K. Tachibana, E. Hitzer, M. T. Pham, T. Yoshikawa, T. Furuhashi
Note on Geometric Algebra and Neural Networks
Proceedings of 20th Intelligent Systems Symposium (FAN 2010), 25-26 Sep. 2010, Tokyo, Japan , pp. 116-117 (2010).

Abstract: This note first explains Clifford’s geometric algebra (GA) as a general form of complex and quaternion algebras. Second, this note describes GA neuron as a natural extension of complex neuron. The GA neuron inputs a vector and outputs another vector of any dimension. Next, point with precision is considered using conformal geometric algebra and shows that addition of conformal vectors works well for precision update. The GA neuron and its use of vectors with precision (or belief) could useful to datasets with different levels of precision/details/belief of any dimension. The conformal vector could be also useful to set a prior distribution of geometric versors.


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