I was confused about this because, for example, the XOR problem is not linearly separable, and a simple Perceptron obviously cannot solve it, so we would need a network like the multilayer perceptron. Furthermore, some sources on the internet say that Adaline's learning algorithm, the LMS (Least Mean Squares) algorithm, converges to the minimum error assumption, regardless of whether the training data is linearly separable or not. However, this refers to minimizing MSE, not correctly classifying all training samples. But this leaves me confused. What does that mean?

An Adaline neuron can solve problems that are not linearly separable ?

If so, what is the difference between Adaline's ability to solve problems that are not linearly separable and other neural networks such as Madaline and multilayer perceptron?


1 Answer 1


Your highlighted Adaline's features is only relative to the traditional perceptron's error correction learning rule such as Rosenblatt's perceptron which cannot even converge facing non linearly separable training data, while Adaline network may converge facing same data albeit likely cannot achieve 100% accuracy by simply providing a linear decision boundary.

For non linearly separable data Madaline network may obtain much better accuracy compared to Adaline as expected due to its combinatory power, in fact one of your own references gives an example Madaline network to solve the XOR problem with just 2 Adaline units in the hidden layer 100% correctly.


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