Hyperellipsoidal neuron

In recent years, the research on neural networks has been guided by the search of new mathematical frameworks, with the hope of finding new features, as geometric interpretation, for facing today problems or reducing the computational cost. In this paper we introduce a new Clifford Neuron [1], extending the conformai neuron, presented in [2] through the generalization of the geometric algebra of quadratic surfaces (G6,3), presented in [3]. In this new neuron, we can obtain decision surfaces with different geometric shapes, depending on the input data: spherical decision surface, ellipsoidal, cylindrical or even decision surface as a pair of planes (all of them can be derived as special case of an ellipse). The above without the need of using a kernel technique, just using a linear activation function over the hiperconformal space.

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