arXiv subjects

Marcos Eduardo Valle

Publications and source records attributed to Marcos Eduardo Valle.

26 records · Page 2Linked to original sources

arXiv2020

Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure

Mathematical morphology (MM) is a theory of non-linear operators used for the processing and analysis of images. Morphological neural networks (MNNs) are neural networks whose neurons compute morphological operators. Dilations and erosions are the elementary operators of MM. From an algebraic point of view, a dilation and an erosion are operators that commute respectively with the supremum and infimum operations. In this paper, we present the \textit{linear dilation-erosion perceptron} ($\ell$-DEP), which is given by applying linear transformations before computing a dilation and an erosion. The decision function of the $\ell$-DEP model is defined by adding a dilation and an erosion. Furthermore, training a $\ell$-DEP can be formulated as a convex-concave optimization problem. We compare the performance of the $\ell$-DEP model with other machine learning techniques using several classification problems. The computational experiments support the potential application of the proposed $\ell$-DEP model for binary classification tasks.

cs.LG↗

arXiv2020

Ensemble of Binary Classifiers Combined Using Recurrent Correlation Associative Memories

An ensemble method should cleverly combine a group of base classifiers to yield an improved classifier. The majority vote is an example of a methodology used to combine classifiers in an ensemble method. In this paper, we propose to combine classifiers using an associative memory model. Precisely, we introduce ensemble methods based on recurrent correlation associative memories (RCAMs) for binary classification problems. We show that an RCAM-based ensemble classifier can be viewed as a majority vote classifier whose weights depend on the similarity between the base classifiers and the resulting ensemble method. More precisely, the RCAM-based ensemble combines the classifiers using a recurrent consult and vote scheme. Furthermore, computational experiments confirm the potential application of the RCAM-based ensemble method for binary classification problems.

cs.LG↗

arXiv2020

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. The dilation-erosion perceptron (DEP) is a morphological neural network obtained by a convex combination of a dilation and an erosion followed by the application of a hard-limiter function for binary classification tasks. A DEP classifier can be trained using a convex-concave procedure along with the minimization of the hinge loss function. As a lattice computing model, the DEP classifier assumes the feature and class spaces are partially ordered sets. In many practical situations, however, there is no natural ordering for the feature patterns. Using concepts from multi-valued mathematical morphology, this paper introduces the reduced dilation-erosion (r-DEP) classifier. An r-DEP classifier is obtained by endowing the feature space with an appropriate reduced ordering. Such reduced ordering can be determined using two approaches: One based on an ensemble of support vector classifiers (SVCs) with different kernels and the other based on a bagging of similar SVCs trained using different samples of the training set. Using several binary classification datasets from the OpenML repository, the ensemble and bagging r-DEP classifiers yielded in mean higher balanced accuracy scores than the linear, polynomial, and radial basis function (RBF) SVCs as well as their ensemble and a bagging of RBF SVCs.

cs.LG↗

arXiv2020

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.

cs.LG↗

arXiv2020

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 (QRPNNs). Briefly, QRPNNs are obtained by combining the non-local projection learning with the quaternion-valued recurrent correlation neural network (QRCNNs). We show that QRPNNs overcome the cross-talk problem of QRCNNs. Thus, they are appropriate to implement associative memories. Furthermore, computational experiments reveal that QRPNNs exhibit greater storage capacity and noise tolerance than their corresponding QRCNNs.

cs.LG↗

arXiv2019

A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks

In this paper, we address the stability of a broad class of discrete-time hypercomplex-valued Hopfield-type neural networks. To ensure the neural networks belonging to this class always settle down at a stationary state, we introduce novel hypercomplex number systems referred to as real-part associative hypercomplex number systems. Real-part associative hypercomplex number systems generalize the well-known Cayley-Dickson algebras and real Clifford algebras and include the systems of real numbers, complex numbers, dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as particular instances. Apart from the novel hypercomplex number systems, we introduce a family of hypercomplex-valued activation functions called $\mathcal{B}$-projection functions. Broadly speaking, a $\mathcal{B}$-projection function projects the activation potential onto the set of all possible states of a hypercomplex-valued neuron. Using the theory presented in this paper, we confirm the stability analysis of several discrete-time hypercomplex-valued Hopfield-type neural networks from the literature. Moreover, we introduce and provide the stability analysis of a general class of Hopfield-type neural networks on Cayley-Dickson algebras.

cs.LG↗

arXiv2019

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 networks (QRPNNs). Briefly, QRPNNs are obtained by combining the non-local projection learning with the quaternion-valued recurrent correlation neural network (QRCNNs). We show that QRPNNs overcome the cross-talk problem of QRCNNs. Thus, they are appropriate to implement associative memories. Furthermore, computational experiments reveal that QRPNNs exhibit greater storage capacity and noise tolerance than their corresponding QRCNNs.

cs.NE↗

arXiv2019

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. In this paper we address the main features of these autoassociative memories, which include unlimited absolute storage capacity, fast retrieval of stored items, few spurious memories, and an excellent tolerance to either dilative noise or erosive noise. Particular attention is given to the so-called PAFMM of Zadeh which, besides performing no floating-point operations, exhibit the largest noise tolerance among max-C and min-D PAFMMs. Computational experiments reveal that Zadeh's max-C PFAMM, combined with a noise masking strategy, yields a fast and robust classifier with strong potential for face recognition.

cs.CV↗