resubLoss

Class: ClassificationTree

Classification error by resubstitution

Syntax

L = resubLoss(tree)
L = resubLoss(tree,Name,Value)
L = resubLoss(tree,'Subtrees',subtreevector)
[L,se] = resubLoss(tree,'Subtrees',subtreevector)
[L,se,NLeaf] = resubLoss(tree,'Subtrees',subtreevector)
[L,se,NLeaf,bestlevel] = resubLoss(tree,'Subtrees',subtreevector)
[L,...] = resubLoss(tree,'Subtrees',subtreevector,Name,Value)

Description

L = resubLoss(tree) returns the resubstitution loss, meaning the loss computed for the data that fitctree used to create tree.

L = resubLoss(tree,Name,Value) returns the loss with additional options specified by one or more Name,Value pair arguments. You can specify several name-value pair arguments in any order as Name1,Value1,…,NameN,ValueN.

L = resubLoss(tree,'Subtrees',subtreevector) returns a vector of classification errors for the trees in the pruning sequence subtreevector.

[L,se] = resubLoss(tree,'Subtrees',subtreevector) returns the vector of standard errors of the classification errors.

[L,se,NLeaf] = resubLoss(tree,'Subtrees',subtreevector) returns the vector of numbers of leaf nodes in the trees of the pruning sequence.

[L,se,NLeaf,bestlevel] = resubLoss(tree,'Subtrees',subtreevector) returns the best pruning level as defined in the TreeSize name-value pair. By default, bestlevel is the pruning level that gives loss within one standard deviation of minimal loss.

[L,...] = resubLoss(tree,'Subtrees',subtreevector,Name,Value) returns loss statistics with additional options specified by one or more Name,Value pair arguments. You can specify several name-value pair arguments in any order as Name1,Value1,…,NameN,ValueN.

Input Arguments

tree

A classification tree constructed by fitctree.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'LossFun'

Function handle or string representing a loss function. Built-in loss functions:

You can write your own loss function in the syntax described in Loss Functions.

Default: 'mincost'

Name,Value arguments associated with pruning subtrees:

'Subtrees'

A vector with integer values from 0 (full unpruned tree) to the maximal pruning level max(tree.PruneList).

Default: 0

'TreeSize'

One of the following strings:

  • 'se'loss returns the highest pruning level with loss within one standard deviation of the minimum (L+se, where L and se relate to the smallest value in Subtrees).

  • 'min'loss returns the element of Subtrees with smallest loss, usually the smallest element of Subtrees.

Output Arguments

L

Classification error, a vector the length of Subtrees. The meaning of the error depends on the values in Weights and LossFun; see Classification Error.

se

Standard error of loss, a vector the length of Subtrees.

NLeaf

Number of leaves (terminal nodes) in the pruned subtrees, a vector the length of Subtrees.

bestlevel

A scalar whose value depends on TreeSize:

  • TreeSize = 'se'loss returns the highest pruning level with loss within one standard deviation of the minimum (L+se, where L and se relate to the smallest value in Subtrees).

  • TreeSize = 'min'loss returns the element of Subtrees with smallest loss, usually the smallest element of Subtrees.

Definitions

Classification Error

The default classification error is the fraction of the training data X that tree misclassifies.

Weighted classification error is the sum of weight i times the Boolean value that is 1 when tree misclassifies the ith row of X, divided by the sum of the weights.

Loss Functions

The built-in loss functions are:

  • 'binodeviance' — For binary classification, assume the classes yn are -1 and 1. With weight vector w normalized to have sum 1, and predictions of row n of data X as f(Xn), the binomial deviance is

    wnlog(1+exp(2ynf(Xn))).

  • 'exponential' — With the same definitions as for 'binodeviance', the exponential loss is

    wnexp(ynf(Xn)).

  • 'classiferror' — Predict the label with the largest posterior probability. The loss is then the fraction of misclassified observations.

  • 'hinge' — Classification error measure that has the form

    L=j=1nwjmax{0,1yjf(Xj)}j=1nwj,

    where:

    • wj is weight j.

    • For binary classification, yj = 1 for the positive class and -1 for the negative class. For problems where the number of classes K > 3, yj is a vector of 0s, but with a 1 in the position corresponding to the true class, e.g., if the second observation is in the third class and K = 4, then y2 = [0 0 1 0]′.

    • f(Xj) is, for binary classification, the posterior probability or, for K > 3, a vector of posterior probabilities for each class given observation j.

  • 'mincost' — Predict the label with the smallest expected misclassification cost, with expectation taken over the posterior probability, and cost as given by the Cost property of the classifier (a matrix). The loss is then the true misclassification cost averaged over the observations.

To write your own loss function, create a function file in this form:

function loss = lossfun(C,S,W,COST)
  • N is the number of rows of X.

  • K is the number of classes in the classifier, represented in the ClassNames property.

  • C is an N-by-K logical matrix, with one true per row for the true class. The index for each class is its position in the ClassNames property.

  • S is an N-by-K numeric matrix. S is a matrix of posterior probabilities for classes with one row per observation, similar to the posterior output from predict.

  • W is a numeric vector with N elements, the observation weights. If you pass W, the elements are normalized to sum to the prior probabilities in the respective classes.

  • COST is a K-by-K numeric matrix of misclassification costs. For example, you can use COST = ones(K) - eye(K), which means a cost of 0 for correct classification, and 1 for misclassification.

  • The output loss should be a scalar.

Pass the function handle @lossfun as the value of the LossFun name-value pair.

True Misclassification Cost

There are two costs associated with 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 name-value pair when you create the classifier using the fitctree method. 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.

Expected Misclassification Cost

There are two costs associated with classification: the true misclassification cost per class, and the expected misclassification cost per observation.

Suppose you have Nobs observations that you want to classify with a trained classifier. Suppose you have K classes. You place the observations into a matrix Xnew with one observation per row.

The expected cost matrix CE has size Nobs-by-K. Each row of CE contains the expected (average) cost of classifying the observation into each of the K classes. CE(n,k) is

i=1KP^(i|Xnew(n))C(k|i),

where

  • K is the number of classes.

  • P^(i|Xnew(n)) is the posterior probability of class i for observation Xnew(n).

  • C(k|i) is the true misclassification cost of classifying an observation as k when its true class is i.

Examples

expand all

Compute the Resubstituted Classification Error

Compute the resubstituted classification error for the ionosphere data.

load ionosphere
tree = fitctree(X,Y);
L = resubLoss(tree)
L = 
    0.0114
Was this topic helpful?