双向模糊形态联想记忆网络及其抗随机噪声的研究

在文献[1]提出的模糊形态联想记忆网络FMAM的基础上,提出了一种新型的模糊形态学双向联想记忆网络FMBAM,证明了FMBAM的双向联想中能够保证记忆在一步之内完成,因此不存在收敛问题,也表明了FMBAM具有优越的抗腐蚀或膨胀噪声的能力.但是,通常的噪声是随机的,为此,本文提出了动态核的方法,从而较好地提高了FMBAM对随机噪声的抗噪能力.仿真实验验证了利用动态核的双向联想记忆网络FMBAM,在加入较大的随机噪声的情况下,仍能保证完全记忆在一步之内完成.     

一种新的形态学联想记忆网络模型研究

针对即使在输入模式无噪声,形态学联想记忆在用于异联想时仍不能保证完全回忆的问题,从扩大记忆矩阵的存储空间的角度入手,提出一种新的形态学联想记忆模型——三维存储矩阵的形态学联想记忆来刻画MAM(Morphological Associative Memories)的记忆性能。该模型能够弥补传统形态学联想记忆的记忆矩阵的不足,解决MAM在异联想时不能保证对模式对集实现完全回忆的问题。详细阐述了构建三维存储矩阵的原理与步骤,并通过实例验证三维存储矩阵的形态学联想记忆的记忆性能远远优于传统的形态学联想记忆。     

形态学联想记忆存储性能的研究

形态学联想记忆（Morphological Associative Memories,MAM）的存储性能是衡量形态学联想记忆能力大小的重要指标。然而,迄今为止,对形态学联想记忆的存储性能,主要是对异联想形态学联想记忆（hetero-MAM）的存储性能的定量分析和定性刻画并未完成。这是一个悬而未决的理论问题,也是一个MAM应用的实际问题。针对这一问题开展研究,站在概率论的角度,提出一个MAM存储性能的概率模型,并进行了证明。通过定量分析和定性讨论,取得一致结论。研究和分析表明,hetero-MAM的存储性能受到输入模式向量维数n、输出模式向量维数m、以及输入、输出模式对数目K的影响,且三者的影响程度不同。提出的概率模型,对形态学联想记忆的研究、分析、设计和应用,具有一定的启发和帮助。     

形态学联想记忆的研究综述*

通过提炼出来的一个形态学联想记忆的研究框架,可以很清晰地概括出形态学联想记忆的研究成果,从而可以很合理地归纳出形态学联想记忆仍存在的问题以及今后的发展方向。此形态学联想记忆的研究框架对形态学联想记忆的进一步研究具有一定的指导意义。     

复形态联想记忆及其性能分析

在Ritter的实域形态联想记忆(real morphological associative memory,简称RMAM)模型的基础上,通过在复数域中序关系的引入构成复数格和环,导出了在复数域上与RMAM相一致的联想规则,构建了一类复域MAM(complex MAM,简称CMAM),从而将RMAM从实域推广至复域,使其可直接处理复信号(如经FFT(fast Fourier Transformation)变换所得数据).证明了该模型的收敛性,分析了其纠错能力和存储能力,并获得了与RMAM相一致的一系列定理和性质.此外,还比较了复形态网络和其他网络(如Hopfield神经网络)的异同.计算机仿真结果表明了CMAM的可行性.     

最小平方形态联想记忆模型的研究与实现

Ritter等人借助形态学理论提出了形态联想记忆模型（MAM Morphological Associatvie Memory)，其中所构建模型的两个权值矩阵和可分别用以回忆腐蚀和膨胀噪声模式，但不能回忆混合噪声模式，故本文提出了一个最小平方形态联想记忆模式（LSMAM least squares MAM)来克服MAM的不足，以达到既可分别识别腐蚀和膨胀噪声模式，也可以识别混合型噪声模式的目的，因此更适用于实际情形，实验结果表明了该方法的可行性。     

对数-指数形态学联想记忆

利用对数和指数算子构建了一种新的形态学联想记忆方法,简称LEMAM.理论分析表明:自联想LEMAM(简称ALEMAM)具有无限存储能力、一步回忆记忆、一定的抵抗腐蚀噪声或膨胀噪声的能力,在输入完全或在一定的噪声范围内,能够保证完全回忆记忆;异联想LEMAM(简称HLEMAM)在输入完全情况下,不能保证完全回忆记忆,但当满足一定条件时,也能够达到完美联想记忆.对比实验结果表明:在一些情况下,LEMAM能够取得较好的联想记忆效果.总体来说,LEMAM丰富了形态学联想记忆的理论和实践,可以作为一种神经计算模型加以研究和利用.     

形态学联想记忆网络记忆性能的定性分析

形态学联想记忆网络基于其前向映射式的网络结构特点,不管有多少个模式对,都可以用一个存储矩阵来进行存储。记忆单个模式对时,该模式对的矩阵信息完全存储在存储矩阵中,所以可以从该模式对的输入模式正确联想出输出模式,但当网络记忆了多个模式对时,各个模式对之间的相互影响就不可避免地存在,在此对其记忆性能进行定性分析,以期对MAM的研究有所裨益。     

形态学联想记忆网络的研究进展

形态学联想记忆网络具有无限存储能力、一步回忆记忆、良好地抵抗腐蚀噪声或者膨胀噪声的噪声容限等许多优点.从形态学联想记忆的概念、基本原理、发展脉络、研究新成果,发展趋势和研究方向等多个方面综述了形态学联想记忆网络的研究进展.对形态学联想记忆方面的研究带来了一定的参考价值.     

形态学联想记忆网络的进展研究

20多年来,形态学联想记忆的研究得到了长足的发展。从形态学联想记忆的基本原理、研究新成果等方面对形态学联想记忆网络的进展进行了研究。期望对形态学联想记忆方面的研究带来裨益。     

On new fuzzy morphological associative memories

In this paper, the new fuzzy morphological associative memories (FMAMs) based on fuzzy operations (/spl and/,/spl middot/) and (/spl or/,/spl middot/) are presented. FMAM with (/spl or/,/spl middot/) is extremely robust for dilative noise and FMAM with (/spl and/,/spl middot/) is extremely robust for erosive noise. Autoassociative FMAM has the unlimited storage capability and can converge in one step. The convex autoassociative FMAM can be used to achieve a reasonable tradeoff for the mixed noise. Finally, comparisons between autoassociative FMAM and the famous FAM are discussed. FMAM, as another new encoding way of fuzzy rules, still has a multitude of open problems worthy to explore in the future.     

The Kosko Subsethood Fuzzy Associative Memory (KS-FAM): Mathematical Background and Applications in Computer Vision

Many well-known fuzzy associative memory (FAM) models can be viewed as (fuzzy) morphological neural networks (MNNs) because they perform an operation of (fuzzy) mathematical morphology at every node, possibly followed by the application of an activation function. The vast majority of these FAMs represent distributive models given by single-layer matrix memories. Although the Kosko subsethood FAM (KS-FAM) can also be classified as a fuzzy morphological associative memory (FMAM), the KS-FAM constitutes a two-layer non-distributive model. In this paper, we prove several theorems concerning the conditions of perfect recall, the absolute storage capacity, and the output patterns produced by the KS-FAM. In addition, we propose a normalization strategy for the training and recall phases of the KS-FAM. We employ this strategy to compare the error correction capabilities of the KS-FAM and other fuzzy and gray-scale associative memories in terms of some experimental results concerning gray-scale image reconstruction. Finally, we apply the KS-FAM to the task of vision-based self-localization in robotics.     

Enhanced FMAM based on empirical kernel map

The existing morphological auto-associative memory models based on the morphological operations, typically including morphological auto-associative memories (auto-MAM) proposed by Ritter et al. and our fuzzy morphological auto-associative memories (auto-FMAM), have many attractive advantages such as unlimited storage capacity, one-shot recall speed and good noise-tolerance to single erosive or dilative noise. However, they suffer from the extreme vulnerability to noise of mixing erosion and dilation, resulting in great degradation on recall performance. To overcome this shortcoming, we focus on FMAM and propose an enhanced FMAM (EFMAM) based on the empirical kernel map. Although it is simple, EFMAM can significantly improve the auto-FMAM with respect to the recognition accuracy under hybrid-noise and computational effort. Experiments conducted on the thumbnail-sized faces (28/spl times/23 and 14/spl times/11) scaled from the ORL database show the average accuracies of 92%, 90%, and 88% with 40 classes under 10%, 20%, and 30% randomly generated hybrid-noises, respectively, which are far higher than the auto-FMAM (67%, 46%, 31%) under the same noise levels.     

Generalizing Operations of Binary Autoassociative Morphological Memories Using Fuzzy Set Theory

Morphological neural networks (MNNs) are a class of artificial neural networks whose operations can be expressed in the mathematical theory of minimax algebra. In a morphological neural net, the usual sum of weighted inputs is replaced by a maximum or minimum of weighted inputs (in this context, the weighting is performed by summing the weight and the input). We speak of a max product, a min product respectively.In recent years, a number of different MNN models and applications have emerged. The emphasis of this paper is on morphological associative memories (MAMs), in particular on binary autoassociative morphological memories (AMMs). We give a new set theoretic interpretation of recording and recall in binary AMMs and provide a generalization using fuzzy set theory.     

模糊形态联想记忆网络抗随机噪声研究及应用

利用灰度图像分解的思想,结合模糊形态联想记忆网络的方法,提高了模糊形态联想记忆网络对随机噪声的抗噪能力。成功地解决了灰度图像在含有随机噪声时的模糊联想记忆问题,并把该方法推广到对彩色图像的处理,从而给出了一种较好地恢复含噪灰度图像和彩色图像的途径。通过实验,验证了该方法的良好性能,取得了较理想的结果。     

Reconstruction of Patterns from Noisy Inputs Using Morphological Associative Memories

Morphological neural networks are based on a new paradigm for neural computing. Instead of adding the products of neural values and corresponding synaptic weights, the basic neural computation in a morphological neuron takes the maximum or minimum of the sums of neural values and their corresponding synaptic weights. By taking the maximum (or minimum) of sums instead of the sum of products, morphological neuron computation is nonlinear before thresholding. As a consequence, the properties of morphological neural networks are drastically different than those of traditional neural network models. In this paper we restrict our attention to morphological associative memories. After a brief review of morphological neural computing and a short discussion about the properties of morphological associative memories, we present new methodologies and associated theorems for retrieving complete stored patterns from noisy or incomplete patterns using morphological associative memories. These methodologies are derived from the notions of morphological independence, strong independence, minimal representations of patterns vectors, and kernels. Several examples are provided in order to illuminate these novel concepts.     

具有抗随机噪声能力的联想记忆网络

形态联想记忆网络具有良好的联想记忆功能和较强的抗膨胀或腐蚀噪声能力,但抗混合噪声的能力很弱.而在实际中,随机噪声往往是混合型的,既有膨胀又有腐蚀噪声,将尺度空间和形态联想记忆网络相结合,得到了一种新的联想记忆网络,它提高了形态自联想记忆网络的抗随机噪声能力.通过仿真实验验证了该方法具有良好的性能.     

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     

利用动态核的形态联想记忆网络的研究

在文献[1]的基础上，提出了一个基于动态核的形态联想记忆网络方法，特点是同一幅图像，如果其所含的噪声情况不同，则其核也将不同，从而较好地解决了图像含有随机噪声时的联想记忆问题。实验证明，此方法具有良好的性能，双向联想记忆的准确率优于文献[1]中介绍的方法。