I know that logistic regression is for binary classification and softmax regression for multi-class problem. Would it be any differences if I train several logistic regression models with the same data and normalize their results to get a multi-class classifier instead of using one softmax model. I assume the result is of the same. Can I say : "all the multi-class classifier is the cascading result of binary classifiers". (except neuron network)
4 Answers
You can relate logistic regression to binary softmax regression when you transfer the latent model outputs pairs (z1, z2) to z = z1-z2 and apply the logistic function
softmax(z1, z2) = exp(z1)/(exp(z1) + exp(z2)) = exp(z1 - z2)/(exp(z1-z2) + exp(0)) = exp(z)/(exp(z) + 1)
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