Hypercomplex-Valued Recurrent Correlation Neural Networks
Recurrent correlation neural networks (RCNNs), introduced by Chiueh and Goodman as an improved version of the bipolar correlation-based Hopfield neural network, can be used to implement high-capacity associative memories. In this paper, we extend the bipolar RCNNs for processing hypercomplex-valued data. Precisely, we present the mathematical background for a broad class of hypercomplex-valued RCNNs. Then, we provide the necessary conditions which ensure that a hypercomplex-valued RCNN always settles at an equilibrium using either synchronous or asynchronous update modes. Examples with bipolar, complex, hyperbolic, quaternion, and octonion-valued RCNNs are given to illustrate the theoretical results. Finally, computational experiments confirm the potential application of hypercomplex-valued RCNNs as associative memories designed for the storage and recall of gray-scale images.
Code (1)
Similar Papers 제목 키워드 기반
Quaternion-Valued Recurrent Projection Neural Networks on Unit Quaternions
Hypercomplex-valued neural networks, including quaternion-valued neural networks, can treat multi-dimensional data as a single entity. In this paper, we present the quaternion-valued recurrent projection neural networks …
An Introduction to Quaternion-Valued Recurrent Projection Neural Networks
Hypercomplex-valued neural networks, including quaternion-valued neural networks, can treat multi-dimensional data as a single entity. In this paper, we introduce the quaternion-valued recurrent projection neural network…
Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networks
Despite the many successful applications of deep learning models for multidimensional signal and image processing, most traditional neural networks process data represented by (multidimensional) arrays of real numbers. T…
An Invitation to Hypercomplex Phase Retrieval: Theory and Applications
Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex re…
RetrievalA General Framework for Hypercomplex-valued Extreme Learning Machines
This paper aims to establish a framework for extreme learning machines (ELMs) on general hypercomplex algebras. Hypercomplex neural networks are machine learning models that feature higher-dimension numbers as parameters…
Time SeriesTime Series AnalysisTime Series Prediction