A decision boundary hyperplane for the vector space of conics using a polinomial kernel in m-Euclidean space.

The concept of linear perceptron or spherical perceptron in confomal geometry is extended to the more general conic perceptron, namely the elliptical perceptron. By means of the d-uple embedding a polynomial kernel of degree d is used, which is widely known in SVMpsilas for neural networks. By associating the Clifford algebra to the vector space of conics the conic separator is introduced, generalizing the notion of separator to a decision boundary hyperconic; which is independent of the dimension of the input space. Experimental results are shown in 2-dimensional Euclidean space where we separate data that are naturally separated by some typical plane conic separators by this polynomial kernel. This is more general in the sense that it is independent of the dimension of the input data and hence we can speak of the hyperconic elliptic perceptron by using a higher degree polynomial kernel.