A fuzzy clustering algorithm enhancing local model interpretability

In this work, simple modifications on the cost index of particular local-model fuzzy clustering algorithms are proposed in order to improve the readability of the resulting models. The final goal is simultaneously providing local linear models (reasonably close to the plant’s Jacobian) and clustering in the input space so that desirable characteristics (regarding final model accuracy, and convexity and smoothness of the cluster membership functions) are improved with respect to other proposals in literature. Some examples illustrate the proposed approach.     

Mining fuzzy association rules for classification problems

The effective development of data mining techniques for the discovery of knowledge from training samples for classification problems in industrial engineering is necessary in applications, such as group technology. This paper proposes a learning algorithm, which can be viewed as a knowledge acquisition tool, to effectively discover fuzzy association rules for classification problems. The consequence part of each rule is one class label. The proposed learning algorithm consists of two phases: one to generate large fuzzy grids from training samples by fuzzy partitioning in each attribute, and the other to generate fuzzy association rules for classification problems by large fuzzy grids. The proposed learning algorithm is implemented by scanning training samples stored in a database only once and applying a sequence of Boolean operations to generate fuzzy grids and fuzzy rules; therefore, it can be easily extended to discover other types of fuzzy association rules. The simulation results from the iris data demonstrate that the proposed learning algorithm can effectively derive fuzzy association rules for classification problems.     

Stabilisation diagrams: Pole identification using fuzzy clustering techniques

In the structural dynamics area, system identification represents one of the most critical steps. Therefore, a great research effort has been made in the last decades to improve the accuracy and reliability of this process. One of the results of this effort is the so-called stabilization diagram, a widespread tool, where the system's poles are represented for several mod el orders. In real applications, the assessment of this diagram is often extremely demanding due to the high number of poles amongst which only a few represent the true or physical ones.Fuzzy clustering was already successfully applied in various fields including economics, finance and marketing. In this paper, fuzzy clustering is introduced into the structural mechanics field as a tool to automatically assess stabilization diagrams. Several advanced algorithms are presented, all based on the Fuzzy-C-Means clustering technique, including the Gustafson–Kessel and Gath–Geva algorithms. In addition, Genetic Algorithms can also be used to cluster a data set as a stand-alone technique as well as in a hybrid combination with fuzzy clustering algorithms.This paper concludes with a comparison of all the mentioned approaches, by applying them on true in-flight test data.     

Attribute weighted mercer kernel based fuzzy clustering algorithm for general non-spherical datasets

Clustering analysis is an important topic in artificial intelligence, data mining and pattern recognition research. Conventional clustering algorithms, for instance, the famous Fuzzy C-means clustering algorithm (FCM), assume that all the attributes are equally relevant to all the clusters. However in most domains, especially for high-dimensional dataset, some attributes are irrelevant, and some relevant ones are less important than others with respect to a specific class. In this paper, such imbalances between the attributes are considered and a new weighted fuzzy kernel-clustering algorithm (WFKCA) is presented. WFKCA performs clustering in a kernel feature space mapped by mercer kernels. Compared with the conventional hard kernel-clustering algorithm, WFKCA can yield the meaningful prototypes (cluster centers) of the clusters. Numerical convergence properties of WFKCA are also discussed. For in-depth studies, WFKCA is extended to WFKCA2, which has been demonstrated as a useful tool for clustering incomplete data. Numerical examples demonstrate the effectiveness of the new WFKCA algorithm     

基于递阶分解聚类的非线性系统递推模糊辨识

提出一种基于递阶分解聚类的递推模糊辨识方法．采用半模糊化方法对论域内的样本进行归类,根据各子集“线性化”程度评判模糊聚类的有效性,通过对性能最差的子集进行分解并辨识新增子模型的参数,逐步完成整个样本空间的模糊划分和模型辨识过程．在线辨识时采用递推最小二乘算法对模糊规则进行修正,同时可根据建模精度的要求删除性能最差的规则,并确立新模糊规则．仿真研究表明了该方法的有效性．     

Data-driven fuzzy modeling for Takagi-Sugeno-Kang fuzzy system

This paper presents a systematic approach to design first order Tagaki-Sugeno-Kang (TSK) fuzzy systems. This approach attempts to obtain the fuzzy rules without any assumption about the structure of the data. The structure identification and parameter optimization steps in this approach are carried out automatically, and are capable of finding the optimal number of the rules with an acceptable accuracy. Starting with an initial structure, the system first tries to improve the structure and, then, as soon as an improved structure is found, it fine tunes its rules’ parameters. Then, it goes back to improve the structure again to find a better structure and re-fine tune the rules’ parameters. This loop continues until a satisfactory solution (TSK model) is found. The proposed approach has successfully been applied to well-known benchmark datasets and real-world problems. The obtained results are compared with those obtained with other methods from the literature. Experimental studies demonstrate that the predicted properties have a good agreement with the measured data by using the elicited fuzzy model with a small number of rules. Finally, as a case study, the proposed approach is applied to the desulfurization process of a real steel industry. Comparing the proposed approach with some other fuzzy systems and neural networks, it is shown that the developed TSK fuzzy system exhibits better results with higher accuracy and smaller size of architecture.     

Multi-objective genetic algorithms based automated clustering for fuzzy association rules mining

Researchers realized the importance of integrating fuzziness into association rules mining in databases with binary and quantitative attributes. However, most of the earlier algorithms proposed for fuzzy association rules mining either assume that fuzzy sets are given or employ a clustering algorithm, like CURE, to decide on fuzzy sets; for both cases the number of fuzzy sets is pre-specified. In this paper, we propose an automated method to decide on the number of fuzzy sets and for the autonomous mining of both fuzzy sets and fuzzy association rules. We achieve this by developing an automated clustering method based on multi-objective Genetic Algorithms (GA); the aim of the proposed approach is to automatically cluster values of a quantitative attribute in order to obtain large number of large itemsets in less time. We compare the proposed multi-objective GA based approach with two other approaches, namely: 1) CURE-based approach, which is known as one of the most efficient clustering algorithms; 2) Chien et al. clustering approach, which is an automatic interval partition method based on variation of density. Experimental results on 100 K transactions extracted from the adult data of USA census in year 2000 showed that the proposed automated clustering method exhibits good performance over both CURE-based approach and Chien et al.’s work in terms of runtime, number of large itemsets and number of association rules.     

基于改进最短邻聚类的最优模糊在线辨识

提出了一种改进的最短邻聚类算法。以输入输出空间为参考,依平均值法实时调整聚类中心,并结合能量函数判据,实现了模糊规则的增加,修改和删除,并保证模糊规则集的优良性。采用最优模糊辨识系统,作为离散时间非线性动态系统的自适应模糊控制器的基本组成单元,实现模型结构和参数的在线辨识及实时更新。仿真结果表明,基于该方法辨识的模糊系统结构简单,规则少,精度高,泛化性好。     

国外先进数据挖掘工具的比较分析

近年来，国外陆续推出了一些先进的数据挖掘工具。国内也在不断地引入这些数据挖掘工具。随着数据挖掘工具的不断涌现，如何选择适合企业自身特定需要的数据挖掘工具，已成为企业引入数据挖掘技术的一大难题。文章在简要概述数据挖掘技术背景的基础上，从企业应用的角度，全面详细地比较分析了当前国外先进的数据挖掘工具。     

基于粗糙-模糊推理系统的化工过程建模研究

根据粗糙集方法所导出的规则构造模糊—神经网络,由规则的参数和离散化结果估计网络参数的初始值,使网络经训练能较快收敛并达到最优值。将其应用于PTA装置溶剂脱水塔精馏过程建模,所建模型的性能优于普通前馈神经网络,粗糙—模糊神经网络可以消除决策系统的冗余信息,降低模型复杂度。     

New dynamic fuzzy structure and dynamic system identification

In this study, a new fuzzy system structure that reduces the number of inputs is proposed for dynamic system identification applications. Algebraic fuzzy systems have some disadvantages due to many inputs. As the number of inputs increase, the number of parameters in the training process increase and hence the classical fuzzy system becomes more complex. In the conventional fuzzy system structure, the past information of both inputs and outputs are also regarded as inputs for dynamic systems, therefore the number of inputs may not be manageable even for single input and single output systems. The new dynamic fuzzy system module (DFM) proposed here has only a single input and a single output. We have carried out identification simulations to test the proposed approach and shown that the DFM can successfully identify non-linear dynamic systems and it performs better than the classical fuzzy system.     

Identification of overlapping and non-overlapping community structure by fuzzy clustering in complex networks

This paper proposes a novel method based on fuzzy clustering to detect community structure in complex networks. In contrast to previous studies, our method does not focus on a graph model, but rather on a fuzzy relation model, which uses the operations of fuzzy relation to replace a traversal search of the graph for identifying community structure. In our method, we first use a fuzzy relation to describe the relation between vertices as well as the similarity in network topology to determine the membership grade of the relation. Then, we transform this fuzzy relation into a fuzzy equivalence relation. Finally, we map the non-overlapping communities as equivalence classes that satisfy a certain equivalence relation. Because most real-world networks are made of overlapping communities (e.g., in social networks, people may belong to multiple communities), we can consider the equivalence classes above as the skeletons of overlapping communities and extend our method by adding vertices to the skeletons to identify overlapping communities. We evaluated our method on artificial networks with built-in communities and real-world networks with known and unknown communities. The experimental results show that our method works well for detecting these communities and gives a new understanding of network division and community formation.     

Online mining of fuzzy multidimensional weighted association rules

This paper addresses the integration of fuzziness with On-Line Analytical Processing (OLAP) based association rules mining. It contributes to the ongoing research on multidimensional online association rules mining by proposing a general architecture that utilizes a fuzzy data cube for knowledge discovery. A data cube is mainly constructed to provide users with the flexibility to view data from different perspectives as some dimensions of the cube contain multiple levels of abstraction. The first step of the process described in this paper involves introducing fuzzy data cube as a remedy to the problem of handling quantitative values of dimensional attributes in a cube. This facilitates the online mining of fuzzy association rules at different levels within the constructed fuzzy data cube. Then, we investigate combining the concepts of weight and multiple-level to mine fuzzy weighted multi-cross-level association rules from the constructed fuzzy data cube. For this purpose, three different methods are introduced for single dimension, multidimensional and hybrid (integrates the other two methods) fuzzy weighted association rules mining. Each of the three methods utilizes a fuzzy data cube constructed to suite the particular method. To the best of our knowledge, this is the first effort in this direction. We compared the proposed approach to an existing approach that does not utilize fuzziness. Experimental results obtained for each of the three methods on a synthetic dataset and on the adult data of the United States census in year 2000 demonstrate the effectiveness and applicability of the proposed fuzzy OLAP based mining approach. OLAP is one of the most popular tools for on-line, fast and effective multidimensional data analysis. In the OLAP framework, data is mainly stored in data hypercubes (simply called cubes).     

Mining the change of customer behavior in fuzzy time-interval sequential patterns

Comprehending changes of customer behavior is an essential problem that must be faced for survival in a fast-changing business environment. Particularly in the management of electronic commerce (EC), many companies have developed on-line shopping stores to serve customers and immediately collect buying logs in databases. This trend has led to the development of data-mining applications. Fuzzy time-interval sequential pattern mining is one type of serviceable data-mining technique that discovers customer behavioral patterns over time. To take a shopping example, (Bread, Short, Milk, Long, Jam), means that Bread is bought before Milk in a Short period, and Jam is bought after Milk in a Long period, where Short and Long are predetermined linguistic terms given by managers. This information shown in this example reveals more general and concise knowledge for managers, allowing them to make quick-response decisions, especially in business. However, no studies, to our knowledge, have yet to address the issue of changes in fuzzy time-interval sequential patterns. The fuzzy time-interval sequential pattern, (Bread, Short, Milk, Long, Jam), became available in last year; however, is not a trend this year, and has been substituted by (Bread, Short, Yogurt, Short, Jam). Without updating this knowledge, managers might map out inappropriate marketing plans for products or services and dated inventory strategies with respect to time-intervals. To deal with this problem, we propose a novel change mining model, MineFuzzChange, to detect the change in fuzzy time-interval sequential patterns. Using a brick-and-mortar transactional dataset collected from a retail chain in Taiwan and a B2C EC dataset, experiments are carried out to evaluate the proposed model. We empirically demonstrate how the model helps managers to understand the changing behaviors of their customers and to formulate timely marketing and inventory strategies.     

Process bottlenecks identification and its root cause analysis using fusion-based clustering and knowledge graph

Drawing the strengths of data science and machine learning, process mining has recently emerged as an effective research approach for process management and its decision support. Bottleneck identification and analysis is a key problem in process mining which is considered a critical component for process improvement. While previous studies focusing on bottlenecks have been reported, visible gaps remain. Most of these studies considered bottleneck identification from local perspectives by quantitative metrics, such as machine operation and resource requirement, which can not be applied to knowledge-intensive processes. Moreover, the root cause of such bottlenecks has not been given enough attention, which limits the impact of process optimisation. This paper proposes an approach that utilises fusion-based clustering and hyperbolic neural network-based knowledge graph embedding for bottleneck identification and root cause analysis. Firstly, a fusion-based clustering is proposed to identify bottlenecks automatically from a global perspective, where the execution frequency of each stage at different periods is calculated to reveal the abnormal stage. Secondly, a process knowledge graph representing tasks, organisations, workforce and relation features as hierarchical and logical patterns is established. Finally, a hyperbolic cluster-based community detection mechanism is researched, based on the process knowledge graph embedding trained by a hyperbolic neural network, to analyse the root cause from a process perspective. Experimental studies using real-world data collected from a multidisciplinary design project revealed the merits of the proposed approach. The execution of the proposed approach is not limited to event logs; it can automatically identify bottlenecks without local quantitative metrics and analyse the causes from a process perspective.     

基于聚类和SVD算法的模糊逻辑系统结构辨识

为了研究模糊逻辑系统新的结构辨识方法, 提出采用基于山峰函数的减法聚类算法构造模糊逻辑系统的初始结构, 并利用奇异值分解(SVD)算法分析了模糊规则与奇异值、累积贡献率以及索引向量的关系, 从而实现了模糊逻辑结构的优化. 最后, 对该算法的可行性和有效性进行了仿真验证和性能比较, 取得了较好的效果.     

Data reconstruction with information granules: An augmented method of fuzzy clustering

Information granules form an abstract and efficient characterization of large volumes of numeric data. Fuzzy clustering is a commonly encountered information granulation approach. A reconstruction (degranulation) is about decoding information granules into numeric data. In this study, to enhance quality of reconstruction, we augment the generic data reconstruction approach by introducing a transformation mapping of the originally produced partition matrix and setting up an adjustment mechanism modifying a localization of the prototypes. We engage several population-based search algorithms to optimize interaction matrices and prototypes. A series of experimental results dealing with both synthetic and publicly available data sets are reported to show the enhancement of the data reconstruction performance provided by the proposed method.     

Ellipsoids and ellipsoid-shaped fuzzy sets as natural multi-variate generalization of intervals and fuzzy numbers: How to elicit them from users, and how to use them in data processing

In this paper, we show that ellipsoids are natural multi-variate generalization of intervals and ellipsoid-shaped fuzzy sets are a natural generalization of fuzzy numbers. We explain how to elicit them from users, and how to use them in data processing.     

An ACS-based framework for fuzzy data mining

Data mining is often used to find out interesting and meaningful patterns from huge databases. It may generate different kinds of knowledge such as classification rules, clusters, association rules, and among others. A lot of researches have been proposed about data mining and most of them focused on mining from binary-valued data. Fuzzy data mining was thus proposed to discover fuzzy knowledge from linguistic or quantitative data. Recently, ant colony systems (ACS) have been successfully applied to optimization problems. However, few works have been done on applying ACS to fuzzy data mining. This thesis thus attempts to propose an ACS-based framework for fuzzy data mining. In the framework, the membership functions are first encoded into binary-bits and then fed into the ACS to search for the optimal set of membership functions. The problem is then transformed into a multi-stage graph, with each route representing a possible set of membership functions. When the termination condition is reached, the best membership function set (with the highest fitness value) can then be used to mine fuzzy association rules from a database. At last, experiments are made to make a comparison with other approaches and show the performance of the proposed framework.     

A fuzzy PID thermal control system for casting dies

In high-pressure die casting processes, proper control of die temperature is essential for producing superior quality components and yielding high production rates. However, die temperature distribution depends on various die design and process variables for which accurate models are normally very difficult to obtain. In this paper, a new intelligent control scheme is proposed for die thermal management. In this scheme, extra cooling waterlines controlled by a pump and solenoid valves are attached to the established cooling channels. A fuzzy PID controller is designed to minimize the temperature differences between channels. The experimental results obtained from a laboratory die casting process simulator indicate that the developed control system is capable of adjusting the desirable supply of cooling water into multiple cooling lines. Hence, the local temperature distribution of the die insert may become more homogeneous.