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Fit knearest neighbor classifier
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
)
Construct 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 neighbors classifier. It is good practice to standardize 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
Mdl
is a trained ClassificationKNN
classifier, and some of its properties display in the Command Window.
To access the properties of Mdl
, use dot notation.
Mdl.ClassNames Mdl.Prior
ans = 3×1 cell array 'setosa' 'versicolor' 'virginica' ans = 0.3333 0.3333 0.3333
Mdl.Prior
contains the class prior probabilities, which are settable using the namevalue pair argument 'Prior'
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, for example, ClassificationKNN.predict
to label new measurements, or ClassificationKNN.crossval
to cross validate the classifier.
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 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
where 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 matrix Z
.
Compare x
to each row of Z
.
Return a vector D
of length
, where
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((bsxfun(@minus,x,Z).^2)*wt);
This example uses arbitrtary weights for illustration.
Train a 3nearest neighbor classifier. It is good practoce 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. The 10fold classification error is 4%.
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.
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  0.08  2.027  0.08  0.08  2  seuclidean   2  Best  0.046667  0.86703  0.046667  0.04886  15  seuclidean   3  Accept  0.33333  0.5505  0.046667  0.06353  3  hamming   4  Accept  0.26  0.71377  0.046667  0.070286  19  hamming   5  Accept  0.12667  0.4618  0.046667  0.04671  75  seuclidean   6  Accept  0.046667  0.3936  0.046667  0.046614  7  seuclidean   7  Accept  0.33333  0.44165  0.046667  0.046592  3  spearman   8  Best  0.033333  0.72445  0.033333  0.033352  4  minkowski   9  Accept  0.073333  0.44745  0.033333  0.033352  44  minkowski   10  Accept  0.046667  0.40982  0.033333  0.033353  1  minkowski   11  Accept  0.08  0.56769  0.033333  0.033353  4  mahalanobis   12  Accept  0.25333  0.50193  0.033333  0.033347  75  mahalanobis   13  Accept  0.086667  0.38483  0.033333  0.033346  1  mahalanobis   14  Best  0.026667  0.48489  0.026667  0.026681  8  chebychev   15  Accept  0.12667  0.3116  0.026667  0.02669  75  chebychev   16  Accept  0.033333  0.3949  0.026667  0.026692  1  chebychev   17  Accept  0.033333  0.2124  0.026667  0.02676  3  chebychev   18  Accept  0.053333  0.22757  0.026667  0.026751  1  cityblock   19  Accept  0.04  0.19883  0.026667  0.026753  22  cityblock   20  Accept  0.046667  0.23964  0.026667  0.026762  5  cityblock  =================================================================================================  Iter  Eval  Objective  Objective  BestSoFar  BestSoFar  NumNeighbors  Distance    result   runtime  (observed)  (estim.)    =================================================================================================  21  Accept  0.073333  0.42708  0.026667  0.026755  1  correlation   22  Accept  0.04  0.37414  0.026667  0.026754  60  correlation   23  Accept  0.04  0.31612  0.026667  0.026763  11  correlation   24  Best  0.02  0.48994  0.02  0.02001  23  cosine   25  Accept  0.04  0.42061  0.02  0.020008  2  cosine   26  Accept  0.04  0.43098  0.02  0.020038  75  cosine   27  Accept  0.12667  0.37649  0.02  0.020016  75  euclidean   28  Accept  0.21333  0.29861  0.02  0.020061  1  jaccard   29  Accept  0.026667  0.19121  0.02  0.020066  9  cosine   30  Accept  0.046667  0.41951  0.02  0.020064  1  euclidean  __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 232.0957 seconds. Total objective function evaluation time: 14.3061 Best observed feasible point: NumNeighbors Distance ____________ ________ 23 cosine Observed objective function value = 0.02 Estimated objective function value = 0.020064 Function evaluation time = 0.48994 Best estimated feasible point (according to models): NumNeighbors Distance ____________ ________ 23 cosine Estimated objective function value = 0.020064 Estimated function evaluation time = 0.38041 Mdl = ClassificationKNN ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' NumObservations: 150 HyperparameterOptimizationResults: [1×1 BayesianOptimization] Distance: 'cosine' NumNeighbors: 23
Tbl
— Sample dataSample 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 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 using formula
.
If Tbl
does not contain the response variable,
then specify a response variable using Y
. The
length of response variable and the number of rows of Tbl
must
be equal.
Data Types: table
ResponseVarName
— Response variable nameTbl
Response variable name, specified as the name of a variable
in Tbl
.
You must specify ResponseVarName
as a character
vector. 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 or character array,
logical or numeric vector, or cell array of character vectors. If Y
is
a character array, then each element must correspond to one row of
the array.
It is good practice to specify the order of the classes using
the ClassNames
namevalue pair argument.
Data Types: char
formula
— Explanatory model of response and subset of predictor variablesExplanatory model of the response and a subset of the predictor
variables, specified as a character vector in the form of 'Y~X1+X2+X3'
.
In this form, Y
represents the response variable,
and X1
, X2
, and X3
represent
the predictor variables. The variables must be variable names in Tbl
(Tbl.Properties.VariableNames
).
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
.
Data Types: char
Y
— Class labelsClass labels, specified as a categorical or character array,
logical or numeric vector, or 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), and <undefined>
values
in Y
to be missing values. Consequently, the
software does not train using observations with a missing response.
Data Types: single
 double
 logical
 char
 cell
X
— Predictor dataPredictor 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
Specify optional commaseparated pairs of Name,Value
arguments.
Name
is the argument
name and Value
is the corresponding
value. Name
must appear
inside single quotes (' '
).
You can specify several name and value pair
arguments in any order as Name1,Value1,...,NameN,ValueN
.
'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 pair along with 
'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 node50
(default)  positive integer valueMaximum 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[]
(default)  '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.
When you set CategoricalPredictors
to 'all'
,
the default Distance
is 'hamming'
.
Example: 'CategoricalPredictors','all'
'ClassNames'
— Names of classes to use for trainingNames of classes to use for training, specified as the commaseparated
pair consisting of 'ClassNames'
and a categorical
or character array, logical or numeric vector, or cell array of character
vectors. ClassNames
must be the same data type
as Y
.
If ClassNames
is a character array, then
each element must correspond to one row of the
array.
Use ClassNames
to:
Order 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 is the set of all distinct class names in Y
.
Example: 'ClassNames',{'b','g'}
Data Types: categorical
 char
 logical
 single
 double
 cell
'Cost'
— Cost of misclassificationCost 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 class j
if
its true class is i
(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
of Cost
, additionally specify the ClassNames
namevalue
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 matrixnancov(X)
(default)  positive definite matrix of scalar valuesCovariance 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
'IncludeTies'
— Tie inclusion flagfalse
(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 K
th 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'
— Create and use
a kdtree to find nearest neighbors. 'kdtree'
is
valid when the distance metric is one of the following:
'euclidean'
'cityblock'
'minkowski'
'chebychev'
'exhaustive'
— Use the exhaustive
search algorithm. The distance values from all points in X
to
each point in Y
are computed to find nearest
neighbors.
The default is 'kdtree'
when X
has 10
or
fewer columns, X
is not sparse, and the distance
metric is a 'kdtree'
type; otherwise, 'exhaustive'
.
Example: 'NSMethod','exhaustive'
'PredictorNames'
— Predictor variable namesPredictor variable names, specified as the commaseparated pair
consisting of 'PredictorNames'
and a 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 give the predictor
variables in X
names.
The order of the names in PredcitorNames
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
the predictor variables in PredictorNames
and the
response only in 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.
It good practice to specify the predictors for training
using one of 'PredictorNames'
or formula
only.
Example: 'PredictorNames',{'SepalLength','SepalWidth','PedalLength','PedalWidth'}
Data Types: cell
'Prior'
— Prior probabilities'empirical'
(default)  'uniform'
 vector of scalar values  structurePrior 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: single
 double
 struct
'ResponseName'
— Response variable name'Y'
(default)  character vectorResponse variable name, specified as the commaseparated pair
consisting of 'ResponseName'
and a character vector.
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
'Scale'
— Distance scalenanstd(X)
(default)  vector of nonnegative scalar valuesDistance 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 transform function'none'
(default)  character vector  function handleScore transform function, specified as the commaseparated pair
consisting of 'ScoreTransform'
and a function handle
or value in this table.
Value  Formula 

'doublelogit'  1/(1 + e^{–2x}) 
'invlogit'  log(x / (1–x)) 
'ismax'  Set the score for the class with the largest score to 1 ,
and 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 
'symmetriclogit'  2/(1 + e^{–x}) – 1 
'symmetricismax'  Set the score for the class with the largest score to 1 ,
and scores for all other classes to 1 . 
For a MATLAB^{®} function, or a function that you define, enter its function handle.
Mdl.ScoreTransform = @function;
function
should accept a matrix (the original
scores) and return a matrix of the same size (the transformed scores).
Example: 'ScoreTransform','logit'
Data Types: function_handle
 char
'Weights'
— Observation weightsObservation 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. 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
'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 later by passing Mdl
to crossval
.
Example: 'CrossVal','on'
'CVPartition'
— Crossvalidation partition[]
(default)  cvpartition
partition objectCrossvalidation partition, specified as the commaseparated
pair consisting of 'CVPartition'
and a cvpartition
partition
object as created by cvpartition
.
The partition object specifies the type of crossvalidation, and also
the indexing for training and validation sets.
To create a crossvalidated model, you can use one of these
four namevalue pair arguments only: CVPartition
, Holdout
, KFold
,
or Leaveout
.
'Holdout'
— Fraction of data for holdout validationFraction of data used for holdout validation, specified as the
commaseparated pair consisting of 'Holdout'
and
a scalar value in the range (0,1). If you specify 'Holdout',
,
then the software: p
Randomly reserves
%
of the data as validation data, and trains the model using the rest
of the datap
*100
Stores the compact, trained model in the Trained
property
of the crossvalidated model.
To create a crossvalidated model, you can use one of these
four namevalue pair arguments only: CVPartition
, Holdout
, KFold
,
or Leaveout
.
Example: 'Holdout',0.1
Data Types: double
 single
'KFold'
— Number of folds10
(default)  positive integer value greater than 1Number of folds to use in a crossvalidated classifier, specified
as the commaseparated pair consisting of 'KFold'
and
a positive integer value greater than 1. If you specify, e.g., 'KFold',k
,
then the software:
Randomly partitions the data into k sets
For each set, reserves the set as validation data, and trains the model using the other k – 1 sets
Stores the k
compact, trained
models in the cells of a k
by1 cell vector
in the Trained
property of the crossvalidated
model.
To create a crossvalidated model, you can use one of these
four namevalue pair arguments only: CVPartition
, Holdout
, KFold
,
or Leaveout
.
Example: 'KFold',5
Data Types: single
 double
'Leaveout'
— Leaveoneout crossvalidation flag'off'
(default)  'on'
Leaveoneout crossvalidation flag, specified as the commaseparated
pair consisting of 'Leaveout'
and 'on'
or 'off'
.
If you specify 'Leaveout','on'
, then, for each
of the n observations, where n is size(Mdl.X,1)
,
the software:
Reserves the observation as validation data, and trains the model using the other n – 1 observations
Stores the n compact, trained models
in the cells of an nby1 cell vector in the Trained
property
of the crossvalidated model.
To create a crossvalidated model, you can use one of these
four namevalue pair arguments only: CVPartition
, Holdout
, KFold
,
or Leaveout
.
Example: 'Leaveout','on'
Data Types: char
'Distance'
— Distance metricDistance 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 nancov(X) . 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 = nanstd(X) . 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. distfun has
the formfunction 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: function_handle
 char
'DistanceWeight'
— Distance weighting function'equal'
(default)  'inverse'
 'squaredinverse'
 function handleDistance 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: function_handle
 char
'Exponent'
— Minkowski distance exponent2
(default)  positive scalar valueMinkowski 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
'NumNeighbors'
— Number of nearest neighbors to find1
(default)  positive integer valueNumber 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
'Standardize'
— Flag to standardize predictorsfalse
(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
'OptimizeHyperparameters'
— Parameters to optimize'none'
(default)  'auto'
 'all'
 cell array of eligible parameter names  vector of optimizableVariable
objectsParameters to optimize, specified as:
'none'
— Do not optimize.
'auto'
— Use {'Distance','NumNeighbors'}
'all'
— Optimize all eligible
parameters.
Cell array of eligible parameter names
Vector of optimizableVariable
objects,
typically the output of hyperparameters
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.
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, 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 log(1 + crossvalidation loss) for
regression, and the misclassification rate for classification. To
control the iterative display, set the HyperparameterOptimizationOptions
namevalue
pair, Verbose
field. To control the plots, set
the HyperparameterOptimizationOptions
namevalue
pair, ShowPlots
field.
For an example, see Optimize Fitted KNN Classifier.
Example: 'auto'
Data Types: char
 cell
'HyperparameterOptimizationOptions'
— Options for optimizationOptions for optimization, specified as a structure. Modifies
the effect of the OptimizeHyperparameters
namevalue
pair. All fields in the structure are optional.
Field Name  Values  Default 

Optimizer 
 'bayesopt' 
AcquisitionFunctionName 
bayesopt AcquisitionFunctionName namevalue
pair, or Acquisition Function Types.  'expectedimprovementpersecondplus' 
MaxObjectiveEvaluations  Maximum number of objective function evaluations.  30 for 'bayesopt' or 'randomsearch' ,
and the entire grid for 'gridsearch' 
NumGridDivisions  For 'gridsearch' , the number of values in
each dimension. Can be a vector of positive integers giving the number
of values for each dimension, or a scalar that applies to all dimensions.
Ignored for categorical variables.  10 
ShowPlots  Logical value indicating whether to show plots. If true ,
plots the best objective function value against iteration number.
If there are one or two optimization parameters, and if Optimizer is 'bayesopt' ,
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 , overwrites a workspace variable named 'BayesoptResults' at
each iteration. The variable is a BayesianOptimization object.  false 
Verbose  Display to the command line.
bayesopt Verbose namevalue
pair.  1 
Repartition  Logical value indicating whether to repartition the crossvalidation
at every iteration. If
 false 
Use no more than one of the following three field names.  
CVPartition  A cvpartition object, as created by cvpartition  Kfold = 5 
Holdout  A scalar in the range (0,1) representing
the holdout fraction.  
Kfold  An integer greater than 1. 
Example: struct('MaxObjectiveEvaluations',60)
Data Types: struct
Mdl
— Trained knearest neighbor classification modelClassificationKNN
model object  ClassificationPartitionedModel
crossvalidated
model objectTrained 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
.
Although fitcknn
can train a multiclass KNN
classifier, you can reduce a multiclass learning problem to a series
of KNN binary learners using fitcecoc
.
ClassificationKNN
predicts the classification
of a point Xnew
using a procedure equivalent to
this:
Find the NumNeighbors
points in
the training set X
that are nearest to Xnew
.
Find the NumNeighbors
response
values Y
to those nearest points.
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.
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',1
)
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 nanmean
and nanstd
on
each predictor.
If you specify the Mahalanobis distance ('Distance','mahalanbois'
)
without its covariance matrix, then fitcknn
removes
rows of X
that contain at least one missing value.
In other words, the software implements nancov
on
the predictor matrix X
.
Suppose that you set 'Standardize',1
.
If you also specify Prior
or Weights
,
then the software takes the observation weights into account. Specifically,
the weighted mean of predictor j is
$${\overline{x}}_{j}={\displaystyle \sum}_{{B}_{j}}^{}{w}_{k}{x}_{jk}$$
and the weighted standard deviation is
$${s}_{j}={\displaystyle \sum _{Bj}^{}{w}_{k}}({x}_{jk}{\overline{x}}_{j}),$$
where B_{j} is the set of indices k for which x_{jk} and w_{k} are not missing.
If you also set 'Distance','mahalanobis'
or 'Distance','seuclidean'
,
then you cannot specify Scale
or Cov
.
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
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,
$$Cov=\frac{{\displaystyle \sum _{B}{w}_{j}}}{{\left({\displaystyle \sum _{B}{w}_{j}}\right)}^{2}{\displaystyle \sum _{B}{w}_{j}^{2}}}{\displaystyle \sum}_{B}^{}{w}_{j}{\left({x}_{j}\overline{x}\right)}^{\prime}\left({x}_{j}\overline{x}\right),$$
where B is the set of indices j for which the observation x_{j} does not have any missing values and w_{j} is not missing.
ClassificationKNN
 ClassificationPartitionedModel
 fitcecoc
 fitensemble
 predict
 templateKNN
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