用神经网络提取特征，再用能量模型分类，准确率99.2%。
A Hybrid Multi-Well Hopfield-CNN with Feature Extraction and K-Means for MNIST Classification
- 先用CNN提取图像特征，再用k-means生成类原型。
- 在多阱能量场中最小化能量，实现99.2%的准确率。
- 决策过程可解释，适合需要透明性的分类任务。
本研究提出一种混合模型，用于对MNIST数据集中的手写数字进行分类，结合卷积神经网络（CNN）与多阱霍普菲尔德网络。该方法利用CNN从输入图像中提取高维特征，随后通过k-means聚类将特征聚为类别特定的原型，这些原型作为多阱能量景观中的吸引子，霍普菲尔德网络通过最小化能量函数实现分类，该能量函数权衡特征相似性与类别分配。模型设计能够有效处理类内变异性（如不同书写风格），同时通过基于能量的决策过程提供可解释性。通过对CNN结构和阱数的系统优化，模型在10,000张测试图像上达到99.2%的高准确率，验证了其在图像分类任务中的有效性。研究强调深度特征提取与充分原型覆盖对高性能的关键作用，具有在模式识别中更广泛应用的潜力。
原文摘要 · Abstract (English)
This study presents a hybrid model for classifying handwritten digits in the MNIST dataset, combining convolutional neural networks (CNNs) with a multi-well Hopfield network. The approach employs a CNN to extract high-dimensional features from input images, which are then clustered into class-specific prototypes using k-means clustering. These prototypes serve as attractors in a multi-well energy landscape, where a Hopfield network performs classification by minimizing an energy function that balances feature similarity and class assignment.The model's design enables robust handling of intraclass variability, such as diverse handwriting styles, while providing an interpretable framework through its energy-based decision process. Through systematic optimization of the CNN architecture and the number of wells, the model achieves a high test accuracy of 99.2% on 10,000 MNIST images, demonstrating its effectiveness for image classification tasks. The findings highlight the critical role of deep feature extraction and sufficient prototype coverage in achieving high performance, with potential for broader applications in pattern recognition.
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