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...     

基于训练空间重构的多模块TSK模糊系统

利用重构训练样本空间的手段,提出一种多训练模块Takagi-Sugeno-Kang （TSK）模糊分类器H-TSK-FS.它具有良好的分类性能和较高的可解释性,可以解决现有层次模糊分类器中间层输出和模糊规则难以解释的难题.为了实现良好的分类性能,H-TSK-FS由多个优化零阶TSK模糊分类器组成.这些零阶TSK模糊分类器内部采用一种巧妙的训练方式.原始训练样本、上一层训练样本中的部分样本点以及所有已训练层中最逼近真实值的部分决策信息均被投影到当前层训练模块中,并构成其输入空间.通过这种训练方式,前层的训练结果对后层的训练起到引导和控制作用.这种随机选取样本点、在一定范围内随机选取训练特征的手段可以打开原始输入空间的流形结构,保证较好或相当的分类性能.另外,该研究主要针对少量样本点且训练特征数不是很大的数据集.在设计每个训练模块时采用极限学习机获取模糊规则后件参数.对于每个中间训练层,采用短规则表达知识.每条模糊规则则通过约束方式确定不固定的输入特征以及高斯隶属函数,目的是保证所选输入特征具有高可解释性.真实数据集和应用案例实验结果表明,H-TSK-FS具有良好的分类性能和高可解释性.     

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.     

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.     

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。     

基于精简随机子空间的多生成树集成一类分类算法

由于高维数据通常存在冗余和噪声,在其上直接构造覆盖模型不能充分反映数据的分布信息,导致分类器性能下降.为此提出一种基于精简随机子空间多树集成分类方法.该方法首先生成多个随机子空间,并在每个子空间上构造独立的最小生成树覆盖模型.其次对每个子空间上构造的分类模型进行精简处理,通过一个评估准则(AUC值),对生成的一类分类器进行精简.最后均值合并融合这些分类器为一个集成分类器.实验结果表明,与其它直接覆盖分类模型和bagging算法相比,多树集成覆盖分类器具有更高的分类正确率.     

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.     

基于FCM的两级集成分类器算法

基于模糊聚类的思想提出了一种新的两级集成分类器算法.将数据集用Fuzzy C-Means算法进行聚类,得到每个实例对应于每个类别的模糊隶属度.一级集成根据Bagging算法获得成员分类器,分类器个数为数据集类别数且每个成员分类器对应一个类别标号,这些成员分类器的采样方式是通过其对应类别的模糊隶属度为每个实例加权后进行随机重采样.二级集成是将一级集成产生的针对类别的成员分类器通过动态加权多数投票法来组合,学习到最终的分类结果.该算法称为EWFuzzyBagging,实验结果表明,该算法与Bagging和AdaBoost相比具有更好的健壮性.     

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.     

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.     

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.     

面向自闭症辅助诊断的无监督模糊特征学习新方法

自闭症患者的行为和认知缺陷与潜在的脑功能异常有关。对于静息态功能磁振图像（functional magnetic resonance imaging, fMRI）高维特征,传统的线性特征提取方法不能充分提取其中的有效信息用于分类。为此,本文面向fMRI数据提出一种新型的无监督模糊特征映射方法,并将其与多视角支持向量机相结合,构建分类模型应用于自闭症的计算机辅助诊断。该方法首先采用多输出TSK模糊系统的规则前件学习方法,将原始特征数据映射到线性可分的高维空间;然后引入流形正则化学习框架,提出新型的无监督模糊特征学习方法,从而得到原输出特征向量的非线性低维嵌入表示;最后使用多视角SVM算法进行分类。实验结果表明:本文方法能够有效提取静息态fMRI数据中的重要特征,在保证模型具有优越且稳定的分类性能的前提下,还可以提高模型的可解释性。     

Building text classifiers using positive,unlabeled and ‘outdated’ examples

Learning from positive and unlabeled examples (PU learning) is a partially supervised classification that is frequently used in Web and text retrieval system. The merit of PU learning is that it can get good performance with less manual work. Motivated by transfer learning, this paper presents a novel method that transfers the ‘outdated data’ into the process of PU learning. We first propose a way to measure the strength of the features and select the strong features and the weak features according to the strength of the features. Then, we extract the reliable negative examples and the candidate negative examples using the strong and the weak features (Transfer‐1DNF). Finally, we construct a classifier called weighted voting iterative support vector machine (SVM) that is made up of several subclassifiers by applying SVM iteratively, and each subclassifier is assigned a weight in each iteration. We conduct the experiments on two datasets: 20 Newsgroups and Reuters‐21578, and compare our method with three baseline algorithms: positive example‐based learning, weighted voting classifier and SVM. The results show that our proposed method Transfer‐1DNF can extract more reliable negative examples with lower error rates, and our classifier outperforms the baseline algorithms. Copyright © 2016 John Wiley & Sons, Ltd.     

Improving the interpretability of TSK fuzzy models by combiningglobal learning and local learning

The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multimodel approach in which simple submodels (typically linear models) are combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance (i.e., the model is capable of approximating the given system with arbitrary accuracy, provided that sufficient rules are used and sufficient training data are available), they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior, which is difficult to interpret. Since one of the important motivations of using the TSK model (also other fuzzy models) is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. We propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user's preference, generating models with good tradeoff in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example     

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.     

一种基于模糊划分和模糊加权的集成深度信念网络

针对DBN算法训练时间复杂度高,容易过拟合等问题,受模糊理论启发,提出了一种基于模糊划分和模糊加权的集成深度信念网络,即FE-DBN（ensemble deep belief network with fuzzy partition and fuzzy weighting）,用于处理大样本数据的分类问题。通过模糊聚类算法FCM将训练数据划分为多个子集,在各个子集上并行训练不同结构的DBN,将每个分类器的结果进行模糊加权。在人工数据集、UCI数据集上的实验结果表明,提出的FE-DBN比DBN精度均有所提升,具有更快的运行时间。