Quaternionic Multilayer Perceptron with Local Analyticity

نویسندگان

  • Teijiro Isokawa
  • Haruhiko Nishimura
  • Nobuyuki Matsui
چکیده

A multi-layered perceptron type neural network is presented and analyzed in this paper. All neuronal parameters such as input, output, action potential and connection weight are encoded by quaternions, which are a class of hypercomplex number system. Local analytic condition is imposed on the activation function in updating neurons’ states in order to construct learning algorithm for this network. An error back-propagation algorithm is introduced for modifying the connection weights of the network.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Classification of Pre-sliced Ham Images with Quaternionic Singular Values Using an Adaptive Multilayer Perceptron

The quaternionic representation of ham images, treating RGB colour components as a single unit instead of as separate components, is very effective. The advantage of using quaternion arithmetic is that the perceptually richer colour images can be represented and analyzed as a single entity, improving the accuracy of pattern recognition models. The quaternionic singular value decomposition (SVD)...

متن کامل

A General Framework for Learning in the Complex Domain

We present a framework that greatly simplifies the evaluations and analyses for optimization in the complex plane through the use of a generalized definition of analyticity. We show how the gradient, relative (natural) gradient, Newton, and Newton variation updates can be easily derived within the framework. We demonstrate application of the framework for training of a multi-layer perceptron ne...

متن کامل

Power series and analyticity over the quaternions

We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a power series P n∈N qnan in its domain of convergence, which is a ball B(0, R) centered at 0. At each p ∈ B(0, R), f admits expansions in terms of appropriately defined regular power series centered at p, P n∈N (q−p)bn. The expansion holds in a ball Σ(p,R− |p|) defined with r...

متن کامل

Engine Model Identification Using Local Model Networks in Comparison with a Multilayer Perceptron Network

This paper features a new nonlinear parameter optimisation technique for a local model network and gives a case based comparison to multilayer perceptron networks in the context of a complex industrial application. The architecture of a local model network as well as an effective training algorithm which allows to build reliable and interpretable models is presented. The performance and suitabi...

متن کامل

Harmonic space and quaternionic manifolds

We find a principle of harmonic analyticity underlying the quaternionic (quaternionKähler) geometry and solve the differential constraints which define this geometry. To this end the original 4n-dimensional quaternionic manifold is extended to a biharmonic space. The latter includes additional harmonic coordinates associated with both the tangent local Sp(1) group and an extra rigid SU(2) group...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Information

دوره 3  شماره 

صفحات  -

تاریخ انتشار 2012