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QdaResubErr =0.2000You have computed the resubstitution error. Usually people are more interested in the test error (also referred to as generalization error), which is the expected prediction error on an independent set. In fact, the resubstitution error will likely under-estimate the test error.In this case you don't have another labeled data set, but you can simulate one by doing cross-validation. A stratified 10-fold cross-validation is a popular choice for estimating the test error on classification algorithms. It randomly divides the training set into 10 disjoint subsets. Each subset has roughly equal size and roughly the same class proportions as in the training set. Remove one subset, train the classification model using the other nine subsets, and use the trained model to classify the removed subset.

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You could repeat this by removing each of the ten subsets one at a time.Because cross-validation randomly divides data, its outcome depends on the initial random seed. To reproduce the exact results in this example, execute the following command. QdaCVErr =0.2200QDA has a slightly larger cross-validation error than LDA. It shows that a simpler model may get comparable, or better performance than a more complicated model. Naive Bayes ClassifiersThe fitcdiscr function has other two other types, 'DiagLinear' and 'DiagQuadratic'.

They are similar to 'linear' and 'quadratic', but with diagonal covariance matrix estimates. These diagonal choices are specific examples of a naive Bayes classifier, because they assume the variables are conditionally independent given the class label. Naive Bayes classifiers are among the most popular classifiers. While the assumption of class-conditional independence between variables is not true in general, naive Bayes classifiers have been found to work well in practice on many data sets.The fitcnb function can be used to create a more general type of naive Bayes classifier.First model each variable in each class using a Gaussian distribution. You can compute the resubstitution error and the cross-validation error. For this data set, the naive Bayes classifier with kernel density estimation gets smaller resubstitution error and cross-validation error than the naive Bayes classifier with a Gaussian distribution. Decision TreeAnother classification algorithm is based on a decision tree.

A decision tree is a set of simple rules, such as 'if the sepal length is less than 5.45, classify the specimen as setosa.' Decision trees are also nonparametric because they do not require any assumptions about the distribution of the variables in each class.The fitctree function creates a decision tree. Create a decision tree for the iris data and see how well it classifies the irises into species. DtResubErr =0.1333dtCVErr =0.3067For the decision tree algorithm, the cross-validation error estimate is significantly larger than the resubstitution error. This shows that the generated tree overfits the training set. In other words, this is a tree that classifies the original training set well, but the structure of the tree is sensitive to this particular training set so that its performance on new data is likely to degrade. It is often possible to find a simpler tree that performs better than a more complex tree on new data.Try pruning the tree.

First compute the resubstitution error for various subsets of the original tree. Then compute the cross-validation error for these sub-trees.

A graph shows that the resubstitution error is overly optimistic. It always decreases as the tree size grows, but beyond a certain point, increasing the tree size increases the cross-validation error rate. Which tree should you choose? A simple rule would be to choose the tree with the smallest cross-validation error.

While this may be satisfactory, you might prefer to use a simpler tree if it is roughly as good as a more complex tree. For this example, take the simplest tree that is within one standard error of the minimum. That's the default rule used by the cvloss method of ClassificationTree.You can show this on the graph by computing a cutoff value that is equal to the minimum cost plus one standard error. The 'best' level computed by the cvloss method is the smallest tree under this cutoff. (Note that bestlevel=0 corresponds to the unpruned tree, so you have to add 1 to use it as an index into the vector outputs from cvloss.). Ans =0.2467ConclusionsThis example shows how to perform classification in MATLAB® using Statistics and Machine Learning Toolbox™ functions.This example is not meant to be an ideal analysis of the Fisher iris data, In fact, using the petal measurements instead of, or in addition to, the sepal measurements may lead to better classification.

Also, this example is not meant to compare the strengths and weaknesses of different classification algorithms. You may find it instructive to perform the analysis on other data sets and compare different algorithms. There are also Toolbox functions that implement other classification algorithms.

For instance, you can use TreeBagger to perform bootstrap aggregation for an ensemble of decision trees, as described in the example.