Marcos Eduardo Valle

Gray-scale morphological associative memories

Neural models of associative memories are usually concerned with the storage and the retrieval of binary or bipolar patterns. Thus far, the emphasis in research on morphological associative memory systems has been on binary models, although a number of notable features of autoassociative morphological memories (AMMs) such as optimal absolute storage capacity and one-step convergence have been shown to hold in the general, gray-scale setting. In this paper, we make extensive use of minimax algebra to analyze gray-scale autoassociative morphological memories. Specifically, we provide a complete characterization of the fixed points and basins of attractions which allows us to describe the storage and recall mechanisms of gray-scale AMMs. Computer simulations using gray-scale images illustrate our rigorous mathematical results on the storage capacity and the noise tolerance of gray-scale morphological associative memories (MAMs). Finally, we introduce a modified gray-scale AMM model that yields a fixed point which is closest to the input pattern with respect to the Chebyshev distance and show how gray-scale AMMs can be used as classifiers

Implicative Fuzzy Associative Memories

Associative neural memories are models of biological phenomena that allow for the storage of pattern associations and the retrieval of the desired output pattern upon presentation of a possibly noisy or incomplete version of an input pattern. In this paper, we introduce implicative fuzzy associative memories (IFAMs), a class of associative neural memories based on fuzzy set theory. An IFAM consists of a network of completely interconnected Pedrycz logic neurons with threshold whose connection weights are determined by the minimum of implications of presynaptic and postsynaptic activations. We present a series of results for autoassociative models including one pass convergence, unlimited storage capacity and tolerance with respect to eroded patterns. Finally, we present some results on fixed points and discuss the relationship between implicative fuzzy associative memories and morphological associative memories

A general framework for fuzzy morphological associative memories

Fuzzy associative memories (FAMs) can be used as a powerful tool for implementing fuzzy rule-based systems. The insight that FAMs are closely related to mathematical morphology (MM) has recently led to the development of new fuzzy morphological associative memories (FMAMs), in particular implicative fuzzy associative memories (IFAMs). As the name FMAM indicates, these models belong to the class of fuzzy morphological neural networks (FMNNs). Thus, each node of an FMAM performs an elementary operation of fuzzy MM. Clarifying several misconceptions about FMAMs that have recently appeared in the literature, we provide a general framework for FMAMs within the class of FMNN. We show that many well-known FAM models fit within this framework and can therefore be classified as FMAMs. Moreover, we employ certain concepts of duality that are defined in the general theory of MM in order to derive a large class of strategies for learning and recall in FMAMs.

Classification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality

Mathematical morphology was originally conceived as a set theoretic approach for the processing of binary images. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory. This paper discusses and compares several well-known and new approaches towards gray-scale and fuzzy mathematical morphology. We show in particular that a certain approach to fuzzy mathematical morphology ultimately depends on the choice of a fuzzy inclusion measure and on a notion of duality. This fact gives rise to a clearly defined scheme for classifying fuzzy mathematical morphologies. The umbra and the level set approach, an extension of the threshold approach to gray-scale mathematical morphology, can also be embedded in this scheme since they can be identified with certain fuzzy approaches.

A Class of Sparsely Connected Autoassociative Morphological Memories for Large Color Images

This brief introduces a new class of sparsely connected autoassociative morphological memories (AMMs) that can be effectively used to process large multivalued patterns, which include color images as a particular case. Such as the single-valued AMMs, the multivalued models exhibit optimal absolute storage capacity and one-step convergence. The remarkable feature of the proposed models is their sparse structure. In fact, the number of synaptic junctions - and consequently the required computational resources - usually decreases considerably as more and more patterns are stored in the novel multivalued AMMs.

Morphological and Certain Fuzzy Morphological Associative Memories for Classification and Prediction

Morphological associative memories (MAMs) are based on a lattice algebra known as minimax algebra. In previous papers, we gained valuable insight into the storage and recall phases of gray-scale autoassociative memories. This article extends these results to the heteroassociative and to the fuzzy case in view of the fact that a gray-scale MAM model can be converted into a fuzzy MAM model that coincides with the Lukasiewicz IFAM by applying an appropriate threshold. The article includes experimental results concerning applications of MAM and fuzzy MAM models in classification and prediction.

Storage and recall capabilities of fuzzy morphological associative memories with adjunction-based learning

We recently employed concepts of mathematical morphology to introduce fuzzy morphological associative memories (FMAMs), a broad class of fuzzy associative memories (FAMs). We observed that many well-known FAM models can be classified as belonging to the class of FMAMs. Moreover, we developed a general learning strategy for FMAMs using the concept of adjunction of mathematical morphology. In this paper, we describe the properties of FMAMs with adjunction-based learning. In particular, we characterize the recall phase of these models. Furthermore, we prove several theorems concerning the storage capacity, noise tolerance, fixed points, and convergence of auto-associative FMAMs. These theorems are corroborated by experimental results concerning the reconstruction of noisy images. Finally, we successfully employ FMAMs with adjunction-based learning in order to implement fuzzy rule-based systems in an application to a time-series prediction problem in industry.

Complex-Valued Recurrent Correlation Neural Networks

In this paper, we generalize the bipolar recurrent correlation neural networks (RCNNs) of Chiueh and Goodman for patterns whose components are in the complex unit circle. The novel networks, referred to as complex-valued RCNNs (CV-RCNNs), are characterized by a possible nonlinear function, which is applied on the real part of the scalar product of the current state and the original patterns. We show that the CV-RCNNs always converge to a stationary state. Thus, they have potential application as associative memories. In this context, we provide sufficient conditions for the retrieval of a memorized vector. Furthermore, computational experiments concerning the reconstruction of corrupted grayscale images reveal that certain CV-RCNNs exhibit an excellent noise tolerance.

Fuzzy associative memories based on subsethood and similarity measures with applications to speaker identification

Recently, we presented a non-distributive fuzzy associative memory (FAM) called the Kosko subsethood FAM, for short KS-FAM. This model can be classified as a morphological neural network because it is based on computing the degree of fuzzy inclusion or subsethood of patterns and this operation can be considered an erosion in fuzzy mathematical morphology. In this paper, we introduce a whole range of extensions of the KS-FAM called S-FAMs, dual S-FAMs, and SM-FAMs. Here, the acronyms S-FAM and SM-FAM stand for respectively subsethood FAM and similarity measure FAM. The new models share some properties with the KS-FAM such as unlimited absolute storage capacity and a small number of spurious memories. The paper finishes some experimental results concerning the problem of text-independent speaker identification. For comparative purposes, we included the recognition rates obtained by some well-known classifiers from the literature.

Introduction to implicative fuzzy associative memories

Associative neural memories are models of biological phenomena that allow for the storage of pattern associations and the retrieval of the desired output pattern upon presentation of a possibly noisy or incomplete version of an input pattern. In this paper, we introduce implicative fuzzy associative memories (IFAMs), a class of associative neural memories models based on fuzzy set theory. An IFAM consists of a network of completely interconnected Pedrycz logic neurons whose connection weights are determined by the minimum of implications of presynaptic and postsynaptic activations. We present a series of results for autoassociative models including one pass convergence, unlimited storage capacity and tolerance with respect to eroded patterns.