Fit k-nearest neighbor classifier
returns a k-nearest 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 name-value pair
arguments, using any of the previous syntaxes. For example, you can specify the
tie-breaking algorithm, distance metric, or observation weights.Mdl
= fitcknn(___,Name,Value
)
Train a k-nearest 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 5-nearest 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'
name-value 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 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 3-nearest 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 double-clicking Mdl
in the Workspace window. This opens the Variable Editor.
Train a k-nearest neighbor classifier using the chi-square distance.
Load Fisher's iris data set.
load fisheriris X = meas; % Predictors Y = species; % Response
The chi-square distance between j-dimensional points x and z is
where is a weight associated with dimension j.
Specify the chi-square 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 arbitrary weights for illustration.
Train a 3-nearest neighbor classifier. It is good practice to standardize noncategorical predictor data.
k = 3; w = [0.3; 0.3; 0.2; 0.2]; KNNMdl = fitcknn(X,Y,'Distance',@(x,Z)chiSqrDist(x,Z,w),... 'NumNeighbors',k,'Standardize',1);
KNNMdl
is a ClassificationKNN
classifier.
Cross validate the KNN classifier using the default 10-fold cross validation. Examine the classification error.
rng(1); % For reproducibility
CVKNNMdl = crossval(KNNMdl);
classError = kfoldLoss(CVKNNMdl)
classError = 0.0600
CVKNNMdl
is a ClassificationPartitionedModel
classifier. The 10-fold 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 out-of-sample 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 five-fold cross-validation loss by using automatic hyperparameter optimization.
For reproducibility, set the random seed and use the 'expected-improvement-plus'
acquisition function.
rng(1) Mdl = fitcknn(X,Y,'OptimizeHyperparameters','auto',... 'HyperparameterOptimizationOptions',... struct('AcquisitionFunctionName','expected-improvement-plus'))
|=====================================================================================================| | Iter | Eval | Objective | Objective | BestSoFar | BestSoFar | NumNeighbors | Distance | | | result | | runtime | (observed) | (estim.) | | | |=====================================================================================================| | 1 | Best | 0.026667 | 0.38032 | 0.026667 | 0.026667 | 30 | cosine |
| 2 | Accept | 0.04 | 0.19092 | 0.026667 | 0.027197 | 2 | chebychev |
| 3 | Accept | 0.19333 | 0.17174 | 0.026667 | 0.030324 | 1 | hamming |
| 4 | Accept | 0.33333 | 0.13321 | 0.026667 | 0.033313 | 31 | spearman |
| 5 | Best | 0.02 | 0.095385 | 0.02 | 0.020648 | 6 | cosine |
| 6 | Accept | 0.073333 | 0.083643 | 0.02 | 0.023082 | 1 | correlation |
| 7 | Accept | 0.06 | 0.12872 | 0.02 | 0.020875 | 2 | cityblock |
| 8 | Accept | 0.04 | 0.079667 | 0.02 | 0.020622 | 1 | euclidean |
| 9 | Accept | 0.24 | 0.16029 | 0.02 | 0.020562 | 74 | mahalanobis |
| 10 | Accept | 0.04 | 0.14001 | 0.02 | 0.020649 | 1 | minkowski |
| 11 | Accept | 0.053333 | 0.13818 | 0.02 | 0.020722 | 1 | seuclidean |
| 12 | Accept | 0.19333 | 0.074169 | 0.02 | 0.020701 | 1 | jaccard |
| 13 | Accept | 0.04 | 0.10282 | 0.02 | 0.029203 | 1 | cosine |
| 14 | Accept | 0.04 | 0.091058 | 0.02 | 0.031888 | 75 | cosine |
| 15 | Accept | 0.04 | 0.095554 | 0.02 | 0.020076 | 1 | cosine |
| 16 | Accept | 0.093333 | 0.29387 | 0.02 | 0.020073 | 75 | euclidean |
| 17 | Accept | 0.093333 | 0.10418 | 0.02 | 0.02007 | 75 | minkowski |
| 18 | Accept | 0.1 | 0.067001 | 0.02 | 0.020061 | 75 | chebychev |
| 19 | Accept | 0.15333 | 0.18021 | 0.02 | 0.020044 | 75 | seuclidean |
| 20 | Accept | 0.1 | 0.10199 | 0.02 | 0.020044 | 75 | cityblock |
|=====================================================================================================| | Iter | Eval | Objective | Objective | BestSoFar | BestSoFar | NumNeighbors | Distance | | | result | | runtime | (observed) | (estim.) | | | |=====================================================================================================| | 21 | Accept | 0.033333 | 0.081121 | 0.02 | 0.020046 | 75 | correlation |
| 22 | Accept | 0.033333 | 0.14341 | 0.02 | 0.02656 | 9 | cosine |
| 23 | Accept | 0.033333 | 0.18846 | 0.02 | 0.02854 | 9 | cosine |
| 24 | Accept | 0.02 | 0.13142 | 0.02 | 0.028607 | 1 | chebychev |
| 25 | Accept | 0.02 | 0.10426 | 0.02 | 0.022264 | 1 | chebychev |
| 26 | Accept | 0.02 | 0.086858 | 0.02 | 0.021439 | 1 | chebychev |
| 27 | Accept | 0.02 | 0.11524 | 0.02 | 0.020999 | 1 | chebychev |
| 28 | Accept | 0.66667 | 0.10936 | 0.02 | 0.020008 | 75 | hamming |
| 29 | Accept | 0.04 | 0.14877 | 0.02 | 0.020008 | 12 | correlation |
| 30 | Best | 0.013333 | 0.12615 | 0.013333 | 0.013351 | 6 | euclidean |
__________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 60.3346 seconds Total objective function evaluation time: 4.048 Best observed feasible point: NumNeighbors Distance ____________ _________ 6 euclidean Observed objective function value = 0.013333 Estimated objective function value = 0.013351 Function evaluation time = 0.12615 Best estimated feasible point (according to models): NumNeighbors Distance ____________ _________ 6 euclidean Estimated objective function value = 0.013351 Estimated function evaluation time = 0.12609
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, a logical or numeric
vector, or a cell array of character vectors. If
Y
is a character array, then each
element of the response variable must correspond to one row of
the array.
A good practice is to specify the order of the classes by using the
ClassNames
name-value pair
argument.
Data Types: char
| string
formula
— Explanatory model of response variable and subset of predictor variablesExplanatory 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. The following code returns logical 1
(true
) for each variable that has a valid variable name.
cellfun(@isvarname,Tbl.Properties.VariableNames)
Tbl
are not valid, then convert them by using the
matlab.lang.makeValidName
function.Tbl.Properties.VariableNames = matlab.lang.makeValidName(Tbl.Properties.VariableNames);
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
name-value pair argument.
Data Types: double
| single
Specify optional
comma-separated 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 three-nearest neighbors using the nearest neighbor search
method and the Minkowski metric.Note
You cannot use any cross-validation name-value pair argument along with the
'OptimizeHyperparameters'
name-value pair argument. You can modify
the cross-validation for 'OptimizeHyperparameters'
only by using the
'HyperparameterOptimizationOptions'
name-value pair
argument.
'BreakTies'
— Tie-breaking algorithm'smallest'
(default) | 'nearest'
| 'random'
Tie-breaking algorithm used by the predict
method
if multiple classes have the same smallest cost, specified as the
comma-separated 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 kd-tree,
specified as the comma-separated 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 comma-separated
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. If Tbl
includes both continuous and categorical values, then you must specify the
value of 'CategoricalPredictors'
so that
fitcknn
can determine how to treat all
predictors, as either continuous or categorical variables.
If the predictor data is a matrix (X
),
fitcknn
assumes that all predictors are
continuous. To identify all predictors in X
as
categorical, specify 'CategoricalPredictors'
as
'all'
.
When you set CategoricalPredictors
to 'all'
,
the default Distance
is 'hamming'
.
Example: 'CategoricalPredictors','all'
'ClassNames'
— Names of classes to use for trainingNames of classes to use for training, specified as the comma-separated 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 comma-separated
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
name-value
pair argument.
Structure S
having two fields: S.ClassNames
containing
the group names as a variable of the same type as Y
,
and S.ClassificationCosts
containing the cost matrix.
The default is Cost(i,j)=1
if i~=j
,
and Cost(i,j)=0
if i=j
.
Data Types: single
| double
| struct
'Cov'
— Covariance matrixcov(X,'omitrows')
(default) | positive definite matrix of scalar valuesCovariance matrix, specified as the comma-separated 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 comma-separated pair consisting
of 'Distance'
and a valid distance metric name
or function handle. The allowable distance metric names depend on
your choice of a neighbor-searcher method (see NSMethod
).
NSMethod | 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' name-value pair
argument. |
'minkowski' | Minkowski distance. The default exponent is 2 .
To specify a different exponent, use the 'Exponent' name-value
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
name-value 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 comma-separated
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/distance2 |
@ | 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 comma-separated
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 flagfalse
(default) | true
Tie inclusion flag, specified as the comma-separated 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 comma-separated
pair consisting of 'NSMethod'
and 'kdtree'
or 'exhaustive'
.
'kdtree'
— Creates and uses a
kd-tree to find nearest neighbors.
'kdtree'
is valid when the distance metric is one of the
following:
'euclidean'
'cityblock'
'minkowski'
'chebychev'
'exhaustive'
— Uses the exhaustive search algorithm.
When predicting the class of a new point xnew
, the software
computes the distance values from all points in X
to
xnew
to find nearest neighbors.
The default is 'kdtree'
when X
has 10
or
fewer columns, X
is not sparse, and the distance
metric is a 'kdtree'
type; otherwise, 'exhaustive'
.
Example: 'NSMethod','exhaustive'
'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 comma-separated
pair consisting of 'NumNeighbors'
and a positive
integer value.
Example: 'NumNeighbors',3
Data Types: single
| double
'PredictorNames'
— Predictor variable namesPredictor variable names, specified as the comma-separated 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 assign names to the predictor
variables in X
.
The order of the names in PredictorNames
must correspond to the column order of X
.
That is, PredictorNames{1}
is the name of
X(:,1)
,
PredictorNames{2}
is the name of
X(:,2)
, and so on. Also,
size(X,2)
and
numel(PredictorNames)
must be
equal.
By default, PredictorNames
is
{'x1','x2',...}
.
If you supply Tbl
, then you can use
'PredictorNames'
to choose which predictor variables
to use in training. That is, fitcknn
uses only the
predictor variables in PredictorNames
and the response
variable during training.
PredictorNames
must be a subset of
Tbl.Properties.VariableNames
and cannot
include the name of the response variable.
By default, PredictorNames
contains the
names of all predictor variables.
A good practice is to specify the predictors for training
using either 'PredictorNames'
or
formula
, but not both.
Example: 'PredictorNames',{'SepalLength','SepalWidth','PetalLength','PetalWidth'}
Data Types: string
| cell
'Prior'
— Prior probabilities'empirical'
(default) | 'uniform'
| vector of scalar values | structurePrior probabilities for each class, specified as the comma-separated
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 name-value
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 comma-separated 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 scalestd(X,'omitnan')
(default) | vector of nonnegative scalar valuesDistance scale, specified as the comma-separated 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 comma-separated 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 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 predictorsfalse
(default) | true
Flag to standardize the predictors, specified as the comma-separated
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 weightsTbl
Observation weights, specified as the comma-separated 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'
— Cross-validation flag'off'
(default) | 'on'
Cross-validation flag, specified as the comma-separated pair
consisting of 'Crossval'
and 'on'
or 'off'
.
If you specify 'on'
, then the software implements
10-fold cross-validation.
To override this cross-validation setting, use one of these
name-value pair arguments: CVPartition
, Holdout
, KFold
,
or Leaveout
. To create a cross-validated model,
you can use one cross-validation name-value pair argument at a time
only.
Alternatively, cross-validate later by passing Mdl
to crossval
.
Example: 'CrossVal','on'
'CVPartition'
— Cross-validation partition[]
(default) | cvpartition
partition objectCross-validation partition, specified as the comma-separated pair consisting of
'CVPartition'
and a cvpartition
partition
object created by cvpartition
. The partition object
specifies the type of cross-validation and the indexing for the training and validation
sets.
To create a cross-validated model, you can use one of these four name-value pair arguments
only: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: Suppose you create a random partition for 5-fold cross-validation on 500
observations by using cvp = cvpartition(500,'KFold',5)
. Then, you can
specify the cross-validated model by using
'CVPartition',cvp
.
'Holdout'
— Fraction of data for holdout validationFraction of the data used for holdout validation, specified as the comma-separated 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 cross-validated model.
To create a cross-validated model, you can use one of these
four name-value 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 cross-validated model, specified as the comma-separated 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
-by-1 cell vector in the Trained
property of the cross-validated model.
To create a cross-validated model, you can use one of these
four name-value pair arguments only: CVPartition
, Holdout
, KFold
,
or Leaveout
.
Example: 'KFold',5
Data Types: single
| double
'Leaveout'
— Leave-one-out cross-validation flag'off'
(default) | 'on'
Leave-one-out cross-validation flag, specified as the comma-separated 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
n-by-1 cell vector in the Trained
property of the cross-validated model.
To create a cross-validated model, you can use one of these
four name-value pair arguments only: 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
objectsParameters to optimize, specified as the comma-separated 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 cross-validation loss
(error) for fitcknn
by varying the parameters. For
information about cross-validation loss (albeit in a different context),
see Classification Loss. To control the
cross-validation type and other aspects of the optimization, use the
HyperparameterOptimizationOptions
name-value
pair.
Note
'OptimizeHyperparameters'
values override any values you set using
other name-value 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 log-scaled in the range [1,
max(2,round(NumObservations/2))]
.
Standardize
—
fitcknn
searches among the values
'true'
and
'false'
.
Set nondefault parameters by passing a vector of
optimizableVariable
objects that have nondefault
values. For example,
load fisheriris params = hyperparameters('fitcknn',meas,species); params(1).Range = [1,20];
Pass params
as the value of
OptimizeHyperparameters
.
By default, 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 + cross-validation loss) for regression and the misclassification rate for classification. To control
the iterative display, set the Verbose
field of the
'HyperparameterOptimizationOptions'
name-value pair argument. To
control the plots, set the ShowPlots
field of the
'HyperparameterOptimizationOptions'
name-value pair argument.
For an example, see Optimize Fitted KNN Classifier.
Example: 'auto'
'HyperparameterOptimizationOptions'
— Options for optimizationOptions for optimization, specified as the comma-separated pair consisting of
'HyperparameterOptimizationOptions'
and a structure. This
argument modifies the effect of the OptimizeHyperparameters
name-value pair argument. All fields in the structure are optional.
Field Name | Values | Default |
---|---|---|
Optimizer |
| 'bayesopt' |
AcquisitionFunctionName |
Acquisition functions whose names include
| 'expected-improvement-per-second-plus' |
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™. Due to the nonreproducibility of parallel timing, parallel Bayesian optimization does not necessarily yield reproducible results. For details, see Parallel Bayesian Optimization. | false |
Repartition | Logical value indicating whether to repartition the cross-validation at every iteration. If
| 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 cross-validation
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 k-nearest neighbor classification modelClassificationKNN
model object | ClassificationPartitionedModel
cross-validated model
objectTrained k-nearest neighbor classification model,
returned as a ClassificationKNN
model object or
a ClassificationPartitionedModel
cross-validated model object.
If you set any of the name-value pair arguments
KFold
, Holdout
,
CrossVal
, or CVPartition
, then
Mdl
is a
ClassificationPartitionedModel
cross-validated model
object. Otherwise, Mdl
is a
ClassificationKNN
model object.
To reference properties of Mdl
, use dot notation. For
example, to display the distance metric at the Command Window, enter
Mdl.Distance
.
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
mean
and std
with the
'omitnan'
option 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 cov
with the
'omitrows'
option 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
and the weighted standard deviation is
where Bj is the set of indices k for which xjk and wk 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,
where B is the set of indices j for which the observation xj does not have any missing values and wj 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 perform parallel hyperparameter optimization, use the
'HyperparameterOptimizationOptions', struct('UseParallel',true)
name-value 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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