共形几何代数神经元实现的几何运算
Geometric operations implemented by conformal geometric algebra neural nodes
摘要：
几何代数是向量计算的最佳框架。空间的几何代数包括表示其所有子空间（线、平面、体积等）的元素。共形几何代数扩展了这种方法的任意点，点对，线，圆，平面和领域的基本表示。除了包括弯曲的物体，共形几何代数有一个优雅的统一的四元数表示所有正确的和不正确的欧几里得变换，包括反射球，一般螺旋变换和缩放。扩展实神经元和复神经元的概念，我们到达新的强大的概念，共形几何代数神经元。这些神经元可以很容易地将上述几何对象或这些对象的集合作为输入，并通过几何代数值权重应用广泛的几何变换。
英文摘要：
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this approach to elementary representations of arbitrary points, point pairs, lines, circles, planes and spheres. Apart from including curved objects, conformal geometric algebra has an elegant unified quaternion like representation for all proper and improper Euclidean transformations, including reflections at spheres, general screw transformations and scaling. Expanding the concepts of real and complex neurons we arrive at the new powerful concept of conformal geometric algebra neurons. These neurons can easily take the above mentioned geometric objects or sets of these objects as inputs and apply a wide range of geometric transformations via the geometric algebra valued weights.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
