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Topic: How to give more importance to a type of error.
Replies: 1   Last Post: Nov 26, 2012 9:19 PM

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 Greg Heath Posts: 6,387 Registered: 12/7/04
Re: How to give more importance to a type of error.
Posted: Nov 26, 2012 9:19 PM

"UVa" wrote in message <k910mm\$1fj\$1@newscl01ah.mathworks.com>...
> Hello.
>
> I am working at a classification problem with 3 different classes. How can I give more importance to one type of error? I mean, suppose than the classes are A, B and C and suppose that to classify a B input as a C is not so important but to classify a C input as a B input is a very serious mistake. So, I want a confusion matrix with as little misclassifications of the type C instead of B as possible and the other types of errors are less important.

The most effective search (e.g., Google) phrase is "Misclassification Cost".

The classical approach explained in any classification text applies to the minimization of Bayes Risk. If there are c classes with apriori probabilities Pi(i=1:c) and misclassification probabilities pji (i,j=1:c) that quantify the probability of classifying a class i input as belonging to class j, then the classical Bayes Classifier minimizes the risk function

R = sum(i=1,j){ pji*Pi } for equal misclassification costs.

However if some misclassifications are more important than others, the risk is modified to

R = sum(i=1,j){ Cij*pji*Pi } , Cii = 0, i=1:c

where Cij is the cost of classifying a class i input as belonging to class j.

How this concept is applied to a particular classifier depends on what type it is (e.g., Linear,
Quadratic, Mahalanobis, Decision Tree, Neural network, etc).

I'm not sure if I can help any more. Regardless, more specifics are needed. For example:
Specify the

1. number of classes and type of classifier
2. prior probabilities of the operational data
3. number of training samples per class
4. misclassification costs.

Hope this helps.

Greg

P.S. Search the MATLAB library to see if any of the classifier functions deal with pairwise misclassification costs.

Date Subject Author
11/26/12 UVa
11/26/12 Greg Heath