One of the main reasons that ANN performs better is due to its influential feature in handling nonlinear data (Wu et al, 2008).
Can anyone explain to me what is this meaning?
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This means that a neural network can have activation functions that aren't linear, which causes the neural network's output to be non-linear with respect to the input.
For further information, this blog post gives some nice illustrations and explanations: http://colah.github.io/posts/2014-03-NN-Manifolds-Topology/