近年来，随着科技水平和生活水平的发展提高，人类追求事件物质的精细程度越来越高，大量的数据记录随之而来。人们在享受科技带来的便利时，面临着大量繁琐的数据处理。如今，数据集之间不仅仅是高维度的数据集，还存在着各种相互作用的关系，这样就对于人类处理数据的能力、速度、效率提出了更高的要求。对数据处理方法的研究日益受到重视，如何高效地记录数据、处理数据、分析数据一直是数据处理领域中活跃的前沿研究课题。

研究过程采用粒子群优化算法、梯度下降法等优化算法对一系列联想记忆网络机制进行了理论研究，并利用数据空间转换、自编码器、模糊聚类处理等方法对一些数据联想记忆机制进行逻辑优化，以期通过提出联想记忆网络的逻辑扩展结构进一步改善这些联想记忆机制，使得可以对数据进行更快速、高效、准确地存储、恢复和处理，为深入了解和发展大数据处理方法提供理论基础，为进一步的实验研究提供理论依据。主要内容概括如下：

1、联想记忆网络是在两个数据集之间，建立一个记忆矩阵，通过输入集与记忆矩阵的逻辑运算得到输出集。在考虑单层数据联想记忆网络的结构时，引入数据空间转换的概念(非线性分段函数映射)对输入输出集分别进行处理。数据集先被数据空间转换到一个新的空间域，其次再以联想记忆矩阵的形式进行存储，回忆数据时利用数据空间转换函数的逆变换得到原数据集的回忆集。数据空间转换模式主要存在三种模式——输入空间转换、输出空间转换以及同时对输入和输出空间转换。具体实验里采用了非线性分段函数处理输入集和输出集，而分段函数的参数，即分段函数的截点数(如何分段)，主要通过以回忆数据集与原数据集的误差为目标函数的粒子群算法优化而得到。实验中重点针对几种常见的数据联想记忆网络——相关联想记忆网络、模糊联想记忆网络和形态联想记忆网络来论证非线性变换的处理能有效地提高数据存储记忆能力。这部分实验揭示了分段函数的截点数的选择与不同的联想记忆网络回忆误差之间的关系，分段函数的截点数越多，数据集回忆的误差越小。证明了非线性变换的引入有助于提高单层数据联想记忆网络的回忆能力。

2、双层联想记忆网络是在单层联想记忆网络中添加了一个隐藏层矩阵，原数据集都与这个隐藏层的数据集进行逻辑运算，即得到两个联想记忆矩阵。在研究双层数据联想记忆网络结构时，引入多层神经网络——数据自编码处理方法对数据集进行处理，提出了基于自编码器接口的双层联想记忆网络结构模型。这个模型由两部分单元组成。第一部分利用自编码器对原高维度数据集进行有效地降维处理，得到输入集的良好表示，这个新表达有助于第二部分的面向逻辑的联想记忆网络实现存储和回忆数据，最后利用解码器得到原数据集的回忆集。在这部分实验中，分别利用粒子群优化算法、差分进化法和梯度下降法对自编码参数设置进行优化。实验表明，随着自编码器中的隐藏层层数的增加和每一层的维数选择不同，可以不同程度地提高数据存储回忆能力。对比结果可知，基于自编码器接口的双层数据联想记忆网络比原双层联想记忆网络、单层联想记忆网络能更有效地存储回忆数据。

3、多个数据集需要同时存储记忆时，需要存储的记忆矩阵就是一个庞大的高维数据，在多数据集联想记忆网络(即张量联想记忆网络)中，引入模糊聚类分析方法——模糊C均值方法对多个数据集进行聚类处理，联想记忆网络的存储对象由原先多个原数据的整体存储记忆矩阵变为多个数据集的聚类中心和隶属度的存储记忆矩阵，减少了联想记忆矩阵的数据存储量和计算量，最后利用聚类中心和隶属度函数还原多个数据集的回忆集。在这部分实验中，主要利用粒子群优化算法和梯度下降法对模糊C均值方法参数进行优化选择。在选择到合适的聚类分析法参数时，对基于模糊C均值的张量联想记忆网络进行了大量的数据实验。计算结果表明，基于模糊C均值的张量联想记忆网络可以有效地提高数据存储能力和减少回忆数据的误差。

 

关键词：单层联想记忆网络， 双层联想记忆网络， 多数据集联想记忆网络， 非线性变换， 自编码器， 模糊C均值

 

Recently, with the development of science and technology, the pursuit of event material is getting higher and higher and a large number of data should be recorded with follow shortly. Nowadays, data sets are not only high-dimensional data sets, but also interact with each other, and higher requirements are put forward for the speed, mechanism and efficiency of data processing. More attention has been paid to the research of data processing methods. Studies on the recording, processing and analysis of data have been the essential parts of data processing.

This main objective of this dissertation is to introduce a logic-oriented associative memory which constitutes the developments of the architecture, to achieve the storage and the recall mechanisms efficiently, quickly, accurately. This dissertation carries out a series of theoretical researches and developments on associative memories used gradient-based learning mechanisms, particle swarm optimization (PSO) and differential evolution (DE), and the logic development of associative memories is optimized by means of nonlinear transformations (mappings) of spaces of data, autoencoding mechanisms and fuzzy clustering processing. The modification and optimization of these association mechanisms can store, process and recall the data more quickly, efficiently and accurately. These results provide a theoretical basis for the in-depth understanding and development of the big-data processing——granular data, and provide some elemental theoretical basis for further experiments. The main results are as follows:

1. A memory matrix is created between the input data set and the output data set. In the single-level fuzzy associative memories, the data are first transformed into a new space and then resulting objects (patterns) are stored in the memory. Then, the recall is obtained by the inverse transformation of the nonlinear transformation. The objective of the transformations is to enhance the recall abilities of the memories. Nonlinear transformations are applied to transform the input space, transform the output space and transform both input and output spaces. The transformations are realized in the form of piecewise linear functions whose parameters are optimized with the use of PSO. A comprehensive suite of experiments involves several types of associative memories such as correlation associative memories, fuzzy associative memories and morphological associative memories. The experiments reveal some interesting relationships between the parameters of the nonlinear mappings and the resulting quality of the recall. They also help quantify the capabilities of the nonlinear mappings to improve the quality of recall.

2. Two-level associative memories have one more hidden layer data set than single-level associative memories. The first memory matrix is established between the input data and the hidden matrix, and the other memory matrix is established between the hidden matrix and the output data. We develop a logic-driven model of two-level fuzzy associative memories augmented by autoencoding processing. It is composed of two functional modules. The first module of this architecture implements an efficient dimensionality reduction of the original high dimensional data with the use of an autoencoder to get a new representation of the input data. This helps achieve storing and completing the recall realized by a logic-oriented associative memory which constitutes the second module of the architecture. Then, the recall data set is obtained by decoder. The optimization of the association matrices studied in the dissertation involves both gradient-based learning mechanisms and the algorithms of population-based optimization, i.e., PSO and DE. A suite of experimental studies is presented to quantify the performance of the proposed approach. With the increase of the number of coding layers and the different nodes in each layer, the data storage and recall capability can be improved to different degrees.

3. Associative memories need to have strong capacity to store numerous data sets with a minimal recall error. With the explosion of the database, a huge dataset could be split into some subsets and these subsets interact with each other through a relationship. Tensor associative memories aim at further improvement of the storage capacity and the performance of the recall. In tensor associative memories, we combined with clustering analysis——fuzzy C-means for multiple data sets. The memory matrix comes from membership degree of multiple data sets, which reduces the storage and calculation amount of original associative memory matrix. Then, the recall is restored by using clustering center and membership function. In this part of experiments, particle swarm optimization algorithm and gradient-based method are used to optimize the parameters of the fuzzy C-means. The results show that for tensor associative memory, the combination of fuzzy C-means can effectively improve the data storage capacity and recall with a minimal error.

 

Key words: single-level associative memories, two-level associative memories, tensor associative memories, nonlinear function, autoencoding, fuzzy C-means

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