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- ArticleOctober 2012
A conic higher order neuron based on geometric algebra and its implementation
MICAI'12: Proceedings of the 11th Mexican international conference on Advances in Computational Intelligence - Volume Part IIPages 223–235https://doi.org/10.1007/978-3-642-37798-3_20This paper presents the implementation of a Multilayer Perceptron (MLP) using a new higher order neuron whose decision region is generated by a conic section (circle, ellipse, parabola, hyperbola). We call it the hyper-conic neuron. The conic neuron is ...
- research-articleApril 2010
A division algebraic framework for multidimensional support vector regression
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics (TSMCPB), Volume 40, Issue 2Pages 517–528https://doi.org/10.1109/TSMCB.2009.2028314In this paper, division algebras are proposed as an elegant basis upon which to extend support vector regression (SVR) to multidimensional targets. Using this framework, a multitarget SVR called εX-SVR is proposed based on an ε-insensitive loss function ...
- research-articleMarch 2010
Steerable wavelet frames based on the Riesz transform
IEEE Transactions on Image Processing (TIP), Volume 19, Issue 3Pages 653–667https://doi.org/10.1109/TIP.2009.2036713We consider an extension of the 1-D concept of analytical wavelet to n-D which is by construction compatible with rotations. This extension, called a monogenic wavelet, yields a decomposition of the wavelet coefficients into amplitude, phase, and phase ...
- ArticleJuly 2004
Symbolic computation in the homogeneous geometric model with clifford algebra
ISSAC '04: Proceedings of the 2004 international symposium on Symbolic and algebraic computationPages 221–228https://doi.org/10.1145/1005285.1005318Clifford algebra provides nice algebraic representations for Euclidean geometry via the homogeneous model, and is suitable for doing geometric reasoning through symbolic computation. In this paper, we propose various symbolic computation techniques in ...
- ArticleMay 2004
Intrinsic differential geometry with geometric calculus
IWMM'04/GIAE'04: Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with ApplicationsPages 207–216https://doi.org/10.1007/11499251_17Setting up a symbolic algebraic system is the first step in mathematics mechanization of any branch of mathematics. In this paper, we establish a compact symbolic algebraic framework for local geometric computing in intrinsic differential geometry, by ...