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.

[PDF] 936 kb

[Geometric Calculus Japan index]