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Found 20 papers, 4 papers with code
Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks
However, hypercomplex-valued neural networks are a type of vector-valued neural network defined on an algebra with additional algebraic or geometric properties.
Training Single-Layer Morphological Perceptron Using Convex-Concave Programming
We introduce an algorithm referred to as K-DDCCP, which combines the existing single-layer morphological perceptron (SLMP) model proposed by Ritter and Urcid with the weighted disciplined convex-concave programming (WDCCP) algorithm by Charisopoulos and Maragos.
Dual Quaternion Rotational and Translational Equivariance in 3D Rigid Motion Modelling
To overcome these limitations, we employ a dual quaternion representation of rigid motions in the 3D space that jointly describes rotations and translations of point sets, processing each of the points as a single entity.
Understanding Vector-Valued Neural Networks and Their Relationship with Real and Hypercomplex-Valued Neural Networks
In contrast, vector-valued neural networks are conceived to process arrays of vectors and naturally consider the intercorrelation between feature channels.
Shortest Length Total Orders Do Not Minimize Irregularity in Vector-Valued Mathematical Morphology
The underlying framework for mathematical morphology is a partially ordered set with well-defined supremum and infimum operations.
Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks
The universal approximation theorem asserts that a single hidden layer neural network approximates continuous functions with any desired precision on compact sets.
Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks
This paper features convolutional neural networks defined on hypercomplex algebras applied to classify lymphocytes in blood smear digital microscopic images.
Quaternion-Valued Convolutional Neural Network Applied for Acute Lymphoblastic Leukemia Diagnosis
The field of neural networks has seen significant advances in recent years with the development of deep and convolutional neural networks.
On the Dynamics of Hopfield Neural Networks on Unit Quaternions
Afterward, we turn our attention to the continuous-valued quaternionic Hopfield neural network (CV-QHNN), which can be derived from the MV-QHNN by means of a limit process.
Least-Squares Linear Dilation-Erosion Regressor Trained using a Convex-Concave Procedure
This paper presents a hybrid morphological neural network for regression tasks called linear dilation-erosion regressor ($\ell$-DER).
A General Framework for Hypercomplex-valued Extreme Learning Machines
This paper aims to establish a framework for extreme learning machines (ELMs) on general hypercomplex algebras.
Linear Dilation-Erosion Perceptron for Binary Classification
In this work, we briefly revise the reduced dilation-erosion perceptron (r-DEP) models for binary classification tasks.
Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure
The decision function of the $\ell$-DEP model is defined by adding a dilation and an erosion.
Ensemble of Binary Classifiers Combined Using Recurrent Correlation Associative Memories
The majority vote is an example of a methodology used to combine classifiers in an ensemble method.
Reduced Dilation-Erosion Perceptron for Binary Classification
Dilation and erosion are two elementary operations from mathematical morphology, a non-linear lattice computing methodology widely used for image processing and analysis.
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.
Quaternion-Valued Recurrent Projection Neural Networks on Unit Quaternions
In this paper, we present the quaternion-valued recurrent projection neural networks (QRPNNs).
An Introduction to Quaternion-Valued Recurrent Projection Neural Networks
In this paper, we introduce the quaternion-valued recurrent projection neural networks (QRPNNs).
A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks
Moreover, we introduce and provide the stability analysis of a general class of Hopfield-type neural networks on Cayley-Dickson algebras.
Max-C and Min-D Projection Autoassociative Fuzzy Morphological Memories: Theory and an Application for Face Recognition
Max-C and min-D projection autoassociative fuzzy morphological memories (max-C and min-D PAFMMs) are two layer feedforward fuzzy morphological neural networks able to implement an associative memory designed for the storage and retrieval of finite fuzzy sets or vectors on a hypercube.
