fitckernel
Fit binary Gaussian kernel classifier using random feature expansion
Syntax
Description
fitckernel
trains or cross-validates a binary Gaussian
kernel classification model for nonlinear classification.
fitckernel
is more practical for big data applications that
have large training sets but can also be applied to smaller data sets that fit in
memory.
fitckernel
maps data in a low-dimensional space into a
high-dimensional space, then fits a linear model in the high-dimensional space by
minimizing the regularized objective function. Obtaining the linear model in the
high-dimensional space is equivalent to applying the Gaussian kernel to the model in the
low-dimensional space. Available linear classification models include regularized
support vector machine (SVM) and logistic regression models.
To train a nonlinear SVM model for binary classification of in-memory data, see
fitcsvm
.
returns a binary Gaussian kernel classification model trained using the
predictor data in Mdl
= fitckernel(X
,Y
)X
and the corresponding class labels in
Y
. The fitckernel
function maps
the predictors in a low-dimensional space into a high-dimensional space, then
fits a binary SVM model to the transformed predictors and class labels. This
linear model is equivalent to the Gaussian kernel classification model in the
low-dimensional space.
returns a kernel classification model Mdl
= fitckernel(Tbl
,ResponseVarName
)Mdl
trained using the
predictor variables contained in the table Tbl
and the
class labels in Tbl.ResponseVarName
.
specifies options using one or more name-value pair arguments in addition to any
of the input argument combinations in previous syntaxes. For example, you can
implement logistic regression, specify the number of dimensions of the expanded
space, or specify to cross-validate.Mdl
= fitckernel(___,Name,Value
)
[
also returns the hyperparameter optimization results when you specify
Mdl
,FitInfo
,HyperparameterOptimizationResults
] = fitckernel(___)OptimizeHyperparameters
.
[
also returns Mdl
,AggregateOptimizationResults
] = fitckernel(___)AggregateOptimizationResults
, which contains
hyperparameter optimization results when you specify the
OptimizeHyperparameters
and
HyperparameterOptimizationOptions
name-value arguments.
You must also specify the ConstraintType
and
ConstraintBounds
options of
HyperparameterOptimizationOptions
. You can use this
syntax to optimize on compact model size instead of cross-validation loss, and
to perform a set of multiple optimization problems that have the same options
but different constraint bounds.
Examples
Train Kernel Classification Model
Train a binary kernel classification model using SVM.
Load the ionosphere
data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b'
) or good ('g'
).
load ionosphere
[n,p] = size(X)
n = 351
p = 34
resp = unique(Y)
resp = 2x1 cell
{'b'}
{'g'}
Train a binary kernel classification model that identifies whether the radar return is bad ('b'
) or good ('g'
). Extract a fit summary to determine how well the optimization algorithm fits the model to the data.
rng('default') % For reproducibility [Mdl,FitInfo] = fitckernel(X,Y)
Mdl = ClassificationKernel ResponseName: 'Y' ClassNames: {'b' 'g'} Learner: 'svm' NumExpansionDimensions: 2048 KernelScale: 1 Lambda: 0.0028 BoxConstraint: 1
FitInfo = struct with fields:
Solver: 'LBFGS-fast'
LossFunction: 'hinge'
Lambda: 0.0028
BetaTolerance: 1.0000e-04
GradientTolerance: 1.0000e-06
ObjectiveValue: 0.2604
GradientMagnitude: 0.0028
RelativeChangeInBeta: 8.2512e-05
FitTime: 0.0960
History: []
Mdl
is a ClassificationKernel
model. To inspect the in-sample classification error, you can pass Mdl
and the training data or new data to the loss
function. Or, you can pass Mdl
and new predictor data to the predict
function to predict class labels for new observations. You can also pass Mdl
and the training data to the resume
function to continue training.
FitInfo
is a structure array containing optimization information. Use FitInfo
to determine whether optimization termination measurements are satisfactory.
For better accuracy, you can increase the maximum number of optimization iterations ('IterationLimit'
) and decrease the tolerance values ('BetaTolerance'
and 'GradientTolerance'
) by using the name-value pair arguments. Doing so can improve measures like ObjectiveValue
and RelativeChangeInBeta
in FitInfo
. You can also optimize model parameters by using the 'OptimizeHyperparameters'
name-value pair argument.
Cross-Validate Kernel Classification Model
Load the ionosphere
data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b'
) or good ('g'
).
load ionosphere rng('default') % For reproducibility
Cross-validate a binary kernel classification model. By default, the software uses 10-fold cross-validation.
CVMdl = fitckernel(X,Y,'CrossVal','on')
CVMdl = ClassificationPartitionedKernel CrossValidatedModel: 'Kernel' ResponseName: 'Y' NumObservations: 351 KFold: 10 Partition: [1x1 cvpartition] ClassNames: {'b' 'g'} ScoreTransform: 'none'
numel(CVMdl.Trained)
ans = 10
CVMdl
is a ClassificationPartitionedKernel
model. Because fitckernel
implements 10-fold cross-validation, CVMdl
contains 10 ClassificationKernel
models that the software trains on training-fold (in-fold) observations.
Estimate the cross-validated classification error.
kfoldLoss(CVMdl)
ans = 0.0940
The classification error rate is approximately 9%.
Optimize Kernel Classifier
Optimize hyperparameters automatically using the OptimizeHyperparameters
name-value argument.
Load the ionosphere
data set. This data set has 34 predictors and 351 binary responses for radar returns, either bad ('b'
) or good ('g'
).
load ionosphere
Find hyperparameters that minimize five-fold cross-validation loss by using automatic hyperparameter optimization. Specify OptimizeHyperparameters
as 'auto'
so that fitckernel
finds optimal values of the KernelScale
, Lambda
, and Standardize
name-value arguments. For reproducibility, set the random seed and use the 'expected-improvement-plus'
acquisition function.
rng('default') [Mdl,FitInfo,HyperparameterOptimizationResults] = fitckernel(X,Y,'OptimizeHyperparameters','auto',... 'HyperparameterOptimizationOptions',struct('AcquisitionFunctionName','expected-improvement-plus'))
|====================================================================================================================| | Iter | Eval | Objective | Objective | BestSoFar | BestSoFar | KernelScale | Lambda | Standardize | | | result | | runtime | (observed) | (estim.) | | | | |====================================================================================================================| | 1 | Best | 0.35897 | 2.3903 | 0.35897 | 0.35897 | 3.8653 | 2.7394 | true | | 2 | Accept | 0.35897 | 0.40434 | 0.35897 | 0.35897 | 429.99 | 0.0006775 | false | | 3 | Accept | 0.35897 | 0.57429 | 0.35897 | 0.35897 | 0.11801 | 0.025493 | false | | 4 | Accept | 0.41311 | 0.50318 | 0.35897 | 0.35898 | 0.0010694 | 9.1346e-06 | true | | 5 | Accept | 0.4245 | 0.68218 | 0.35897 | 0.35898 | 0.0093918 | 2.8526e-06 | false | | 6 | Best | 0.17094 | 0.39654 | 0.17094 | 0.17102 | 15.285 | 0.0038931 | false | | 7 | Accept | 0.18234 | 0.47982 | 0.17094 | 0.17099 | 9.9078 | 0.0090818 | false | | 8 | Accept | 0.35897 | 0.35852 | 0.17094 | 0.17097 | 26.961 | 0.46727 | false | | 9 | Best | 0.082621 | 0.4906 | 0.082621 | 0.082677 | 7.7184 | 0.0025676 | false | | 10 | Best | 0.059829 | 0.62044 | 0.059829 | 0.059839 | 5.6125 | 0.0013416 | false | | 11 | Accept | 0.062678 | 0.55309 | 0.059829 | 0.059793 | 7.3294 | 0.00062394 | false | | 12 | Best | 0.048433 | 0.93641 | 0.048433 | 0.050198 | 3.7772 | 0.00032964 | false | | 13 | Accept | 0.051282 | 0.95284 | 0.048433 | 0.049662 | 3.4417 | 0.00077524 | false | | 14 | Accept | 0.054131 | 1.0627 | 0.048433 | 0.051494 | 4.3694 | 0.00055199 | false | | 15 | Accept | 0.051282 | 1.225 | 0.048433 | 0.04872 | 1.7463 | 0.00012886 | false | | 16 | Accept | 0.048433 | 0.88001 | 0.048433 | 0.048475 | 3.9086 | 3.1147e-05 | false | | 17 | Accept | 0.054131 | 0.98807 | 0.048433 | 0.050325 | 3.1489 | 9.1315e-05 | false | | 18 | Accept | 0.051282 | 0.73412 | 0.048433 | 0.049131 | 2.3414 | 4.8238e-06 | false | | 19 | Accept | 0.062678 | 1.0564 | 0.048433 | 0.049062 | 7.2203 | 3.2694e-06 | false | | 20 | Accept | 0.054131 | 0.58096 | 0.048433 | 0.051225 | 3.5381 | 1.0341e-05 | false | |====================================================================================================================| | Iter | Eval | Objective | Objective | BestSoFar | BestSoFar | KernelScale | Lambda | Standardize | | | result | | runtime | (observed) | (estim.) | | | | |====================================================================================================================| | 21 | Accept | 0.068376 | 0.58595 | 0.048433 | 0.05111 | 1.4267 | 1.7614e-05 | false | | 22 | Accept | 0.054131 | 0.81825 | 0.048433 | 0.05127 | 3.2173 | 2.9573e-06 | false | | 23 | Accept | 0.05698 | 1.0053 | 0.048433 | 0.051187 | 2.4241 | 0.0003272 | false | | 24 | Accept | 0.059829 | 1.4387 | 0.048433 | 0.051097 | 2.5948 | 4.5059e-05 | false | | 25 | Accept | 0.059829 | 0.95757 | 0.048433 | 0.051018 | 7.2989 | 2.6908e-05 | false | | 26 | Accept | 0.068376 | 1.261 | 0.048433 | 0.048938 | 3.9585 | 6.9173e-06 | false | | 27 | Accept | 0.05698 | 0.98149 | 0.048433 | 0.051222 | 4.2751 | 0.0002231 | false | | 28 | Accept | 0.062678 | 0.54509 | 0.048433 | 0.051232 | 1.4533 | 2.8533e-06 | false | | 29 | Accept | 0.051282 | 0.90554 | 0.048433 | 0.051122 | 3.8449 | 0.00059747 | false | | 30 | Accept | 0.21083 | 1.0227 | 0.048433 | 0.0512 | 45.588 | 3.056e-06 | false | __________________________________________________________ Optimization completed. MaxObjectiveEvaluations of 30 reached. Total function evaluations: 30 Total elapsed time: 40.3496 seconds Total objective function evaluation time: 25.3913 Best observed feasible point: KernelScale Lambda Standardize ___________ __________ ___________ 3.7772 0.00032964 false Observed objective function value = 0.048433 Estimated objective function value = 0.05162 Function evaluation time = 0.93641 Best estimated feasible point (according to models): KernelScale Lambda Standardize ___________ __________ ___________ 3.8449 0.00059747 false Estimated objective function value = 0.0512 Estimated function evaluation time = 0.89718
Mdl = ClassificationKernel ResponseName: 'Y' ClassNames: {'b' 'g'} Learner: 'svm' NumExpansionDimensions: 2048 KernelScale: 3.8449 Lambda: 5.9747e-04 BoxConstraint: 4.7684
FitInfo = struct with fields:
Solver: 'LBFGS-fast'
LossFunction: 'hinge'
Lambda: 5.9747e-04
BetaTolerance: 1.0000e-04
GradientTolerance: 1.0000e-06
ObjectiveValue: 0.1006
GradientMagnitude: 0.0114
RelativeChangeInBeta: 9.3027e-05
FitTime: 0.1755
History: []
HyperparameterOptimizationResults = BayesianOptimization with properties: ObjectiveFcn: @createObjFcn/inMemoryObjFcn VariableDescriptions: [5x1 optimizableVariable] Options: [1x1 struct] MinObjective: 0.0484 XAtMinObjective: [1x3 table] MinEstimatedObjective: 0.0512 XAtMinEstimatedObjective: [1x3 table] NumObjectiveEvaluations: 30 TotalElapsedTime: 40.3496 NextPoint: [1x3 table] XTrace: [30x3 table] ObjectiveTrace: [30x1 double] ConstraintsTrace: [] UserDataTrace: {30x1 cell} ObjectiveEvaluationTimeTrace: [30x1 double] IterationTimeTrace: [30x1 double] ErrorTrace: [30x1 double] FeasibilityTrace: [30x1 logical] FeasibilityProbabilityTrace: [30x1 double] IndexOfMinimumTrace: [30x1 double] ObjectiveMinimumTrace: [30x1 double] EstimatedObjectiveMinimumTrace: [30x1 double]
For big data, the optimization procedure can take a long time. If the data set is too large to run the optimization procedure, you can try to optimize the parameters using only partial data. Use the datasample
function and specify 'Replace','false'
to sample data without replacement.
Input Arguments
X
— Predictor data
numeric matrix
Predictor data, specified as an n-by-p numeric matrix, where n is the number of observations and p is the number of predictors.
The length of Y
and the number of observations in
X
must be equal.
Data Types: single
| double
Y
— Class labels
categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors
Class labels, specified as a categorical, character, or string array, logical or numeric vector, or cell array of character vectors.
fitckernel
supports only binary classification. EitherY
must contain exactly two distinct classes, or you must specify two classes for training by using theClassNames
name-value pair argument. For multiclass learning, seefitcecoc
.The length of
Y
must be equal to the number of observations inX
orTbl
.If
Y
is a character array, then each label must correspond to one row of the array.A good practice is to specify the class order by using the
ClassNames
name-value pair argument.
Data Types: categorical
| char
| string
| logical
| single
| double
| cell
Tbl
— Sample data
table
Sample data used to train the model, specified as a table. Each row of Tbl
corresponds to one observation, and each column corresponds to one predictor variable. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.
Optionally, Tbl
can contain a column for the response variable and a column for the observation weights.
The response variable must be a categorical, character, or string array, a logical or numeric vector, or a cell array of character vectors.
fitckernel
supports only binary classification. Either the response variable must contain exactly two distinct classes, or you must specify two classes for training by using theClassNames
name-value argument. For multiclass learning, seefitcecoc
.A good practice is to specify the order of the classes in the response variable by using the
ClassNames
name-value argument.
The column for the weights must be a numeric vector.
You must specify the response variable in
Tbl
by usingResponseVarName
orformula
and specify the observation weights inTbl
by usingWeights
.Specify the response variable by using
ResponseVarName
—fitckernel
uses the remaining variables as predictors. To use a subset of the remaining variables inTbl
as predictors, specify predictor variables by usingPredictorNames
.Define a model specification by using
formula
—fitckernel
uses a subset of the variables inTbl
as predictor variables and the response variable, as specified informula
.
If Tbl
does not contain the response variable, then specify a response variable by using Y
. The length of the response variable Y
and the number of rows in Tbl
must be equal. To use a subset of the variables in Tbl
as predictors, specify predictor variables by using PredictorNames
.
Data Types: table
ResponseVarName
— Response variable name
name of variable in Tbl
Response variable name, specified as the name of a variable in
Tbl
.
You must specify ResponseVarName
as a character vector or string scalar.
For example, if the response variable Y
is
stored as Tbl.Y
, then specify it as
"Y"
. Otherwise, the software
treats all columns of Tbl
, including
Y
, as predictors when training
the model.
The response variable must be a categorical, character, or string array; a logical or numeric
vector; or a cell array of character vectors. If
Y
is a character array, then each
element of the response variable must correspond to one row of
the array.
A good practice is to specify the order of the classes by using the
ClassNames
name-value
argument.
Data Types: char
| string
formula
— Explanatory model of response variable and subset of predictor variables
character vector | string scalar
Explanatory model of the response variable and a subset of the predictor variables,
specified as a character vector or string scalar in the form
"Y~x1+x2+x3"
. In this form, Y
represents the
response variable, and x1
, x2
, and
x3
represent the predictor variables.
To specify a subset of variables in Tbl
as predictors for
training the model, use a formula. If you specify a formula, then the software does not
use any variables in Tbl
that do not appear in
formula
.
The variable names in the formula must be both variable names in Tbl
(Tbl.Properties.VariableNames
) and valid MATLAB® identifiers. You can verify the variable names in Tbl
by
using the isvarname
function. If the variable names
are not valid, then you can convert them by using the matlab.lang.makeValidName
function.
Data Types: char
| string
Note
The software treats NaN
, empty character vector
(''
), empty string (""
),
<missing>
, and <undefined>
elements as missing values, and removes observations with any of these characteristics:
Missing value in the response variable
At least one missing value in a predictor observation (row in
X
orTbl
)NaN
value or0
weight ('Weights'
)
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: Mdl =
fitckernel(X,Y,'Learner','logistic','NumExpansionDimensions',2^15,'KernelScale','auto')
implements logistic regression after mapping the predictor data to the
2^15
dimensional space using feature expansion with a kernel
scale parameter selected by a heuristic procedure.
Note
You cannot use any cross-validation name-value argument together with the
OptimizeHyperparameters
name-value argument. You can modify the
cross-validation for OptimizeHyperparameters
only by using the
HyperparameterOptimizationOptions
name-value argument.
Learner
— Linear classification model type
'svm'
(default) | 'logistic'
Linear classification model type, specified as the comma-separated pair consisting of 'Learner'
and 'svm'
or 'logistic'
.
In the following table,
x is an observation (row vector) from p predictor variables.
is a transformation of an observation (row vector) for feature expansion. T(x) maps x in to a high-dimensional space ().
β is a vector of coefficients.
b is the scalar bias.
Value | Algorithm | Response Range | Loss Function |
---|---|---|---|
'svm' | Support vector machine | y ∊ {–1,1}; 1 for the positive class and –1 otherwise | Hinge: |
'logistic' | Logistic regression | Same as 'svm' | Deviance (logistic): |
Example: 'Learner','logistic'
NumExpansionDimensions
— Number of dimensions of expanded space
'auto'
(default) | positive integer
Number of dimensions of the expanded space, specified as the comma-separated
pair consisting of 'NumExpansionDimensions'
and
'auto'
or a positive integer. For
'auto'
, the fitckernel
function selects the number of dimensions using
2.^ceil(min(log2(p)+5,15))
, where
p
is the number of predictors.
For details, see Random Feature Expansion.
Example: 'NumExpansionDimensions',2^15
Data Types: char
| string
| single
| double
KernelScale
— Kernel scale parameter
1
(default) | "auto"
| positive scalar
Kernel scale parameter, specified as "auto"
or a positive scalar. The
software obtains a random basis for random feature expansion by using the kernel scale
parameter. For details, see Random Feature Expansion.
If you specify "auto"
, then the software selects an appropriate kernel
scale parameter using a heuristic procedure. This heuristic procedure uses subsampling,
so estimates can vary from one call to another. Therefore, to reproduce results, set a
random number seed by using rng
before training.
Example: KernelScale="auto"
Data Types: char
| string
| single
| double
BoxConstraint
— Box constraint
1 (default) | positive scalar
Box constraint, specified as the comma-separated pair consisting of
'BoxConstraint'
and a positive scalar.
This argument is valid only when 'Learner'
is
'svm'
(default) and you do not
specify a value for the regularization term strength
'Lambda'
. You can specify
either 'BoxConstraint'
or
'Lambda'
because the box
constraint (C) and the
regularization term strength (λ)
are related by C =
1/(λn), where n is the
number of observations.
Example: 'BoxConstraint',100
Data Types: single
| double
Lambda
— Regularization term strength
'auto'
(default) | nonnegative scalar
Regularization term strength, specified as the comma-separated pair consisting of 'Lambda'
and 'auto'
or a nonnegative scalar.
For 'auto'
, the value of Lambda
is
1/n, where n is the number of
observations.
When Learner
is 'svm'
, you can specify either
BoxConstraint
or Lambda
because the box
constraint (C) and the regularization term strength
(λ) are related by C =
1/(λn).
Example: 'Lambda',0.01
Data Types: char
| string
| single
| double
Standardize
— Flag to standardize predictor data
false
or 0
(default) | true
or 1
Since R2023b
Flag to standardize the predictor data, specified as a numeric or logical 0
(false
) or 1
(true
). If you
set Standardize
to true
, then the software
centers and scales each numeric predictor variable by the corresponding column mean and
standard deviation. The software does not standardize the categorical predictors.
Example: "Standardize",true
Data Types: single
| double
| logical
CrossVal
— Flag to train cross-validated classifier
'off'
(default) | 'on'
Flag to train a cross-validated classifier, specified as the
comma-separated pair consisting of 'Crossval'
and
'on'
or 'off'
.
If you specify 'on'
, then the software trains a
cross-validated classifier with 10 folds.
You can override this cross-validation setting using the
CVPartition
, Holdout
,
KFold
, or Leaveout
name-value pair argument. You can use only one cross-validation
name-value pair argument at a time to create a cross-validated
model.
Example: 'Crossval','on'
CVPartition
— Cross-validation partition
[]
(default) | cvpartition
object
Cross-validation partition, specified as a cvpartition
object that specifies the type of cross-validation and the
indexing for the training and validation sets.
To create a cross-validated model, you can specify only one of these four name-value
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: Suppose you create a random partition for 5-fold cross-validation on 500
observations by using cvp = cvpartition(500,KFold=5)
. Then, you can
specify the cross-validation partition by setting
CVPartition=cvp
.
Holdout
— Fraction of data for holdout validation
scalar value in the range (0,1)
Fraction of the data used for holdout validation, specified as a scalar value in the range
(0,1). If you specify Holdout=p
, then the software completes these
steps:
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 specify only one of these four name-value
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: Holdout=0.1
Data Types: double
| single
KFold
— Number of folds
10
(default) | positive integer value greater than 1
Number of folds to use in the cross-validated model, specified as a positive integer value
greater than 1. If you specify KFold=k
, then the software completes
these steps:
Randomly partition the data into
k
sets.For each set, reserve the set as validation data, and train the model using the other
k
– 1 sets.Store the
k
compact trained models in ak
-by-1 cell vector in theTrained
property of the cross-validated model.
To create a cross-validated model, you can specify only one of these four name-value
arguments: CVPartition
, Holdout
,
KFold
, or Leaveout
.
Example: KFold=5
Data Types: single
| double
Leaveout
— Leave-one-out cross-validation flag
'off'
(default) | 'on'
Leave-one-out cross-validation flag, specified as 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), 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'
BetaTolerance
— Relative tolerance on linear coefficients and bias term
1e–4
(default) | nonnegative scalar
Relative tolerance on the linear coefficients and the bias term (intercept), specified as a nonnegative scalar.
Let , that is, the vector of the coefficients and the bias term at optimization iteration t. If , then optimization terminates.
If you also specify GradientTolerance
, then optimization terminates when the software satisfies either stopping criterion.
Example: BetaTolerance=1e–6
Data Types: single
| double
GradientTolerance
— Absolute gradient tolerance
1e–6
(default) | nonnegative scalar
Absolute gradient tolerance, specified as a nonnegative scalar.
Let be the gradient vector of the objective function with respect to the coefficients and bias term at optimization iteration t. If , then optimization terminates.
If you also specify BetaTolerance
, then optimization terminates when the
software satisfies either stopping criterion.
Example: GradientTolerance=1e–5
Data Types: single
| double
IterationLimit
— Maximum number of optimization iterations
positive integer
Maximum number of optimization iterations, specified as a positive integer.
The default value is 1000 if the transformed data fits in memory, as specified by the
BlockSize
name-value argument. Otherwise, the default value is
100.
Example: IterationLimit=500
Data Types: single
| double
BlockSize
— Maximum amount of allocated memory
4e^3
(4GB) (default) | positive scalar
Maximum amount of allocated memory (in megabytes), specified as the comma-separated pair consisting of 'BlockSize'
and a positive scalar.
If fitckernel
requires more memory than the value of
'BlockSize'
to hold the transformed predictor data, then the
software uses a block-wise strategy. For details about the block-wise strategy, see
Algorithms.
Example: 'BlockSize',1e4
Data Types: single
| double
RandomStream
— Random number stream
global stream (default) | random stream object
Random number stream for reproducibility of data transformation, specified as a random stream object. For details, see Random Feature Expansion.
Use RandomStream
to reproduce the random basis functions used by
fitckernel
to transform the predictor data to a
high-dimensional space. For details, see Managing the Global Stream Using RandStream
and Creating and Controlling a Random Number Stream.
Example: RandomStream=RandStream("mlfg6331_64")
HessianHistorySize
— Size of history buffer for Hessian approximation
15
(default) | positive integer
Size of the history buffer for Hessian approximation, specified as the comma-separated pair
consisting of 'HessianHistorySize'
and a positive integer. At each
iteration, fitckernel
composes the Hessian approximation by using
statistics from the latest HessianHistorySize
iterations.
Example: 'HessianHistorySize',10
Data Types: single
| double
Verbose
— Verbosity level
0
(default) | 1
Verbosity level, specified as the comma-separated pair consisting of
'Verbose'
and either 0
or
1
. Verbose
controls the
display of diagnostic information at the command line.
Value | Description |
---|---|
0 | fitckernel does not display
diagnostic information. |
1 | fitckernel displays and stores
the value of the objective function, gradient magnitude,
and other diagnostic information.
FitInfo.History contains the
diagnostic information. |
Example: 'Verbose',1
Data Types: single
| double
CategoricalPredictors
— Categorical predictors list
vector of positive integers | logical vector | character matrix | string array | cell array of character vectors | 'all'
Categorical predictors list, specified as one of the values in this table.
Value | Description |
---|---|
Vector of positive integers |
Each entry in the vector is an index value indicating that the corresponding predictor is
categorical. The index values are between 1 and If |
Logical vector |
A |
Character matrix | Each row of the matrix is the name of a predictor variable. The names must match the entries in PredictorNames . Pad the names with extra blanks so each row of the character matrix has the same length. |
String array or cell array of character vectors | Each element in the array is the name of a predictor variable. The names must match the entries in PredictorNames . |
"all" | All predictors are categorical. |
By default, if the
predictor data is in a table (Tbl
), fitckernel
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 the predictor data is a matrix
(X
), fitckernel
assumes that all predictors are
continuous. To identify any other predictors as categorical predictors, specify them by using
the CategoricalPredictors
name-value argument.
For the identified categorical predictors, fitckernel
creates dummy variables using two different schemes, depending on whether a categorical variable is unordered or ordered. For an unordered categorical variable, fitckernel
creates one dummy variable for each level of the categorical variable. For an ordered categorical variable, fitckernel
creates one less dummy variable than the number of categories. For details, see Automatic Creation of Dummy Variables.
Example: 'CategoricalPredictors','all'
Data Types: single
| double
| logical
| char
| string
| cell
ClassNames
— Names of classes to use for training
categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors
Names of classes to use for training, specified as a categorical, character, or string
array; a logical or numeric vector; or a cell array of character vectors.
ClassNames
must have the same data type as the response variable
in Tbl
or Y
.
If ClassNames
is a character array, then each element must correspond to one row of the array.
Use ClassNames
to:
Specify the order of the classes during training.
Specify the order of any input or output argument dimension that corresponds to the class order. For example, use
ClassNames
to specify the order of the dimensions ofCost
or the column order of classification scores returned bypredict
.Select a subset of classes for training. For example, suppose that the set of all distinct class names in
Y
is["a","b","c"]
. To train the model using observations from classes"a"
and"c"
only, specify"ClassNames",["a","c"]
.
The default value for ClassNames
is the set of all distinct class names in the response variable in Tbl
or Y
.
Example: "ClassNames",["b","g"]
Data Types: categorical
| char
| string
| logical
| single
| double
| cell
Cost
— Misclassification cost
square matrix | structure array
Misclassification cost, specified as the comma-separated pair consisting of
'Cost'
and a square matrix or structure.
If you specify the square matrix
cost
('Cost',cost
), thencost(i,j)
is the cost of classifying a point into classj
if its true class isi
. That is, the rows correspond to the true class, and the columns correspond to the predicted class. To specify the class order for the corresponding rows and columns ofcost
, use theClassNames
name-value pair argument.If you specify the structure
S
('Cost',S
), then it must have two fields:S.ClassNames
, which contains the class names as a variable of the same data type asY
S.ClassificationCosts
, which contains the cost matrix with rows and columns ordered as inS.ClassNames
The default value for Cost
is
ones(
, where K
) –
eye(K
)K
is
the number of distinct classes.
fitckernel
uses Cost
to adjust the prior
class probabilities specified in Prior
. Then,
fitckernel
uses the adjusted prior probabilities for
training.
Example: 'Cost',[0 2; 1 0]
Data Types: single
| double
| struct
PredictorNames
— Predictor variable names
string array of unique names | cell array of unique character vectors
Predictor variable names, specified as a string array of unique names or cell array of unique
character vectors. The functionality of PredictorNames
depends on the
way you supply the training data.
If you supply
X
andY
, then you can usePredictorNames
to assign names to the predictor variables inX
.The order of the names in
PredictorNames
must correspond to the column order ofX
. That is,PredictorNames{1}
is the name ofX(:,1)
,PredictorNames{2}
is the name ofX(:,2)
, and so on. Also,size(X,2)
andnumel(PredictorNames)
must be equal.By default,
PredictorNames
is{'x1','x2',...}
.
If you supply
Tbl
, then you can usePredictorNames
to choose which predictor variables to use in training. That is,fitckernel
uses only the predictor variables inPredictorNames
and the response variable during training.PredictorNames
must be a subset ofTbl.Properties.VariableNames
and cannot include the name of the response variable.By default,
PredictorNames
contains the names of all predictor variables.A good practice is to specify the predictors for training using either
PredictorNames
orformula
, but not both.
Example: "PredictorNames",["SepalLength","SepalWidth","PetalLength","PetalWidth"]
Data Types: string
| cell
Prior
— Prior probabilities
'empirical'
(default) | 'uniform'
| numeric vector | structure array
Prior probabilities for each class, specified as the comma-separated pair consisting
of 'Prior'
and 'empirical'
,
'uniform'
, a numeric vector, or a structure array.
This table summarizes the available options for setting prior probabilities.
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 their order in Y . If you specify
the order using the 'ClassNames' name-value
pair argument, then order the elements accordingly. |
structure array |
A structure
|
fitckernel
normalizes the prior probabilities in
Prior
to sum to 1.
Example: 'Prior',struct('ClassNames',{{'setosa','versicolor'}},'ClassProbs',1:2)
Data Types: char
| string
| double
| single
| struct
ResponseName
— Response variable name
"Y"
(default) | character vector | string scalar
Response variable name, specified as a character vector or string scalar.
If you supply
Y
, then you can useResponseName
to specify a name for the response variable.If you supply
ResponseVarName
orformula
, then you cannot useResponseName
.
Example: ResponseName="response"
Data Types: char
| string
ScoreTransform
— Score transformation
"none"
(default) | "doublelogit"
| "invlogit"
| "ismax"
| "logit"
| function handle | ...
Score transformation, specified as a character vector, string scalar, or function handle.
This table summarizes the available character vectors and string scalars.
Value | Description |
---|---|
"doublelogit" | 1/(1 + e–2x) |
"invlogit" | log(x / (1 – x)) |
"ismax" | Sets the score for the class with the largest score to 1, and sets the scores for all other classes to 0 |
"logit" | 1/(1 + e–x) |
"none" or "identity" | x (no transformation) |
"sign" | –1 for x < 0 0 for x = 0 1 for x > 0 |
"symmetric" | 2x – 1 |
"symmetricismax" | Sets the score for the class with the largest score to 1, and sets the scores for all other classes to –1 |
"symmetriclogit" | 2/(1 + e–x) – 1 |
For a MATLAB function or a function you define, use its function handle for the score transform. The function handle must accept a matrix (the original scores) and return a matrix of the same size (the transformed scores).
Example: "ScoreTransform","logit"
Data Types: char
| string
| function_handle
Weights
— Observation weights
nonnegative numeric vector | name of variable in Tbl
Observation weights, specified as a nonnegative numeric vector or the name of a
variable in Tbl
. The software weights each observation in
X
or Tbl
with the corresponding value in
Weights
. The length of Weights
must equal
the number of observations in 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 variable when training the model.
By default, Weights
is ones(n,1)
, where
n
is the number of observations in X
or
Tbl
.
The software normalizes Weights
to sum to the value of the prior
probability in the respective class.
Data Types: single
| double
| char
| string
OptimizeHyperparameters
— Parameters to optimize
'none'
(default) | 'auto'
| 'all'
| string array or cell array of eligible parameter names | vector of optimizableVariable
objects
Parameters to optimize, specified as the comma-separated pair
consisting of 'OptimizeHyperparameters'
and one of
these values:
'none'
— Do not optimize.'auto'
— Use{'KernelScale','Lambda','Standardize'}
.'all'
— Optimize all eligible parameters.Cell array of eligible parameter names.
Vector of
optimizableVariable
objects, typically the output ofhyperparameters
.
The optimization attempts to minimize the cross-validation loss
(error) for fitckernel
by varying the parameters. To control the
cross-validation type and other aspects of the optimization, use the
HyperparameterOptimizationOptions
name-value argument. When you use
HyperparameterOptimizationOptions
, you can use the (compact) model size
instead of the cross-validation loss as the optimization objective by setting the
ConstraintType
and ConstraintBounds
options.
Note
The values of OptimizeHyperparameters
override any values you
specify using other name-value arguments. For example, setting
OptimizeHyperparameters
to "auto"
causes
fitckernel
to optimize hyperparameters corresponding to the
"auto"
option and to ignore any specified values for the
hyperparameters.
The eligible parameters for fitckernel
are:
KernelScale
—fitckernel
searches among positive values, by default log-scaled in the range[1e-3,1e3]
.Lambda
—fitckernel
searches among positive values, by default log-scaled in the range[1e-3,1e3]/n
, wheren
is the number of observations.Learner
—fitckernel
searches among'svm'
and'logistic'
.NumExpansionDimensions
—fitckernel
searches among positive integers, by default log-scaled in the range[100,10000]
.Standardize
—fitckernel
searches amongtrue
andfalse
.
Set nondefault parameters by passing a vector of
optimizableVariable
objects that have nondefault
values. For example:
load fisheriris params = hyperparameters('fitckernel',meas,species); params(2).Range = [1e-4,1e6];
Pass params
as the value of
'OptimizeHyperparameters'
.
By default, the iterative display appears at the command line,
and plots appear according to the number of hyperparameters in the optimization. For the
optimization and plots, the objective function is the misclassification rate. To control the
iterative display, set the Verbose
option of the
HyperparameterOptimizationOptions
name-value argument. To control the
plots, set the ShowPlots
field of the
HyperparameterOptimizationOptions
name-value argument.
For an example, see Optimize Kernel Classifier.
Example: 'OptimizeHyperparameters','auto'
HyperparameterOptimizationOptions
— Options for optimization
HyperparameterOptimizationOptions
object | structure
Options for optimization, specified as a HyperparameterOptimizationOptions
object or a structure. This argument
modifies the effect of the OptimizeHyperparameters
name-value
argument. If you specify HyperparameterOptimizationOptions
, you must
also specify OptimizeHyperparameters
. All the options are optional.
However, you must set ConstraintBounds
and
ConstraintType
to return
AggregateOptimizationResults
. The options that you can set in a
structure are the same as those in the
HyperparameterOptimizationOptions
object.
Option | Values | Default |
---|---|---|
Optimizer |
| "bayesopt" |
ConstraintBounds | Constraint bounds for N optimization problems,
specified as an N-by-2 numeric matrix or
| [] |
ConstraintTarget | Constraint target for the optimization problems, specified as
| If you specify ConstraintBounds and
ConstraintType , then the default value is
"matlab" . Otherwise, the default value is
[] . |
ConstraintType | Constraint type for the optimization problems, specified as
| [] |
AcquisitionFunctionName | Type of acquisition function:
Acquisition functions whose names include
| "expected-improvement-per-second-plus" |
MaxObjectiveEvaluations | Maximum number of objective function evaluations. If you specify multiple
optimization problems using ConstraintBounds , the value of
MaxObjectiveEvaluations applies to each optimization
problem individually. | 30 for "bayesopt" and
"randomsearch" , and the entire grid for
"gridsearch" |
MaxTime | Time limit for the optimization, specified as a nonnegative real
scalar. The time limit is in seconds, as measured by | Inf |
NumGridDivisions | For Optimizer="gridsearch" , the number of values in each
dimension. The value can be a vector of positive integers giving the number of
values for each dimension, or a scalar that applies to all dimensions. This
option is ignored for categorical variables. | 10 |
ShowPlots | Logical value indicating whether to show plots of the optimization progress.
If this option is true , the software plots the best observed
objective function value against the iteration number. If you use Bayesian
optimization (Optimizer ="bayesopt" ), then
the software also plots the best estimated objective function value. The best
observed objective function values and best estimated objective function values
correspond to the values in the BestSoFar (observed) and
BestSoFar (estim.) columns of the iterative display,
respectively. You can find these values in the properties ObjectiveMinimumTrace and EstimatedObjectiveMinimumTrace of
Mdl.HyperparameterOptimizationResults . If the problem
includes one or two optimization parameters for Bayesian optimization, then
ShowPlots also plots a model of the objective function
against the parameters. | true |
SaveIntermediateResults | Logical value indicating whether to save the optimization results. If this
option is true , the software overwrites a workspace variable
named "BayesoptResults" at each iteration. The variable is a
BayesianOptimization object. If you
specify multiple optimization problems using
ConstraintBounds , the workspace variable is an AggregateBayesianOptimization object named
"AggregateBayesoptResults" . | false |
Verbose | Display level at the command line:
For details, see the | 1 |
UseParallel | Logical value indicating whether to run the Bayesian optimization in parallel, which requires Parallel Computing Toolbox™. Due to the nonreproducibility of parallel timing, parallel Bayesian optimization does not necessarily yield reproducible results. For details, see Parallel Bayesian Optimization. | false |
Repartition | Logical value indicating whether to repartition the cross-validation at
every iteration. If this option is A value of
| false |
Specify only one of the following three options. | ||
CVPartition | cvpartition object created by cvpartition | Kfold=5 if you do not specify a
cross-validation option |
Holdout | Scalar in the range (0,1) representing the holdout
fraction | |
Kfold | Integer greater than 1 |
Example: HyperparameterOptimizationOptions=struct(UseParallel=true)
Output Arguments
Mdl
— Trained kernel classification model
ClassificationKernel
model object | ClassificationPartitionedKernel
cross-validated model
object
Trained kernel classification model, returned as a ClassificationKernel
model object or ClassificationPartitionedKernel
cross-validated model
object.
If you set any of the name-value pair arguments
CrossVal
, CVPartition
,
Holdout
, KFold
, or
Leaveout
, then Mdl
is a
ClassificationPartitionedKernel
cross-validated
classifier. Otherwise, Mdl
is a
ClassificationKernel
classifier.
To reference properties of Mdl
, use dot notation. For
example, enter Mdl.NumExpansionDimensions
in the Command
Window to display the number of dimensions of the expanded space.
If you specify OptimizeHyperparameters
and
set the ConstraintType
and ConstraintBounds
options of
HyperparameterOptimizationOptions
, then Mdl
is an
N-by-1 cell array of model objects, where N is equal
to the number of rows in ConstraintBounds
. If none of the optimization
problems yields a feasible model, then each cell array value is []
.
Note
Unlike other classification models, and for economical memory usage, a
ClassificationKernel
model object does not store
the training data or training process details (for example, convergence
history).
AggregateOptimizationResults
— Aggregate optimization results
AggregateBayesianOptimization
object
Aggregate optimization results for multiple optimization problems, returned as an AggregateBayesianOptimization
object. To return
AggregateOptimizationResults
, you must specify
OptimizeHyperparameters
and
HyperparameterOptimizationOptions
. You must also specify the
ConstraintType
and ConstraintBounds
options of HyperparameterOptimizationOptions
. For an example that
shows how to produce this output, see Hyperparameter Optimization with Multiple Constraint Bounds.
FitInfo
— Optimization details
structure array
Optimization details, returned as a structure array including fields described in this table. The fields contain final values or name-value pair argument specifications.
Field | Description |
---|---|
Solver | Objective function minimization technique:
|
LossFunction | Loss function. Either 'hinge' or
'logit' depending on the type of
linear classification model. See Learner . |
Lambda | Regularization term strength. See Lambda . |
BetaTolerance | Relative tolerance on the linear coefficients and the
bias term. See BetaTolerance . |
GradientTolerance | Absolute gradient tolerance. See
GradientTolerance . |
ObjectiveValue | Value of the objective function when optimization terminates. The classification loss plus the regularization term compose the objective function. |
GradientMagnitude | Infinite norm of the gradient vector of the objective
function when optimization terminates. See
GradientTolerance . |
RelativeChangeInBeta | Relative changes in the linear coefficients and the bias
term when optimization terminates. See
BetaTolerance . |
FitTime | Elapsed, wall-clock time (in seconds) required to fit the model to the data. |
History | History of optimization information. This field is empty
([] ) if you specify
'Verbose',0 . For details, see
Verbose and Algorithms. |
To access fields, use dot notation. For example, to access the vector of
objective function values for each iteration, enter
FitInfo.ObjectiveValue
in the Command Window.
If you specify
OptimizeHyperparameters
and set the
ConstraintType
and
ConstraintBounds
options of
HyperparameterOptimizationOptions
, then
Fitinfo
is an N-by-1 cell array of
structure arrays, where N is equal to the number of rows
in ConstraintBounds
.
A good practice is to examine FitInfo
to assess whether
convergence is satisfactory.
HyperparameterOptimizationResults
— Cross-validation optimization of hyperparameters
BayesianOptimization
object | AggregateBayesianOptimization
object | table of hyperparameters and associated values
Cross-validation optimization of hyperparameters, returned as a BayesianOptimization
object, an AggregateBayesianOptimization
object, or a table of hyperparameters and
associated values. The output is nonempty when
OptimizeHyperparameters
has a value other than
"none"
.
If you set the ConstraintType
and
ConstraintBounds
options in
HyperparameterOptimizationOptions
, then
HyperparameterOptimizationResults
is an AggregateBayesianOptimization
object. Otherwise, the value of
HyperparameterOptimizationResults
depends on the value of the
Optimizer
option in
HyperparameterOptimizationOptions
.
Value of Optimizer Option | Value of HyperparameterOptimizationResults |
---|---|
"bayesopt" (default) | Object of class BayesianOptimization |
"gridsearch" or "randomsearch" | Table of hyperparameters used, observed objective function values (cross-validation loss), and rank of observations from lowest (best) to highest (worst) |
More About
Random Feature Expansion
Random feature expansion, such as Random Kitchen Sinks [1] or Fastfood [2], is a scheme to approximate Gaussian kernels of the kernel classification algorithm to use for big data in a computationally efficient way. Random feature expansion is more practical for big data applications that have large training sets, but can also be applied to smaller data sets that fit in memory.
The kernel classification algorithm searches for an optimal hyperplane that separates the data into two classes after mapping features into a high-dimensional space. Nonlinear features that are not linearly separable in a low-dimensional space can be separable in the expanded high-dimensional space. All the calculations for hyperplane classification use only dot products. You can obtain a nonlinear classification model by replacing the dot product x1x2' with the nonlinear kernel function , where xi is the ith observation (row vector) and φ(xi) is a transformation that maps xi to a high-dimensional space (called the “kernel trick”). However, evaluating G(x1,x2) (Gram matrix) for each pair of observations is computationally expensive for a large data set (large n).
The random feature expansion scheme finds a random transformation so that its dot product approximates the Gaussian kernel. That is,
where T(x) maps x in to a high-dimensional space (). The Random Kitchen Sinks scheme uses the random transformation
where is a sample drawn from and σ is a kernel scale. This scheme requires O(mp) computation and storage.
The Fastfood scheme introduces another random
basis V instead of Z using Hadamard matrices combined
with Gaussian scaling matrices. This random basis reduces the computation cost to O(mlog
p) and reduces storage to O(m).
You can specify values for m and
σ by setting NumExpansionDimensions
and
KernelScale
, respectively, of fitckernel
.
The fitckernel
function uses the Fastfood scheme for random feature expansion and uses linear classification to train a Gaussian kernel classification model. Unlike solvers in the fitcsvm
function, which require computation of the n-by-n Gram matrix, the solver in fitckernel
only needs to form a matrix of size n-by-m, with m typically much less than n for big data.
Box Constraint
A box constraint is a parameter that controls the maximum penalty imposed on margin-violating observations, and aids in preventing overfitting (regularization). Increasing the box constraint can lead to longer training times.
The box constraint (C) and the regularization term strength (λ) are related by C = 1/(λn), where n is the number of observations.
Tips
Standardizing predictors before training a model can be helpful.
You can standardize training data and scale test data to have the same scale as the training data by using the
normalize
function.Alternatively, use the
Standardize
name-value argument to standardize the numeric predictors before training. The returned model includes the predictor means and standard deviations in itsMu
andSigma
properties, respectively. (since R2023b)
After training a model, you can generate C/C++ code that predicts labels for new data. Generating C/C++ code requires MATLAB Coder™. For details, see Introduction to Code Generation.
Algorithms
fitckernel
minimizes the regularized objective function using a Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) solver with ridge (L2) regularization. To find the type of LBFGS solver used for training, typeFitInfo.Solver
in the Command Window.'LBFGS-fast'
— LBFGS solver.'LBFGS-blockwise'
— LBFGS solver with a block-wise strategy. Iffitckernel
requires more memory than the value ofBlockSize
to hold the transformed predictor data, then the function uses a block-wise strategy.'LBFGS-tall'
— LBFGS solver with a block-wise strategy for tall arrays.
When
fitckernel
uses a block-wise strategy, it implements LBFGS by distributing the calculation of the loss and gradient among different parts of the data at each iteration. Also,fitckernel
refines the initial estimates of the linear coefficients and the bias term by fitting the model locally to parts of the data and combining the coefficients by averaging. If you specify'Verbose',1
, thenfitckernel
displays diagnostic information for each data pass and stores the information in theHistory
field ofFitInfo
.When
fitckernel
does not use a block-wise strategy, the initial estimates are zeros. If you specify'Verbose',1
, thenfitckernel
displays diagnostic information for each iteration and stores the information in theHistory
field ofFitInfo
.If you specify the
Cost
,Prior
, andWeights
name-value arguments, the output model object stores the specified values in theCost
,Prior
, andW
properties, respectively. TheCost
property stores the user-specified cost matrix (C) without modification. ThePrior
andW
properties store the prior probabilities and observation weights, respectively, after normalization. For model training, the software updates the prior probabilities and observation weights to incorporate the penalties described in the cost matrix. For details, see Misclassification Cost Matrix, Prior Probabilities, and Observation Weights.
References
[1] Rahimi, A., and B. Recht. “Random Features for Large-Scale Kernel Machines.” Advances in Neural Information Processing Systems. Vol. 20, 2008, pp. 1177–1184.
[2] Le, Q., T. Sarlós, and A. Smola. “Fastfood — Approximating Kernel Expansions in Loglinear Time.” Proceedings of the 30th International Conference on Machine Learning. Vol. 28, No. 3, 2013, pp. 244–252.
[3] Huang, P. S., H. Avron, T. N. Sainath, V. Sindhwani, and B. Ramabhadran. “Kernel methods match Deep Neural Networks on TIMIT.” 2014 IEEE International Conference on Acoustics, Speech and Signal Processing. 2014, pp. 205–209.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
The
fitckernel
function supports tall arrays with the following usage
notes and limitations:
fitckernel
does not support talltable
data.Some name-value pair arguments have different defaults compared to the default values for the in-memory
fitckernel
function. Supported name-value pair arguments, and any differences, are:'Learner'
'NumExpansionDimensions'
'KernelScale'
'BoxConstraint'
'Lambda'
'BetaTolerance'
— Default value is relaxed to1e–3
.'GradientTolerance'
— Default value is relaxed to1e–5
.'IterationLimit'
— Default value is relaxed to20
.'BlockSize'
'RandomStream'
'HessianHistorySize'
'Verbose'
— Default value is1
.'ClassNames'
'Cost'
'Prior'
'ScoreTransform'
'Weights'
— Value must be a tall array.'OptimizeHyperparameters'
'HyperparameterOptimizationOptions'
— For cross-validation, tall optimization supports only'Holdout'
validation. By default, the software selects and reserves 20% of the data as holdout validation data, and trains the model using the rest of the data. You can specify a different value for the holdout fraction by using this argument. For example, specify'HyperparameterOptimizationOptions',struct('Holdout',0.3)
to reserve 30% of the data as validation data.
If
'KernelScale'
is'auto'
, thenfitckernel
uses the random stream controlled bytallrng
for subsampling. For reproducibility, you must set a random number seed for both the global stream and the random stream controlled bytallrng
.If
'Lambda'
is'auto'
, thenfitckernel
might take an extra pass through the data to calculate the number of observations inX
.fitckernel
uses a block-wise strategy. For details, see Algorithms.
For more information, see Tall Arrays.
Automatic Parallel Support
Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.
To perform parallel hyperparameter optimization, use the UseParallel=true
option in the HyperparameterOptimizationOptions
name-value argument in
the call to the fitckernel
function.
For more information on parallel hyperparameter optimization, see Parallel Bayesian Optimization.
For general information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).
Version History
Introduced in R2017bR2023b: Kernel models support standardization of predictors
Starting in R2023b, fitckernel
supports the standardization
of numeric predictors. That is, you can specify the Standardize
value as true
to center and scale each numeric predictor variable
by the corresponding column mean and standard deviation. The software does not
standardize the categorical predictors.
You can also optimize the Standardize
hyperparameter by using
the OptimizeHyperparameters
name-value argument. Unlike in
previous releases, when you specify "auto"
as the
OptimizeHyperparameters
value,
fitckernel
includes Standardize
as an
optimizable hyperparameter.
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