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Fit knearest neighbor classifier
Mdl = fitcknn(Tbl,ResponseVarName)
Mdl = fitcknn(Tbl,formula)
Mdl = fitcknn(Tbl,Y)
Mdl = fitcknn(X,Y)
Mdl = fitcknn(___,Name,Value)
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
)
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 array
{'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.
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
$$\chi (x,z)=\sqrt{{\displaystyle \sum _{j=1}^{J}{w}_{j}{({x}_{j}{z}_{j})}^{2}}},$$
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 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((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. 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  0.026667  0.90935  0.026667  0.026667  30  cosine   2  Accept  0.04  0.46004  0.026667  0.027197  2  chebychev   3  Accept  0.19333  0.50426  0.026667  0.030324  1  hamming   4  Accept  0.33333  0.38262  0.026667  0.033313  31  spearman   5  Best  0.02  0.35025  0.02  0.020648  6  cosine   6  Accept  0.073333  0.24222  0.02  0.023082  1  correlation   7  Accept  0.06  0.40771  0.02  0.020875  2  cityblock   8  Accept  0.04  0.26969  0.02  0.020622  1  euclidean   9  Accept  0.24  1.003  0.02  0.020562  74  mahalanobis   10  Accept  0.04  0.20723  0.02  0.020649  1  minkowski   11  Accept  0.053333  0.43734  0.02  0.020722  1  seuclidean   12  Accept  0.19333  0.33721  0.02  0.020701  1  jaccard   13  Accept  0.04  0.18783  0.02  0.029203  1  cosine   14  Accept  0.04  0.45488  0.02  0.031888  75  cosine   15  Accept  0.04  0.19287  0.02  0.020076  1  cosine   16  Accept  0.093333  0.3058  0.02  0.020073  75  euclidean   17  Accept  0.093333  0.20237  0.02  0.02007  75  minkowski   18  Accept  0.1  0.21554  0.02  0.020061  75  chebychev   19  Accept  0.15333  0.26104  0.02  0.020044  75  seuclidean   20  Accept  0.1  0.31269  0.02  0.020044  75  cityblock  =====================================================================================================  Iter  Eval  Objective  Objective  BestSoFar  BestSoFar  NumNeighbors  Distance    result   runtime  (observed)  (estim.)    =====================================================================================================  21  Accept  0.033333  0.23383  0.02  0.020046  75  correlation   22  Accept  0.033333  0.31701  0.02  0.02656  9  cosine   23  Accept  0.033333  0.25937  0.02  0.02854  9  cosine   24  Accept  0.02  0.36054  0.02  0.028607  1  chebychev   25  Accept  0.02  0.38704  0.02  0.022264  1  chebychev   26  Accept  0.02  0.28015  0.02  0.021439  1  chebychev   27  Accept  0.02  0.34856  0.02  0.020999  1  chebychev   28  Accept  0.66667  0.28547  0.02  0.020008  75  hamming   29  Accept  0.04  0.33266  0.02  0.020008  12  correlation   30  Best  0.013333  0.30233  0.013333  0.013351  6  euclidean  __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 117.7982 seconds. Total objective function evaluation time: 10.7509 Best observed feasible point: NumNeighbors Distance ____________ _________ 6 euclidean Observed objective function value = 0.013333 Estimated objective function value = 0.013351 Function evaluation time = 0.30233 Best estimated feasible point (according to models): NumNeighbors Distance ____________ _________ 6 euclidean Estimated objective function value = 0.013351 Estimated function evaluation time = 0.30487
Mdl = ClassificationKNN ResponseName: 'Y' CategoricalPredictors: [] ClassNames: {'setosa' 'versicolor' 'virginica'} ScoreTransform: 'none' NumObservations: 150 HyperparameterOptimizationResults: [1x1 BayesianOptimization] Distance: 'euclidean' NumNeighbors: 6 Properties, Methods
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 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.
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 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, logical or numeric
vector, or 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.
It is a good practice to specify the order of the classes by using the
ClassNames
namevalue pair argument.
Data Types: char
 string
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 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.
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
 string
Y
— Class labelsClass 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 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 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.You cannot use any crossvalidation namevalue pair argument along with the
'OptimizeHyperparameters'
namevalue pair argument. You can modify
the crossvalidation for 'OptimizeHyperparameters'
only by using the
'HyperparameterOptimizationOptions'
namevalue pair
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 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, character, or string array, a
logical or numeric vector, or a cell array of character vectors.
ClassNames
must have 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 value for ClassNames
is the set of all distinct class names in
Y
.
Example: 'ClassNames',{'b','g'}
Data Types: categorical
 char
 string
 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'
— 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 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, 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 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 give the predictor variables
in X
names.
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 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 is a good practice to specify the predictors for training
using either 'PredictorNames'
or
formula
only.
Example: 'PredictorNames',{'SepalLength','SepalWidth','PetalLength','PetalWidth'}
Data Types: string
 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: char
 string
 single
 double
 struct
'ResponseName'
— Response variable name'Y'
(default)  character vector  string scalarResponse variable name, specified as the commaseparated pair consisting of
'ResponseName'
and 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 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 transformation'none'
(default)  'doublelogit'
 'invlogit'
 'ismax'
 'logit'
 function handle  ...Score transformation, specified as the commaseparated pair consisting of
'ScoreTransform'
and 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 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
'Weights'
— Observation weightsTbl
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, crossvalidate 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 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 use one of these four namevalue pair arguments
only: 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 validationFraction of the 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',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 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 model, specified as the commaseparated pair
consisting of 'KFold'
and 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 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 the
number of observations excluding missing observations, specified in the
NumObservations
property of the model), the software completes
these steps:
Reserve the observation as validation data, and train the model using the other n – 1 observations.
Store 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'
'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
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. 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 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: char
 string
 function_handle
'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'
 string array or cell array of eligible parameter names  vector of optimizableVariable
objectsParameters 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 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.
'OptimizeHyperparameters'
values override any values you set using
other namevalue pair arguments. For example, setting
'OptimizeHyperparameters'
to 'auto'
causes the
'auto'
values to apply.
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 Verbose
field of the
'HyperparameterOptimizationOptions'
namevalue pair argument. To
control the plots, set the ShowPlots
field of the
'HyperparameterOptimizationOptions'
namevalue pair argument.
For an example, see Optimize Fitted KNN Classifier.
Example: 'auto'
'HyperparameterOptimizationOptions'
— Options for optimizationOptions for optimization, specified as the commaseparated pair consisting of
'HyperparameterOptimizationOptions'
and a structure. This
argument modifies the effect of the OptimizeHyperparameters
namevalue pair 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' or 'randomsearch' , and the entire grid for 'gridsearch' 
MaxTime  Time limit, specified as a positive real. 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 objective function value against the
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 , this field overwrites a
workspace variable named
'BayesoptResults' at each
iteration. The variable is a BayesianOptimization object.  false 
Verbose  Display to the command line.
For details, see the
 1 
UseParallel  Logical value indicating whether to run Bayesian optimization in parallel, which requires Parallel Computing Toolbox™. For details, see Parallel Bayesian Optimization.  false 
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 if you do not specify any 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
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
.
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.
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.
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.
Although fitcknn
can train a multiclass KNN classifier, you can
reduce a multiclass learning problem to a series of KNN binary learners using fitcecoc
.
To run in parallel, set the 'UseParallel'
option to true
.
To perform parallel hyperparameter optimization, use the 'HyperparameterOptions', struct('UseParallel',true)
namevalue pair argument in the call to this function.
For more information on parallel hyperparameter optimization, see Parallel Bayesian Optimization.
For more general information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).
ClassificationKNN
 ClassificationPartitionedModel
 fitcecoc
 fitcensemble
 predict
 templateKNN
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