离散时间迟滞神经网络中多个不动点的吸引域
Basins of Attraction to Multiple Fixed Points in Discrete-time Hysteresis Neural Networks
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中文总结 AI 辅助
本文针对离散时间迟滞神经网络，以二元数据集分类规避维度灾难，利用阈值参数控制吸引域的熵并实现最大化，结合教育项目反应数据集验证，明确了吸引域分布的调控机制。
中文摘要 AI 辅助
本文研究离散时间迟滞神经网络中的多个不动点，该网络由具有阈值参数的二元迟滞神经元构成，根据参数不同，网络可呈现多种二元不动点组合。每个不动点的稳定性由吸引域（BOA）表征，即落入该不动点的初始点集合。为评估吸引域大小的分布，本文引入熵概念；为规避维度灾难，本文采用二元数据集分类这一简单问题，其中吸引域对应类别。研究明确阈值参数可控制熵，尤其能最大化熵，使分布趋近均匀。作为具体示例，本文采用教育领域的项目反应数据集，运用项目反应理论中的两个基本指标对分类结果进行评估。
英文摘要
This paper studies multiple fixed points in a discrete-time hysteresis neural network. The network consists of binary hysteresis neurons characterized by the threshold parameter. Depending on the parameter, the network can have a variety of multiple binary fixed points. Stability of each fixed point is characterized by basin of attraction (BOA): the set of initial points falling into the fixed point. In order to evaluate the distribution of BOA sizes, we present entropy. In order to escape from the curse of dimensionality, we introduce a simple problem: classification of binary data set. In the classification, BOAs correspond to classes. In the problem, we clarify that the threshold parameter can control the entropy, especially, can maximize the entropy: the distribution approaches to uniform. As a concrete example, we consider an item response data set in education. Using two fundamental metrics in the item response theory, the classification results are evaluated.
