How do I do weighted classification?

Hello

I'm using classifiers in Matlab (e.g. [fitcsvm](<http://ch.mathworks.com/help/stats/fitcsvm.html>) or [fitcknn](<http://ch.mathworks.com/help/stats/classificationknn-class.html))>. Because I have highly unbalanced classes (10% negative class and 90% positive class), I would like to use weighting. Usually I calculate the weight for class i as follows:

weight_i = numSamples / (numClasses * numSamplesClass_i)

That means the total number of observations divided by the product of the number of classes and the number of samples for class i.

Matlab offers the 'Weights' flag to set weights for each observation. But in the description the following is written:

The software normalizes Weights to sum up to the value of the prior probability in the respective class.

I'm completely unsure how I should now use the weights. Can I just set the weight calculated from the above formula for each data point according to its class belonging?

Answer 1

[MHN]

You can easily change 'prior' to 'uniform'. 'uniform' sets all class probabilities equal. The default value is 'empirical' which determines class probabilities from class frequencies in Y. For example if you are using decision tree as a classifier then:

tree = fitctree(X,Y, 'prior', 'uniform')

[MHN]

There are many tricks to handle an unbalanced data. e.g. you can also define a cost matrix in a way that misclassification of your minor class costs much more than the misclassification of another class. e.g the following cost matrix: [0 9/10; 1/10 0]

[MHN]

You can also use weight. "The software normalizes Weights to sum up to the value of the prior probability in the respective class" means that your weight must be a distribution. For example if you define all the weights equal to 1 and change the 'prior' to 'empirical', then Matlab normalizes your weights to 1/M (M:number of samples) to make it a distribution which sums up to 1.

[Tom Gerard]

Thank you very much for your answer. Which of the three possibilities (prior, cost, weight) is best or is there no difference?

So, technically I can use my above formula weight_i = numSamples / (numClasses * numSamplesClass_i) for setting a cost matrix but not for settings weights for each data point. Correct?

Answer 2

[MHN]

It depends on your evaluation criteria and does not have a straight forward answer. I suggest you to try them and see which gives you the best answer according to your evaluation criteria.