Neural networks in non-Euclidean metric spaces
نویسندگان
چکیده
Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons providing decision borders using combinations of soft hyperplanes. The weighted fun-in activation function corresponds to Euclidean distance functions used to compute similarities between input and weight vector. Replacing the fan-in activation function by non-Euclidean distance function offers a natural generalization of the standard MLP model, providing more flexible decision borders. An alternative way leading to similar results is based on renormalization of the input vectors using nonEuclidean norms in extended feature spaces. Both approaches influence the shapes of decision borders dramatically, allowing to reduce the complexity
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