一种面向中小规模数据集的模糊分类方法

虽然Takagi-Sugeno-Kang （TSK）模糊分类器在一些重要场合已经取得了广泛应用,但如何提高其分类性能和增强其可解释性,仍然是目前的研究热点.提出一种随机划分与组合特征且规则具有高可解释性的深度TSK模糊分类器（RCC-DTSK-C）,但和其他分类器构造不同的是：（1） RCC-DTSK-C由很多基训练单元构成,这些基训练单元可以被独立训练;（2）每一个基训练单元的隐含层通过模糊规则的可解释性来表达,而这些模糊规则又是通过随机划分、随机组合来进行特征选择的;（3）基于栈式结构理论,源数据集作为相同的输入空间被映射到每一个独立的基训练单元中,这样就有效地保证了源数据的所有特征在每一个独立的训练单元中都得以保留.实验结果表明,RCC-DTSK-C具有良好的分类性能和可解释性.     

并行集成具有高可解释的TSK模糊分类器

针对分层Takagi-Sugeno-Kang(TSK)模糊分类器可解释性差,以及当增加或删除一个TSK模糊子分类器时Boosting模糊分类器需要重新训练所有TSK模糊子分类器等问题,提出一种并行集成具有高可解释的TSK模糊分类器EP-Q-TSK.该集成模糊分类器每个TSK模糊子分类器可以使用最小学习机(LLM)被并行地快速构建.作为一种新的集成学习方式,该分类器利用每个TSK模糊子分类器的增量输出来扩展原始验证数据空间,然后采用经典的模糊聚类算法FCM获取一系列代表性中心点,最后利用KNN对测试数据进行分类.在标准UCI数据集上,分别从分类性能和可解释性两方面验证了EP-Q-TSK的有效性.     

基于增强深度特征和TSK模糊分类器的癫痫脑电信号识别

识别癫痫脑电信号的关键在于获取有效的特征和构建可解释的分类器.为此,提出一种基于增强深度特征的TSK模糊分类器(ED-TSK-FC).首先,ED-TSK-FC使用一维卷积神经网络(1D-CNN)自动获取癫痫脑电信号的深度特征与潜在类别信息,并将深度特征和潜在类别信息合并为增强深度特征;其次,将增强深度特征作为ED-TSK-FC模糊规则前件与后件部分的训练变量,保证原始输入的深度特征及其潜在意义都出现在模糊规则中,进而对增强深度特征作出良好的解释;然后,采用岭回归极限学习算法对模糊规则的后件参数进行快速求解,在不显著降低分类准确度的情况下,ED-TSK-FC的廉价训练方法可以缩短模型的训练时间;最后,在Bonn癫痫数据集上,分别从分类性能、学习效率和可解释性3个方面,验证ED-TSK-FC的优越性.     

面向不平衡数据的深度TSK模糊分类器

为了进一步提升Takagi-Sugeno-Kang(TSK)模糊分类器在不平衡数据集上的泛化能力和保持其较好的语义可解释性，受集成学习的启发，提出面向不平衡数据的深度TSK模糊分类器(A Deep TSK Fuzzy Classifier for Imbalanced Data, ID-TSK-FC).ID-TSK-FC主要由一个不平衡全局线性回归子分类器(Imbalanced Global Linear Regression Sub-Classifier, IGLRc)和多个不平衡TSK模糊子分类器(Imbalanced TSK Fuzzy Sub-Classifier, I-TSK-FC)组成.根据人类“从全局粗糙到局部精细”的认知行为和栈式叠加泛化原理，ID-TSK-FC首先在所有原始训练样本上训练一个IGLRc,获得全局粗糙的分类结果.然后根据IGLRc的输出，识别原始训练样本中的非线性分布训练样本.在非线性分布训练样本上，以栈式深度结构生成多个局部I-TSK-FC,获得局部精细的结果.最后，对于栈式堆叠IGLRc和所有I-TSK-FC的输出，使用基于最小距离投票原理，得到ID...     

区间二型模糊子空间0阶TSK系统

人们倾向于使用少量的有代表性的特征来描述一条规则,而忽略极为次要的冗余的信息。经典的区间二型TSK(Takagi-Sugeno-Kang)模糊系统,在规则前件和后件部分会使用完整的数据特征空间,对于高维数据而言,易导致系统的复杂度增加和可解释性的损失。针对于此,提出了区间二型模糊子空间0阶TSK系统。在规则前件部分,使用模糊子空间聚类和网格划分相结合的方法生成稀疏的规整的规则中心,在规则后件部分,使用简化的0阶形式,从而得到规则语义更为简洁的区间二型模糊系统。在模拟和真实数据上的实验结果表明该方法分类效果良好,可解释性更好。     

基于模糊子空间聚类的0 阶岭回归TSK 模糊系统

经典数据驱动型TSK模糊系统在利用高维数据训练模型时,由于规则前件采用的特征过多,导致规则的解释性和简洁性下降.对此,根据模糊子空间聚类算法的子空间特性,为TSK模型添加特征抽取机制,并进一步利用岭回归实现后件的学习,提出一种基于模糊子空间聚类的0阶岭回归TSK模型构建方法.该方法不仅能为规则抽取出重要子空间特征,而且可为不同规则抽取不同的特征.在模拟和真实数据集上的实验结果验证了所提出方法的优势.     

适合大规模数据集且基于LLM的0阶TSK模糊分类器

针对传统分类器的泛化性能差、可解释性及学习效率低等问题, 提出0阶TSK-FC模糊分类器.为了将该分类器 应用到大规模数据的分类中, 提出增量式0阶TSK-IFC模糊分类器, 采用增量式模糊聚类算 法(IFCM($c+p$))训练模糊规则参数并通过适当的矩阵变换提升参数学习效率.仿真实验表明, 与FCPM-IRLS模糊分类器、径向基函数神经网 络相比, 所提出的模糊分类器在不同规模数据集中均能保持很好的性能, 且TSK-IFC模糊分类器在大规模数据分类中尤为突出.     

基于视角-规则的深度TSK模糊分类器及其在多元癫痫脑电信号识别中的应用

在癫痫脑电信号分类检测中,传统机器学习方法分类效果不理想,深度学习模型虽然具有较好的特征学习优势,但其“黑盒”学习方式不具备可解释性,不能很好地应用于临床辅助诊断;并且,现有的多视角深度TSK模糊系统难以有效表征各视角特征之间的相关性.针对以上问题,提出一种基于视角-规则的深度Takagi-SugenoKang (TSK)模糊分类器(view-to-rule Takagi-Sugeno-Kang fuzzy classifier, VR-TSK-FC),并将其应用于多元癫痫脑电信号检测中.该算法在原始数据上构建前件规则以保证模型的可解释性,利用一维卷积神经网络(1-dimensional convolutional neural network, 1D-CNN)从多角度抓取多元脑电信号深度特征.每个模糊规则的后件部分分别采用一个视角的脑电信号深度特征作为其后件变量,视角-规则的学习方式提高了VR-TSK-FC表征能力.在Bonn和CHB-MIT数据集上, VR-TSK-FC算法模糊逻辑推理过程保证可解释的基础上达到了较好分类效果.     

基于Boosting算法集成遗传模糊分类器的文本分类

提出一种新颖的基于Boosting模糊分类的文本分类方法。首先采用潜在语义索引(LSI)对文本特征进行选择;然后提出Boosting算法集成模糊分类器学习,在每轮迭代训练过程中,算法通过调整训练样本的分布,利用遗传算法产生分类规则。减少分类规则能够正确分类样本的权值,使得新产生的分类规则重点考虑难于分类的样本。实验结果表明,该文本分类算法具有良好分类的性能。     

特征扩展的随机向量函数链神经网络

基于宽度学习的动态模糊推理系统(broad-learning-based dynamic fuzzy inference system , BL-DFIS)能自动构建出精简的模糊规则并获得良好的分类性能. 然而, 当遇到大型复杂的数据集时, BL-DFIS因会使用较多模糊规则来试图达到令人满意的识别精度, 从而对其可解释性造成了不利影响. 对此, 提出一种兼顾分类性能和可解释性的模糊神经网络, 将其称为特征扩展的随机向量函数链神经网络(FA-RVFLNN). 在该网络中, 一个以原始数据为输入的RVFLNN被作为主体结构, BL-DFIS则用作性能补充, 这意味着FA-RVFLNN包含具有性能增强作用的直接链接. 由于主体结构的增强节点使用Sigmoid激活函数, 因此, 其推理过程可借助一种模糊逻辑算子(I-OR)来解释. 而且, 具有明确含义的原始输入数据也有助于解释主体结构的推理规则. 在直接链接的支撑下, FA-RVFLNN可利用增强节点、特征节点和模糊节点学到更丰富的有用信息. 实验表明: FA-RVFLNN既减缓了主体结构RVFLNN中过多增强节点带来的“规则爆炸”问题, 也提高了性能补充结构BL-DFIS的可解释性(平均模糊规则数降低了50%左右), 在泛化性能和网络规模上仍具有竞争力.     

A faster convergence and concise interpretability TSK fuzzy classifier deep-wide-based integrated learning

Hierarchical TSK fuzzy system was proposed to approach the exponential growth of IF-THEN rules which named “fuzzy rule explosion”. However, it could not get better performance in few layers for instability of TSK fuzzy system, such that hierarchical TSK fuzzy system suffers from bad interpretability and slow convergence along with too much layers. To get a better solution, this study employs a faster convergence and concise interpretability TSK fuzzy classifier deep-wide-based integrated learning (FCCI-TSK) which has a wide structure to adopt several ensemble units learning in a meantime, and the best performer will be picked up to transfer its learning knowledge to next layer with the help of stacked generalization principle. The ensemble units are integrated by negative correlation learning (NCL). FCCI-TSK adjusts the input of the next layer with a better guidance such that it can quicken the speed of convergence and reduce the number of layers. Besides, leading with guidance, it can achieve higher accuracy and better interpretability with more simple structure. The contributions of this study include: (1) To enhance the performance of fuzzy classifier, we mix NCL and stacked generalization principle together in FCCI-TSK; (2) To overcome the phenomenon of “fuzzy rule explosion”, we adopt deep-wide integrated learning and information discarding to accelerate convergence and obtain concise interpretability in the meantime. Comparing with other 11 algorithms, the results on twelve UCI datasets show that FCCI-TSK has the best performance overall and the convergence of FCCI-TSK is also examined.     

Takagi-Sugeno-Kang fuzzy system fusion: A survey at hierarchical,wide and stacked levels

With excellent global approximation performance and interpretability, Takagi-Sugeno-Kang (TSK) fuzzy systems have enjoyed a wide range of applications in various fields, such as smart control, medical, and finance. However, in handling high-dimensional complex data, the performance and interpretability of a single TSK fuzzy system are easily degraded by rule explosion due to the curse of dimensionality. Ensemble learning comes into play to deal with the problem by the fusion of multiple TSK fuzzy systems using appropriate ensemble learning strategies, which has shown to be effective in eliminating the issue of the curse of dimensionality curse problem and reducing the number of fuzzy rules, thereby maintaining the interpretability of fuzzy systems. To this end, this paper gives a comprehensive survey of TSK fuzzy system fusion to provide insights into further research development. First, we briefly review the fundamental concepts related to TSK fuzzy systems, including fuzzy rule structures, training methods, and interpretability, and discuss the three different development directions of TSK fuzzy systems. Next, along the direction of TSK fuzzy system fusion, we investigate in detail the current ensemble strategies for fusion at hierarchical, wide and stacked levels, and discuss their differences, merits and weaknesses from the aspects of time complexity, interpretability (model complexity) and classification performance. We then present some applications of TSK fuzzy systems in real-world scenarios. Finally, the challenges and future directions of TSK fuzzy system fusion are discussed to foster prospective research.     

Bayesian zero-order TSK fuzzy system modeling

Different from the existing TSK fuzzy system modeling methods, a novel zero-order TSK fuzzy modeling method called Bayesian zero-order TSK fuzzy system (B-ZTSK-FS) is proposed from the perspective of Bayesian inference in this paper. The proposed method B-ZTSK-FS constructs zero-order TSK fuzzy system by using the maximum a posteriori (MAP) framework to maximize the corresponding posteriori probability. First, a joint likelihood model about zero-order TSK fuzzy system is defined to derive a new objective function which can assure that both antecedents and consequents of fuzzy rules rather than only their antecedents of the most existing TSK fuzzy systems become interpretable. The defined likelihood model is composed of three aspects: clustering on the training set for antecedents of fuzzy rules, the least squares (LS) error for consequent parameters of fuzzy rules, and a Dirichlet prior distribution for fuzzy cluster memberships which is considered to not only automatically match the “sum-to-one” constraints on fuzzy cluster memberships, but also make the proposed method B-ZTSK-FS scalable for large-scale datasets by appropriately setting the Dirichlet index. This likelihood model indeed indicates that antecedent and consequent parameters of fuzzy rules can be linguistically interpreted and simultaneously optimized by the proposed method B-ZTSK-FS which is based on the MAP framework with the iterative sampling algorithm, which in fact implies that fuzziness and probability can co-jointly work for TSK fuzzy system modeling in a collaborative rather than repulsive way. Finally, experimental results on 28 synthetic and real-world datasets are reported to demonstrate the effectiveness of the proposed method B-ZTSK-FS in the sense of approximation accuracy, interpretability and scalability.     

How good are fuzzy If-Then classifiers?

This paper gives some known theoretical results about fuzzy rule-based classifiers and offers a few new ones. The ability of Takagi-Sugeno-Kang (TSK) fuzzy classifiers to match exactly and to approximate classification boundaries is discussed. The lemma by Klawonn and Klement about the exact match of a classification boundary in R (2) is extended from monotonous to arbitrary functions. Equivalence between fuzzy rule-based and nonfuzzy classifiers (1-nn and Parzen) is outlined. We specify the conditions under which a class of fuzzy TSK classifiers turn into lookup tables. It is shown that if the rule base consists of all possible rules (all combinations of linguistic labels on the input features), the fuzzy TSK model is a lookup classifier with hyperbox cells, regardless of the type (shape) of the membership functions used. The question "why fuzzy?" is addressed in the light of these results.     

双层模糊系统融合中心约束型最小包含球

与传统的TSK模糊系统相比,改进的双层TSK模糊系统CTSK(Central TSK Fuzzy System)有如下优点:良好的可解释性、更好的鲁棒性、较强的逼近能力。但对于大样本或超大样本数据集,其时间复杂度和空间复杂度的开销都极大地限制了它的实用性。针对此不足,通过模糊系统融合中心约束型最小包含球(CCMEB)理论提出了CCMEB-CTSK(CCMEB-based CTSK)算法。该算法在继承CTSK优点的同时,又较好地实现了处理大样本和超大样本数据集的有效性和快速性。仿真实验研究分析了采用不同模糊规则数的CCMEB-CTSK的性能指标和运行时间的比较,以及训练样本不加噪声和加入噪声情况下CCMEB-CTSK泛化能力和鲁棒性能的测试。     

Fuzzy rule weight modification with particle swarm optimisation

The most challenging problem in developing fuzzy rule-based classification systems is the construction of a fuzzy rule base for the target problem. In many practical applications, fuzzy sets that are of particular linguistic meanings, are often predefined by domain experts and required to be maintained in order to ensure interpretability of any subsequent inference results. However, learning fuzzy rules using fixed fuzzy quantity space without any qualification will restrict the accuracy of the resulting rules. Fortunately, adjusting the weights of fuzzy rules can help improve classification accuracy without degrading the interpretability. There have been different proposals for fuzzy rule weight tuning through the use of various heuristics with limited success. This paper proposes an alternative approach using Particle Swarm Optimisation in the search of a set of optimal rule weights, entailing high classification accuracy. Systematic experimental studies are carried out using common benchmark data sets, in comparison to popular rule based learning classifiers. The results demonstrate that the proposed approach can boost classification performance, especially when the size of the initially built rule base is relatively small, and is competitive to popular rule-based learning classifiers.