Optimal Absolute Storage Capacity Research Articles

Permutation-based finite implicative fuzzy associative memories

Implicative fuzzy associative memories (IFAMs) are single layer feedforward fuzzy neural networks whose synaptic weights and threshold values are given by implicative fuzzy learning. Despite an excellent tolerance with respect to either pasitive or negative noise, IFAMs are not suited for patterns corrupted by mixed noise. This paper presents a solution to this problem. Precisely, we first introduce the class of finite IFAMs by replacing the unit interval by a finite chain L . Then, we generalize both finite IFAMs and their dual versions by means of a permutation on L . The resulting models are referred to as permutation-based finite IFAMs ( π-IFAMs). We show that a π-IFAM can be viewed as a finite IFAM, but defined on an alternative lattice structure ( L , ≼ ) . Thus, π-IFAMs also exhibit optimal absolute storage capacity and one step convergence in the autoassociative case. Furthermore, computational experiments revealed that a certain π-IFAM, called Lukasiewicz π μ -IFAM, outperformed several other associative memory models for the reconstruction of gray-scale patterns corrupted by salt and pepper noise.

Sparsely connected autoassociative fuzzy implicative memories and their application for the reconstruction of large gray-scale images

Autoassociative fuzzy implicative memories (AFIMs) are models that exhibit optimal absolute storage capacity and an excellent tolerance with respect to incomplete or eroded patterns. As a consequence, they can be effectively used for the reconstruction of gray-scale images. In practice, however, applications of AFIMs are confined to images of small size due to computational limitations. In order to circumvent this computational overhead and, motivated by the sparsity of biological neural networks, this paper introduces the class of sparsely connected AFIMs (SCAFIMs). Such as the original AFIMs, SCAFIMs exhibit optimal absolute storage capacity and tolerance with respect to incomplete or eroded patterns. By means of computational experiments, we investigate the performance of SCAFIMs with different network topologies and compare the novel models with other techniques for the reconstruction of gray-scale images.

Behavior of morphological associative memories with true-color image patterns

Morphological associative memories (MAMs) are a special type of associative memory which exhibit optimal absolute storage capacity and one-step convergence. This associative model substitutes the additions and multiplications used by other models by computing maximums and minimums. This type of associative model has been applied to different pattern recognition problems including face localization and gray scale image restoration. Despite of his power, MAMs have not been applied in problems that involve true-color patterns. In this paper it is described how a MAM can be applied in problems involving true-color patterns. Furthermore, a complete study of the behavior of this associative model in the restoration of true-color images is performed using a benchmark of 14 400 images altered by different type of noises.

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.

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.

Associative morphological memories based on variations of the kernel and dual kernel methods

Morphological associative memories (MAMs) belong to the class of morphological neural networks. The recording scheme used in the original MAM models is similar to the correlation recording recipe. Recording is achieved by means of a maximum ( M XY model) or minimum ( W XY model) of outer products. Notable features of autoassociative morphological memories (AMMs) include optimal absolute storage capacity and one-step convergence. Heteroassociative morphological memories (HMMs) do not have these properties and are not very well understood. The fixed points of AMMs can be characterized exactly in terms of the original patterns. Unfortunately, AMM fixed points include a large number of spurious memories. In this paper, we combine the M XX model and variations of the kernel method to produce new autoassociative and heteroassociative memories. We also introduce a dual kernel method. A new, dual model is given by a combination of the W XX model and a variation of the dual kernel method. The new MAM models exhibit better error correction capabilities than M XX and W XX and a reduced number of spurious memories which can be easily described in terms of the fundamental memories.