structure. This argument modifies the effect of the
OptimizeHyperparameters
namevalue argument. All fields in the
structure are optional.
Field Name  Values  Default 

Optimizer 
 'bayesopt' 
AcquisitionFunctionName 
Acquisition functions whose names include
 'expectedimprovementpersecondplus' 
MaxObjectiveEvaluations  Maximum number of objective function evaluations.  30 for 'bayesopt' and
'randomsearch' , and the entire grid for
'gridsearch' 
MaxTime  Time limit, specified as a positive real scalar. The time limit is in seconds, as
measured by  Inf 
NumGridDivisions  For '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. This field is ignored
for categorical variables.  10 
ShowPlots  Logical value indicating whether to show plots. If true , this field plots
the best observed objective function value against the iteration number. If you
use Bayesian optimization (Optimizer is
'bayesopt' ), then this field 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 results when Optimizer is
'bayesopt' . If
true , this field overwrites a
workspace variable named
'BayesoptResults' at each
iteration. The variable is a BayesianOptimization object.  false 
Verbose  Display at the command line:
For details, see the  1 
UseParallel  Logical value indicating whether to run 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 crossvalidation at every
iteration. If this field is The setting
 false 
Use no more than one of the following three options.  
CVPartition  A cvpartition object, as created by cvpartition  'Kfold',5 if you do not specify a crossvalidation
field 
Holdout  A scalar in the range (0,1) representing the holdout fraction  
Kfold  An integer greater than 1 
Example: 'HyperparameterOptimizationOptions',struct('MaxObjectiveEvaluations',60)
Data Types: struct
Output Arguments
Mdl
— Trained knearest neighbor classification model
ClassificationKNN
model object  ClassificationPartitionedModel
crossvalidated model
object
Trained knearest neighbor classification model,
returned as a ClassificationKNN
model object or
a ClassificationPartitionedModel
crossvalidated model object.
If you set any of the namevalue pair arguments
KFold
, Holdout
,
CrossVal
, or CVPartition
, then
Mdl
is a
ClassificationPartitionedModel
crossvalidated 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
.
More About
Prediction
ClassificationKNN
predicts the
classification of a point xnew
using a procedure equivalent to
this:
Find the
NumNeighbors
points in the training setX
that are nearest toxnew
.Find the
NumNeighbors
response valuesY
to those nearest points.Assign the classification label
ynew
that has the largest posterior probability among the values inY
.
For details, see Posterior Probability in the predict
documentation.
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
NaNs
or<undefined>
s indicate missing observations. The following describes the behavior offitcknn
when the data set or weights contain missing observations.If any value of
Y
or any weight is missing, thenfitcknn
removes those values fromY
, the weights, and the corresponding rows ofX
from the data. The software renormalizes the weights to sum to1
.If you specify to standardize predictors (
'Standardize',1
) or the standardized Euclidean distance ('Distance','seuclidean'
) without a scale, thenfitcknn
removes missing observations from individual predictors before computing the mean and standard deviation. In other words, the software implementsmean
andstd
with the'omitnan'
option on each predictor.If you specify the Mahalanobis distance (
'Distance','mahalanbois'
) without its covariance matrix, thenfitcknn
removes rows ofX
that contain at least one missing value. In other words, the software implementscov
with the'omitrows'
option on the predictor matrixX
.
If you specify the
Cost
,Prior
, andWeights
namevalue arguments, the output model object stores the specified values in theCost
,Prior
, andW
properties, respectively. TheCost
property stores the userspecified cost matrix (C) as is. ThePrior
andW
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 readonly; 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
orWeights
namevalue pair argument, thenfitcknn
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 specifyScale
orCov
. Instead, the software:Computes the means and standard deviations of each predictor.
Standardizes the data using the results of step 1.
Computes the distance parameter values using their respective default.
If you specify
Scale
and either ofPrior
orWeights
, then the software scales observed distances by the weighted standard deviations.If you specify
Cov
and either ofPrior
orWeights
, then the software applies the weighted covariance matrix to the distances. In other words,$$Cov=\frac{{\displaystyle \sum _{k}{w}_{k}}}{{\left({\displaystyle \sum _{k}{w}_{k}}\right)}^{2}{\displaystyle \sum _{k}{w}_{k}^{2}}}{\displaystyle \sum _{j}{\displaystyle \sum}_{k}^{}{w}_{k}{\left({x}_{jk}{\mu}_{j}^{*}\right)}^{\prime}\left({x}_{j}{\mu}_{j}^{*}\right)}.$$
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
'HyperparameterOptimizationOptions', struct('UseParallel',true)
namevalue 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 forgpuArray
input arguments.You cannot specify the namevalue argument
'NSMethod'
as'kdtree'
.You cannot specify the namevalue argument
'Distance'
as a function handle.You cannot specify the namevalue argument
'IncludeTies'
astrue
.fitcknn
fits the model on a GPU if either of the following apply:The input argument
X
is agpuArray
object.The input argument
Tbl
containsgpuArray
predictor variables.
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2014a
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