Loss of k-nearest neighbor classifier
returns a scalar representing how well L
= loss(mdl
,tbl
,ResponseVarName
)mdl
classifies the data
in tbl
when tbl.ResponseVarName
contains the
true classifications. If tbl
contains the response variable
used to train mdl
, then you do not need to specify
ResponseVarName
.
When computing the loss, the loss
function normalizes the
class probabilities in tbl.ResponseVarName
to the class
probabilities used for training, which are stored in the Prior
property of mdl
.
The meaning of the classification loss (L
) depends on the
loss function and weighting scheme, but, in general, better classifiers yield
smaller classification loss values. For more details, see Classification Loss.
returns a scalar representing how well L
= loss(mdl
,tbl
,Y
)mdl
classifies the data
in tbl
when Y
contains the true
classifications.
When computing the loss, the loss
function normalizes the
class probabilities in Y
to the class probabilities used for
training, which are stored in the Prior
property of
mdl
.
returns a scalar representing how well L
= loss(mdl
,X
,Y
)mdl
classifies the data
in X
when Y
contains the true
classifications.
When computing the loss, the loss
function normalizes the
class probabilities in Y
to the class probabilities used for
training, which are stored in the Prior
property of
mdl
.
specifies options using one or more name-value pair arguments in addition to the
input arguments in previous syntaxes. For example, you can specify the loss function
and the classification weights.L
= loss(___,Name,Value
)
Create a k-nearest neighbor classifier for the Fisher iris data, where k = 5.
Load the Fisher iris data set.
load fisheriris
Create a classifier for five nearest neighbors.
mdl = fitcknn(meas,species,'NumNeighbors',5);
Examine the loss of the classifier for a mean observation classified as 'versicolor'
.
X = mean(meas);
Y = {'versicolor'};
L = loss(mdl,X,Y)
L = 0
All five nearest neighbors classify as 'versicolor'
.
mdl
— k-nearest neighbor classifier modelClassificationKNN
objectk-nearest neighbor classifier model, specified as a
ClassificationKNN
object.
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
used to train mdl
, then you do not need to specify ResponseVarName
or Y
.
If you train mdl
using sample data contained in a
table
, then the input data for loss
must also be in a table.
Data Types: table
ResponseVarName
— Response variable nametbl
Response variable name, specified as the name of a variable
in tbl
. If tbl
contains
the response variable used to train mdl
, then
you do not need to specify ResponseVarName
.
You must specify ResponseVarName
as a character vector or string scalar.
For example, if the response variable is stored as tbl.response
, then
specify it as 'response'
. Otherwise, the software treats all columns
of tbl
, including tbl.response
, as
predictors.
The response variable must be a categorical, character, or string array, logical or numeric vector, or cell array of character vectors. If the response variable is a character array, then each element must correspond to one row of the array.
Data Types: char
| string
X
— Predictor dataPredictor data, specified as a numeric matrix. Each row of X
represents one observation, and each column represents one variable.
Data Types: single
| double
Y
— Class labelsClass labels, specified as a categorical, character, or string array, logical or
numeric vector, or cell array of character vectors. Each row of Y
represents the classification of the corresponding row of X
.
Data Types: categorical
| char
| string
| logical
| single
| double
| cell
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
.
loss(mdl,tbl,'response','LossFun','exponential','Weights','w')
returns the weighted exponential loss of mdl
classifying the data
in tbl
. Here, tbl.response
is the response
variable, and tbl.w
is the weight variable.'LossFun'
— Loss function'mincost'
(default) | 'binodeviance'
| 'classiferror'
| 'exponential'
| 'hinge'
| 'logit'
| 'quadratic'
| function handleLoss function, specified as the comma-separated pair consisting of
'LossFun'
and a built-in loss function name or a
function handle.
The following table lists the available loss functions.
Value | Description |
---|---|
'binodeviance' | Binomial deviance |
'classiferror' | Classification error |
'exponential' | Exponential |
'hinge' | Hinge |
'logit' | Logistic |
'mincost' | Minimal expected misclassification cost (for classification scores that are posterior probabilities) |
'quadratic' | Quadratic |
'mincost'
is appropriate for
classification scores that are posterior probabilities. By
default, k-nearest neighbor models return
posterior probabilities as classification scores (see
predict
).
You can specify a function handle for a custom loss
function using @
(for example,
@lossfun
). Let n
be the number of observations in X
and
K be the number of distinct classes
(numel(mdl.ClassNames)
). Your custom
loss function must have this form:
function lossvalue = lossfun(C,S,W,Cost)
C
is an
n-by-K
logical matrix with rows indicating the class to
which the corresponding observation belongs. The
column order corresponds to the class order in
mdl.ClassNames
. Construct
C
by setting C(p,q) =
1
, if observation p
is in class q
, for each row.
Set all other elements of row p
to 0
.
S
is an
n-by-K
numeric matrix of classification scores. The
column order corresponds to the class order in
mdl.ClassNames
. The argument
S
is a matrix of classification
scores, similar to the output of
predict
.
W
is an
n-by-1 numeric vector of
observation weights. If you pass
W
, the software normalizes the
weights to sum to 1
.
Cost
is a
K-by-K
numeric matrix of misclassification costs. For
example, Cost = ones(K) –
eye(K)
specifies a cost of
0
for correct classification
and 1
for
misclassification.
The output argument
lossvalue
is a scalar.
For more details on loss functions, see Classification Loss.
Data Types: char
| string
| function_handle
'Weights'
— Observation weightsones(size(X,1),1)
(default) | numeric vector | name of a variable in tbl
Observation weights, specified as the comma-separated pair consisting
of 'Weights'
and a numeric vector or the name of a
variable in tbl
.
If you specify Weights
as a numeric vector, then
the size of Weights
must be equal to the number of
rows in X
or tbl
.
If you specify Weights
as the name of a variable
in tbl
, the name must be a character vector or
string scalar. For example, if the weights are stored as
tbl.w
, then specify Weights
as 'w'
. Otherwise, the software treats all columns of
tbl
, including tbl.w
, as
predictors.
loss
normalizes the weights so that observation
weights in each class sum to the prior probability of that class. When
you supply Weights
, loss
computes the weighted classification loss.
Example: 'Weights','w'
Data Types: single
| double
| char
| string
Classification loss functions measure the predictive inaccuracy of classification models. When you compare the same type of loss among many models, a lower loss indicates a better predictive model.
Consider the following scenario.
L is the weighted average classification loss.
n is the sample size.
For binary classification:
y_{j} is the observed class label. The software codes it as –1 or 1, indicating the negative or positive class, respectively.
f(X_{j}) is the raw classification score for observation (row) j of the predictor data X.
m_{j} = y_{j}f(X_{j}) is the classification score for classifying observation j into the class corresponding to y_{j}. Positive values of m_{j} indicate correct classification and do not contribute much to the average loss. Negative values of m_{j} indicate incorrect classification and contribute significantly to the average loss.
For algorithms that support multiclass classification (that is, K ≥ 3):
y_{j}^{*}
is a vector of K – 1 zeros, with 1 in the
position corresponding to the true, observed class
y_{j}. For example,
if the true class of the second observation is the third class and
K = 4, then
y^{*}_{2}
= [0 0 1 0]′. The order of the classes corresponds to the order in
the ClassNames
property of the input
model.
f(X_{j})
is the length K vector of class scores for
observation j of the predictor data
X. The order of the scores corresponds to the
order of the classes in the ClassNames
property
of the input model.
m_{j} = y_{j}^{*}′f(X_{j}). Therefore, m_{j} is the scalar classification score that the model predicts for the true, observed class.
The weight for observation j is w_{j}. The software normalizes the observation weights so that they sum to the corresponding prior class probability. The software also normalizes the prior probabilities so they sum to 1. Therefore,
$$\sum _{j=1}^{n}{w}_{j}}=1.$$
Given this scenario, the following table describes the supported loss
functions that you can specify by using the 'LossFun'
name-value pair
argument.
Loss Function | Value of LossFun | Equation |
---|---|---|
Binomial deviance | 'binodeviance' | $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}\mathrm{log}\left\{1+\mathrm{exp}\left[-2{m}_{j}\right]\right\}}.$$ |
Exponential loss | 'exponential' | $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}\mathrm{exp}\left(-{m}_{j}\right)}.$$ |
Classification error | 'classiferror' | $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}}I\left\{{\widehat{y}}_{j}\ne {y}_{j}\right\}.$$ It is the weighted fraction of misclassified observations where $${\widehat{y}}_{j}$$ is the class label corresponding to the class with the maximal posterior probability. I{x} is the indicator function. |
Hinge loss | 'hinge' | $$L={\displaystyle \sum}_{j=1}^{n}{w}_{j}\mathrm{max}\left\{0,1-{m}_{j}\right\}.$$ |
Logit loss | 'logit' | $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}\mathrm{log}\left(1+\mathrm{exp}\left(-{m}_{j}\right)\right)}.$$ |
Minimal cost | 'mincost' | Minimal cost. The software computes the weighted minimal cost using this procedure for observations j = 1,...,n.
The weighted, average, minimum cost loss is $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}{c}_{j}}.$$ |
Quadratic loss | 'quadratic' | $$L={\displaystyle \sum _{j=1}^{n}{w}_{j}{\left(1-{m}_{j}\right)}^{2}}.$$ |
This figure compares the loss functions (except 'mincost'
) for one
observation over m. Some functions are normalized to pass through [0,1].
Two costs are associated with KNN classification: the true misclassification cost per class and the expected misclassification cost per observation.
You can set the true misclassification cost per class by using the 'Cost'
name-value pair argument when you run fitcknn
. The value Cost(i,j)
is the cost of classifying
an observation into class j
if its true class is i
. By
default, Cost(i,j) = 1
if i ~= j
, and
Cost(i,j) = 0
if i = j
. In other words, the cost
is 0
for correct classification and 1
for incorrect
classification.
Two costs are associated with KNN classification: the true misclassification cost per class
and the expected misclassification cost per observation. The third output of predict
is the expected misclassification cost per
observation.
Suppose you have Nobs
observations that you want to classify with a trained
classifier mdl
, and you have K
classes. You place the
observations into a matrix Xnew
with one observation per row. The
command
[label,score,cost] = predict(mdl,Xnew)
returns a matrix cost
of size
Nobs
-by-K
, among other outputs. Each row of the
cost
matrix contains the expected (average) cost of classifying the
observation into each of the K
classes. cost(n,j)
is
$$\sum _{i=1}^{K}\widehat{P}\left(i|Xnew(n)\right)C\left(j|i\right)},$$
where
K is the number of classes.
$$\widehat{P}\left(i|Xnew(n)\right)$$ is the posterior probability of class i for observation Xnew(n).
$$C\left(j|i\right)$$ is the true misclassification cost of classifying an observation as j when its true class is i.
This function fully supports tall arrays. For more information, see Tall Arrays (MATLAB).
ClassificationKNN
| edge
| fitcknn
| margin
A modified version of this example exists on your system. Do you want to open this version instead?
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
Select web siteYou can also select a web site from the following list:
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.