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I want to add nonlinear character into multi-class logistic regression. I know kernel logistic regression can do it. Is there any kind of neural network which has similar characteristic?

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  • $\begingroup$ If you want an output between zero and one can't you just use a logit/sigmoid activation function on your output layer nodes? I don't see how the output would differ conceptually from logistic regression. $\endgroup$
    – Dan
    Commented Jan 29, 2015 at 6:05
  • $\begingroup$ But multi-class probabilistic result can not be gained by using just one output between zero and one. I know Pairwise Coupling can solve it. Is there any NN model that can do it more directly? $\endgroup$
    – Yang
    Commented Jan 29, 2015 at 7:50
  • $\begingroup$ So you should have one output node for each class. Each output will be a probability of membership of that class. However they won't all add up to 1. $\endgroup$
    – Dan
    Commented Jan 29, 2015 at 7:53
  • $\begingroup$ And then use Maximum likelihood to train the NN model? $\endgroup$
    – Yang
    Commented Jan 29, 2015 at 8:02
  • $\begingroup$ Just normal back propagation I would think... $\endgroup$
    – Dan
    Commented Jan 29, 2015 at 8:03

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Yes, most good implementations of multi-layer perceptron (e.g. netlab) and Radial Basis Function neural networks ought to support this, using a softmax output function and cross-entropy loss function. See section 6.9 of Chris Bishop's excellent book "Neural Networks for Pattern Recognition"

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