Class: ClassificationKNN
Predict resubstitution response of knearest neighbor classifier
label = resubPredict(mdl)
[label,score]
= resubPredict(mdl)
[label,score,cost]
= resubPredict(mdl)
returns
the labels label
= resubPredict(mdl
)mdl
predicts for the data mdl.X
. label
is
the predictions of mdl
on the data that fitcknn
used to create mdl
.
[
returns the posterior
class probabilities for the predictions.label
,score
]
= resubPredict(mdl
)
[
returns the misclassification
costs.label
,score
,cost
]
= resubPredict(mdl
)

Predicted class labels for the points in the training data 

Numeric matrix of size 

Matrix of expected costs of size 
For a vector (single query point) X
and model mdl
,
let
K
be the number of nearest neighbors
used in prediction, mdl.NumNeighbors
nbd(mdl,X)
be the K
nearest
neighbors to X
in mdl.X
Y(nbd)
be the classifications of
the points in nbd(mdl,X)
, namely mdl.Y(nbd)
W(nbd)
be the weights of the points
in nbd(mdl,X)
prior
be the priors of the classes
in mdl.Y
If there is a vector of prior probabilities, then the observation
weights W
are normalized by class to sum to the
priors. This might involve a calculation for the point X
,
because weights can depend on the distance from X
to
the points in mdl.X
.
The posterior probability p(jX) is
$$p\left(j\text{X}\right)=\frac{{\displaystyle \sum _{i\in \text{nbd}}W(i){1}_{Y(X(i)=j)}}}{{\displaystyle \sum _{i\in \text{nbd}}W(i)}}.$$
Here $${1}_{Y(X(i)=j)}$$ means 1
when mdl.Y(i) = j
, and 0
otherwise.
There are two costs 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
.
Suppose you have K
classes. You place the observations
into a matrix X
with one observation per row. The
command
[label,score,cost] = predict(mdl,X)
returns, among other outputs, a cost
matrix
of size Nobs
byK
. Each row
of the cost
matrix contains the expected (average)
cost of classifying the observation into each of the K
classes. cost(n,k)
is
$$\sum _{i=1}^{K}\widehat{P}\left(iX(n)\right)C\left(ki\right)},$$
where
K is the number of classes.
$$\widehat{P}\left(iX(n)\right)$$ is the posterior probability of class i for observation X(n).
$$C\left(ki\right)$$ is the true misclassification cost of classifying an observation as k when its true class is i.
There are two costs 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 in the Cost
namevalue
pair when you run fitcknn
. 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.
If you specified to standardize the predictor data, that is, mdl.Mu
and mdl.Sigma
are
not empty ([]
), then resubPredict
standardizes
the predictor data before predicting labels.
ClassificationKNN
 fitcknn
 predict
 resubEdge
 resubLoss
 resubMargin