An Extended Multilayer Perceptron Model Using Reduced Geometric Algebra

An extended model of multilayer perceptron (MLP) based on reduced geometric algebra (RGA), namely RGA-MLP, is proposed for multi-dimensional signal processing. The RGA-MLP model treats multi-dimensional signals as multivectors in RGA space and all neuronal parameters such as inputs, connection weights, activation function and outputs, and also operators are encoded by RGA. The RGA-based back propagation (BP) algorithm is also provided. Thanks to the commutative property of RGA, multi-dimensional signals can be processed in a holistic manner which avoids losing relationship of multiple dimensions. The experiments demonstrate that the RGA-MLP model outperforms the traditional real-valued MLP model and quaternion based MLP model (QMLP) with faster convergence rate, higher classification accuracy and Lower computational complexity.