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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...
We discuss sparse support vector machines (sparse SVMs) trained in the reduced empirical feature space. Namely, we select the linearly independent training data by the Cholesky factorization of the kernel matrix, and train the SVM in the dual form in the reduced empirical feature space. Since the mapped linearly independent training data span the empirical feature space, the linearly independent training...
This paper introduces the recurrent Clifford support vector machines (RCSVM). First we explain the generalization of the real- and complex-valued support vector machines using the Clifford geometric algebra. In this framework we handle the design of kernels involving the Clifford or geometric product and one redefines the optimization variables as multivectors. This allows us to have a multivector...
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