The existence of large volumes of time series data in many applications has motivated data miners to investigate specialized methods for mining time series data. Clustering is a popular data mining method due to its powerful exploratory nature and its usefulness as a preprocessing step for other data mining techniques. This article develops two novel clustering algorithms for time series data that are extensions of a crisp c-shapes algorithm. The two new algorithms are heuristic derivatives of fuzzy c-means (FCM). Fuzzy c-Shapes plus (FCS+) replaces the inner product norm in the FCM model with a shape-based distance function. Fuzzy c-Shapes double plus (FCS++) uses the shape-based distance, and also replaces the FCM cluster centers with shape-extracted prototypes. Numerical experiments on 48 real time series data sets show that the two new algorithms outperform state-of-the-art shape-based clustering algorithms in terms of accuracy and efficiency. Four external cluster validity indices (the Rand index, Adjusted Rand Index, Variation of Information, and Normalized Mutual Information) are used to match candidate partitions generated by each of the studied algorithms. All four indices agree that for these finite waveform data sets, FCS++ gives a small improvement over FCS+, and in turn, FCS+ is better than the original crisp c-shapes method. Finally, we apply two tests of statistical significance to the three algorithms. The Wilcoxon and Friedman statistics both rank the three algorithms in exactly the same way as the four cluster validity indices.
Jiangnan University（江南大学）；Hong Kong Polytechnic University（香港理工大学）；Osaka Prefecture University（大阪府立大学）
The traditional prototype based clustering methods, such as the well-known fuzzy c-mean (FCM) algorithm, usually need sufficient data to find a good clustering partition. If the available data is limited or scarce, most of the existing prototype based clustering algorithms will no longer be effective. While the data for the current clustering task may be scarce, there is usually some useful knowledge available in the related scenes/domains. In this study, the concept of transfer learning is applied to prototype based fuzzy clustering (PFC). Specifically, the idea of leveraging knowledge from t…
Inner Mongolia University（内蒙古大学）；Jilin University（吉林大学）；Beijing University of Technology（北京工业大学）；Hainan University（海南大学）
In semi-supervised fuzzy clustering, this paper extends the traditional pairwise constraint (i.e., must-link or cannot-link) to fuzzy pairwise constraint. The fuzzy pairwise constraint allows a supervisor to provide the grade of similarity or dissimilarity between the implicit fuzzy vectors of a pair of samples. This constraint can present more complicated relationship between the pair of samples and avoid eliminating the fuzzy characteristics. We propose a fuzzy discriminant clustering model (FDC) to fuse the fuzzy pairwise constraints. The nonconvex optimization problem in our FDC is solved …
The purpose of this paper is to study the algorithm FCM and some of its famous innovations, analyse and discover the method of applying hedge algebra theory that uses algebra to represent linguistic-valued variables, to FCM. Then, this paper will propose a new FCM-based algorithm which uses hedge algebra to model FCM's exponent parameter. Finally, the design, analysis and implementation of the new algorithm as well some experimental results will be presented to prove our algorithm's capacity of solving clustering problems in practice.
Central China Normal University（华中师范大学）；Kharkiv National University of Radio Electronics（哈尔科夫国立无线电电子大学）
A task of clustering data given in the ordinal scale under conditions of overlapping clusters has been considered. It's proposed to use an approach based on memberhsip and likelihood functions sharing. A number of performed experiments proved effectiveness of the proposed method. The proposed method is characterized by robustness to outliers due to a way of ordering values while constructing membership functions.
West Bengal University of Technology（西孟加拉邦理工大学）；Pailan College of Management & Technology（派兰管理与技术学院）
This paper presents a new hybrid Fuzzy-ART based K-Means Clustering technique to solve the part machine grouping problem in cellular manufacturing systems considering operational time. The performance of the proposed technique is tested with problems from open literature and the results are compared to the existing clustering models such as simple K-means algorithm and modified ART1 algorithm using an efficient modified performance measure known as modified grouping efficiency (MGE) as found in the literature. The results support the better performance of the proposed algorithm. The Novelty of…
Imam Abdulrahman Bin Faisal University（伊玛目阿卜杜勒拉赫曼·本·费萨尔大学）
Fuzzy clustering is a famous unsupervised learning method used to collecting similar data elements within cluster according to some similarity measurement. But, clustering algorithms suffer from some drawbacks. Among the main weakness including, selecting the initial cluster centres and the appropriate clusters number is normally unknown. These weaknesses are considered the most challenging tasks in clustering algorithms. This paper introduces a comprehensive review of metahueristic search to solve fuzzy clustering algorithms problems.
Federated Learning (FL) is a setting where multiple parties with distributed data collaborate in training a joint Machine Learning (ML) model while keeping all data local at the parties. Federated clustering is an area of research within FL that is concerned with grouping together data that is globally similar while keeping all data local. We describe how this area of research can be of interest in itself, or how it helps addressing issues like non-independently-identically-distributed (i.i.d.) data in supervised FL frameworks. The focus of this work, however, is an extension of the federated …
Xidian University（西安电子科技大学）；University of Alberta（阿尔伯塔大学）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；King Abdulaziz University（阿卜杜勒阿齐兹国王大学）
Fuzzy C-Means (FCM) is a widely used clustering method. However, FCM and its many accelerated variants have low efficiency in the mid-to-late stage of the clustering process. In this stage, all samples are involved in the update of their non-affinity centers, and the fuzzy membership grades of the most of samples, whose assignment is unchanged, are still updated by calculating the samples-centers distances. All those lead to the algorithms converging slowly. In this paper, a new affinity filtering technique is developed to recognize a complete set of the non-affinity centers for each sample wi…
Huazhong University of Science and Technology（华中科技大学）；Shandong University of Finance and Economics（山东财经大学）
Fuzzy c-means based clustering algorithms are frequently used for Takagi-Sugeno-Kang (TSK) fuzzy classifier antecedent parameter estimation. One rule is initialized from each cluster. However, most of these clustering algorithms are unsupervised, which waste valuable label information in the training data. This paper proposes a supervised enhanced soft subspace clustering (SESSC) algorithm, which considers simultaneously the within-cluster compactness, between-cluster separation, and label information in clustering. It can effectively deal with high-dimensional data, be used as a classifier al…
University of Michigan – Ann Arbor（密歇根大学安娜堡分校）；University of Missouri – Rolla（密苏里大学罗拉分校）；GE Global Research（通用电气全球研究中心）
In this paper, we describe an algorithm FARDiff (Fuzzy Adaptive Resonance Dif- fusion) which combines Diffusion Maps and Fuzzy Adaptive Resonance Theory to do clustering on high dimensional data. We describe some applications of this method and some problems for future research.
Universidade Federal de Pernambuco（伯南布哥联邦大学）；Centro de Informática（信息中心）
The clustering methods have been used in a variety of fields such as image processing, data mining, pattern recognition, and statistical analysis. Generally, the clustering algorithms consider all variables equally relevant or not correlated for the clustering task. Nevertheless, in real situations, some variables can be correlated or may be more or less relevant or even irrelevant for this task. This paper proposes partitioning fuzzy clustering algorithms based on Euclidean, City-block and Mahalanobis distances and entropy regularization. These methods are an iterative three steps algorithms …
In recent years, the problem of fuzzy clustering has been widely concerned. The membership iteration of existing methods is mostly considered globally, which has considerable problems in noisy environments, and iterative calculations for clusters with a large number of different sample sizes are not accurate and efficient. In this paper, starting from the strategy of large-scale priority, the data is fuzzy iterated using granular-balls, and the membership degree of data only considers the two granular-balls where it is located, thus improving the efficiency of iteration. The formed fuzzy granu…
Singapore-MIT Alliance（新加坡-麻省理工学院联盟）；Nanyang Technological University（南洋理工大学）；National University of Singapore（新加坡国立大学）
In this paper, a similarity-driven cluster merging method is proposed for unsuper-vised fuzzy clustering. The cluster merging method is used to resolve the problem of cluster validation. Starting with an overspecified number of clusters in the data, pairs of similar clusters are merged based on the proposed similarity-driven cluster merging criterion. The similarity between clusters is calculated by a fuzzy cluster similarity matrix, while an adaptive threshold is used for merging. In addition, a modified generalized ob- jective function is used for prototype-based fuzzy clustering. The functi…
With the membership function being strictly positive, the conventional fuzzy c-means clustering method sometimes causes imbalanced influence when clusters of vastly different sizes exist. That is, an outstandingly large cluster drags to its center all the other clusters, however far they are separated. To solve this problem, we propose a hybrid fuzzy-crisp clustering algorithm based on a target function combining linear and quadratic terms of the membership function. In this algorithm, the membership of a data point to a cluster is automatically set to exactly zero if the data point is ``suffi…
Huazhong University of Science and Technology（华中科技大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
To effectively optimize Takagi-Sugeno-Kang (TSK) fuzzy systems for regression problems, a mini-batch gradient descent with regularization, DropRule, and AdaBound (MBGD-RDA) algorithm was recently proposed. This paper further proposes FCM-RDpA, which improves MBGD-RDA by replacing the grid partition approach in rule initialization by fuzzy c-means clustering, and AdaBound by Powerball AdaBelief, which integrates recently proposed Powerball gradient and AdaBelief to further expedite and stabilize parameter optimization. Extensive experiments on 22 regression datasets with various sizes and dimen…
Higher Institution of Technology（高等技术学院）；Benha University（本哈大学）
This paper introduces an evaluation methodologies for the e-learners' behaviour that will be a feedback to the decision makers in e-learning system. Learner's profile plays a crucial role in the evaluation process to improve the e-learning process performance. The work focuses on the clustering of the e-learners based on their behaviour into specific categories that represent the learner's profiles. The learners' classes named as regular, workers, casual, bad, and absent. The work may answer the question of how to return bad students to be regular ones. The work presented the use of different …
Clustering data is a popular feature in the field of unsupervised machine learning. Most algorithms aim to find the best method to extract consistent clusters of data, but very few of them intend to cluster data that share the same intersections between two features or more. This paper proposes a method to do so. The main idea of this novel method is to generate fuzzy clusters of data using a Fuzzy C-Means (FCM) algorithm. The second part involves applying a filter that selects a range of minimum and maximum membership values, emphasizing the border data. A μ parameter defines the amplitude of…
In data dominated systems and applications, a concept of representing words in a numerical format has gained a lot of attention. There are a few approaches used to generate such a representation. An interesting issue that should be considered is the ability of such representations - called embeddings - to imitate human-based semantic similarity between words. In this study, we perform a fuzzy-based analysis of vector representations of words, i.e., word embeddings. We use two popular fuzzy clustering algorithms on count-based word embeddings, known as GloVe, of different dimensionality. Words …
International University of Business Agriculture and Technology（国际商业农业与技术大学）；Mississippi State University（密西西比州立大学）；Rajshahi College（拉杰沙希学院）
In this paper, several two-dimensional clustering scenarios are given. In those scenarios, soft partitioning clustering algorithms (Fuzzy C-means (FCM) and Possibilistic c-means (PCM)) are applied. Afterward, VAT is used to investigate the clustering tendency visually, and then in order of checking cluster validation, three types of indices (e.g., PC, DI, and DBI) were used. After observing the clustering algorithms, it was evident that each of them has its limitations; however, PCM is more robust to noise than FCM as in case of FCM a noise point has to be considered as a member of any of the …
Data mining techniques can be used to discover useful patterns by exploring and analyzing data and it's feasible to synergitically combine machine learning tools to discover fuzzy classification rules.In this paper, an adaptive Neuro fuzzy network with TSK fuzzy type and an improved quantum subtractive clustering has been developed. Quantum clustering (QC) is an intuition from quantum mechanics which uses Schrodinger potential and time-consuming gradient descent method. The principle advantage and shortcoming of QC is analyzed and based on its shortcomings, an improved algorithm through a subt…
Federal University of Lavras (UFLA)（拉夫拉斯联邦大学（UFLA））
Time-varying classifiers, namely, evolving classifiers, play an important role in a scenario in which information is available as a never-ending online data stream. We present a new unsupervised learning method for numerical data called evolving Internal-eXternal Fuzzy clustering method (Fuzzy eIX). We develop the notion of double-boundary fuzzy granules and elaborate on its implications. Type 1 and type 2 fuzzy inference systems can be obtained from the projection of Fuzzy eIX granules. We perform the principle of the balanced information granularity within Fuzzy eIX classifiers to achieve a …
Costa Rica Institute of Technology（哥斯达黎加理工学院）；CIMPA（国际纯粹与应用数学中心）；University of Costa Rica（哥斯达黎加大学）；Universidade Federal de Rio de Janeiro（里约热内卢联邦大学）
We propose a novel method for building fuzzy clusters of large data sets, using a smoothing numerical approach. The usual sum-of-squares criterion is relaxed so the search for good fuzzy partitions is made on a continuous space, rather than a combinatorial space as in classical methods \cite{Hartigan}. The smoothing allows a conversion from a strongly non-differentiable problem into differentiable subproblems of optimization without constraints of low dimension, by using a differentiable function of infinite class. For the implementation of the algorithm we used the statistical software $R$ an…
Changes in the UK electricity market mean that domestic users will be required to modify their usage behaviour in order that supplies can be maintained. Clustering allows usage profiles collected at the household level to be clustered into groups and assigned a stereotypical profile which can be used to target marketing campaigns. Fuzzy C Means clustering extends this by allowing each household to be a member of many groups and hence provides the opportunity to make personalised offers to the household dependent on their degree of membership of each group. In addition, feedback can be provided…
Boston University（波士顿大学）；University of Toronto（多伦多大学）；Amirkabir University of Technology（阿米尔卡比尔理工大学）
Both FCM and PCM clustering methods have been widely applied to pattern recognition and data clustering. Nevertheless, FCM is sensitive to noise and PCM occasionally generates coincident clusters. PFCM is an extension of the PCM model by combining FCM and PCM, but this method still suffers from the weaknesses of PCM and FCM. In the current paper, the weaknesses of the PFCM algorithm are corrected and the enhanced possibilistic fuzzy c-means (EPFCM) clustering algorithm is presented. EPFCM can still be sensitive to noise. Therefore, we propose an interval type-2 enhanced possibilistic fuzzy c-m…
Clustering is one of the widely used data mining techniques for medical diagnosis. Clustering can be considered as the most important unsupervised learning technique. Most of the clustering methods group data based on distance and few methods cluster data based on similarity. The clustering algorithms classify gene expression data into clusters and the functionally related genes are grouped together in an efficient manner. The groupings are constructed such that the degree of relationship is strong among members of the same cluster and weak among members of different clusters. In this work, we…
University of Southampton（南安普顿大学）；University of Oxford（牛津大学）；Harvard University（哈佛大学）；University of Warwick（华威大学）
Persistence diagrams concisely represent the topology of a point cloud whilst having strong theoretical guarantees, but the question of how to best integrate this information into machine learning workflows remains open. In this paper we extend the ubiquitous Fuzzy c-Means (FCM) clustering algorithm to the space of persistence diagrams, enabling unsupervised learning that automatically captures the topological structure of data without the topological prior knowledge or additional processing of persistence diagrams that many other techniques require. We give theoretical convergence guarantees …
Sleep apnea is a disorder that has serious consequences for the pediatric population. There has been recent concern that traditional diagnosis of the disorder using the apnea-hypopnea index may be ineffective in capturing its multi-faceted outcomes. In this work, we take a first step in addressing this issue by phenotyping patients using a clustering analysis of airflow time series. This is approached in three ways: using feature-based fuzzy clustering in the time and frequency domains, and using persistent homology to study the signal from a topological perspective. The fuzzy clusters are ana…
College of Information and Communications University of South Carolina（南卡罗来纳大学信息与通信学院）；Arnold School of Public Health at the University of South Carolina（南卡罗来纳大学阿诺德公共卫生学院）
Large textual corpora are often represented by the document-term frequency matrix whose elements are the frequency of terms; however, this matrix has two problems: sparsity and high dimensionality. Four dimension reduction strategies are used to address these problems. Of the four strategies, unsupervised feature transformation (UFT) is a popular and efficient strategy to map the terms to a new basis in the document-term frequency matrix. Although several UFT-based methods have been developed, fuzzy clustering has not been considered for dimensionality reduction. This research explores fuzzy c…
The University of Melbourne（墨尔本大学）；University of New South Wales Canberra（新南威尔士大学堪培拉分校）
A rainfall-runoff model predicts surface runoff either using a physically-based approach or using a systems-based approach. Takagi-Sugeno (TS) Fuzzy models are systems-based approaches and a popular modeling choice for hydrologists in recent decades due to several advantages and improved accuracy in prediction over other existing models. In this paper, we propose a new rainfall-runoff model developed using Gustafson-Kessel (GK) clustering-based TS Fuzzy model. We present comparative performance measures of GK algorithms with two other clustering algorithms: (i) Fuzzy C-Means (FCM), and (ii)Sub…
School of Wangzheng Microelectronics, Changzhou University（常州大学王正微电子学院）；School of Electrical Engineering and Automation, Changshu Institute of Technology（常熟理工学院电气与自动化工程学院）
School of Digital Media, Jiangnan University（江南大学数字媒体学院）；Jiangsu Key Laboratory of Digital Design and Software Technology（江苏省数字设计与软件技术重点实验室）
As the multi-view data grows in the real world, multi-view clus-tering has become a prominent technique in data mining, pattern recognition, and machine learning. How to exploit the relation-ship between different views effectively using the characteristic of multi-view data has become a crucial challenge. Aiming at this, a hidden space sharing multi-view fuzzy clustering (HSS-MVFC) method is proposed in the present study. This method is based on the classical fuzzy c-means clustering model, and obtains associ-ated information between different views by introducing shared hidden space. Especia…
Indian Institute of Technology-Kharagpur（印度理工学院卡尔哈普尔分校）；VIT University（VIT大学）
Fuzzy logic deals with degrees of truth. In this paper, we have shown how to apply fuzzy logic in text mining in order to perform document clustering. We took an example of document clustering where the documents had to be clustered into two categories. The method involved cleaning up the text and stemming of words. Then, we chose m number of features which differ significantly in their word frequencies (WF), normalized by document length, between documents belonging to these two clusters. The documents to be clustered were represented as a collection of m normalized WF values. Fuzzy c-means (…
Efficient Anti-exploration via VQVAE and Fuzzy Clustering in Offline Reinforcement Learning
State Key Laboratory of Multimodal Artificial Intelligence Systems（多模态人工智能系统国家重点实验室）；State Key Laboratory of Management and Control for Complex Systems（复杂系统管理与控制国家重点实验室）；Chinese Academy of Sciences（中国科学院）；WAYTOUS Inc.（WAYTOUS公司）；Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ)（广东人工智能与数字经济实验室（深圳））；Institute of Artificial Intelligence and Robotics（人工智能与机器人研究院）；Xi’an Jiaotong University（西安交通大学）；School of Artificial Intelligence（人工智能学院）；Key Laboratory of Intelligent Sensing System and Security (Hubei University)（智能感知系统与安全重点实验室（湖北大学））；Ministry of Education（教育部）；Department of Electrical and Computer Engineering（电气与计算机工程系）
Fuzzy clustering of ordinal time series based on two novel distances with economic applications
Research Center for Information and Communication Technologies (CITIC)（信息与通信技术研究中心（CITIC））；University of A Coruña（拉科鲁尼亚大学）；Helmut Schmidt University（赫尔穆特·施密特大学）
Institute for Infocomm Research, A*STAR（新加坡科技研究局资讯通信研究院）；Nanyang Technological University（南洋理工大学）
Multi-view data clustering refers to categorizing a data set by making good use of related information from multiple representations of the data. It becomes important nowadays because more and more data can be collected in a variety of ways, in different settings and from different sources, so each data set can be represented by different sets of features to form different views of it. Many approaches have been proposed to improve clustering performance by exploring and integrating heterogeneous information underlying different views. In this paper, we propose a new multi-view fuzzy clustering…
Jiangnan University（江南大学）；The Hong Kong Polytechnic University（香港理工大学）
The superior interpretability and uncertainty modeling ability of Takagi-Sugeno-Kang fuzzy system (TSK FS) make it possible to describe complex nonlinear systems intuitively and efficiently. However, classical TSK FS usually adopts the whole feature space of the data for model construction, which can result in lengthy rules for high-dimensional data and lead to degeneration in interpretability. Furthermore, for highly nonlinear modeling task, it is usually necessary to use a large number of rules which further weakens the clarity and interpretability of TSK FS. To address these issues, a conci…
Institute for Infocomm Research, A*STAR（新加坡科技研究局资讯通信研究院）；Nanyang Technological University（南洋理工大学）
Incremental clustering approaches have been proposed for handling large data when given data set is too large to be stored. The key idea of these approaches is to find representatives to represent each cluster in each data chunk and final data analysis is carried out based on those identified representatives from all the chunks. However, most of the incremental approaches are used for single view data. As large multi-view data generated from multiple sources becomes prevalent nowadays, there is a need for incremental clustering approaches to handle both large and multi-view data. In this paper…
In some complicated datasets, due to the presence of noisy data points and outliers, cluster validity indices can give conflicting results in determining the optimal number of clusters. This paper presents a new validity index for fuzzy-possibilistic c-means clustering called Fuzzy-Possibilistic (FP) index, which works well in the presence of clusters that vary in shape and density. Moreover, FPCM like most of the clustering algorithms is susceptible to some initial parameters. In this regard, in addition to the number of clusters, FPCM requires a priori selection of the degree of fuzziness an…
National Observatory of Athens（雅典国家天文台）；National Technical University of Athens（雅典国立技术大学）
Crop phenology is crucial information for crop yield estimation and agricultural management. Traditionally, phenology has been observed from the ground; however Earth observation, weather and soil data have been used to capture the physiological growth of crops. In this work, we propose a new approach for the within-season phenology estimation for cotton at the field level. For this, we exploit a variety of Earth observation vegetation indices (derived from Sentinel-2) and numerical simulations of atmospheric and soil parameters. Our method is unsupervised to address the ever-present problem o…
Tel Aviv University（特拉维夫大学）；University of California, San Diego（加利福尼亚大学圣迭戈分校）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
The fuzzy or soft $k$-means objective is a popular generalization of the well-known $k$-means problem, extending the clustering capability of the $k$-means to datasets that are uncertain, vague, and otherwise hard to cluster. In this paper, we propose a semi-supervised active clustering framework, where the learner is allowed to interact with an oracle (domain expert), asking for the similarity between a certain set of chosen items. We study the query and computational complexities of clustering in this framework. We prove that having a few of such similarity queries enables one to get a polyn…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
Like k-means and Gaussian Mixture Model (GMM), fuzzy c-means (FCM) with soft partition has also become a popular clustering algorithm and still is extensively studied. However, these algorithms and their variants still suffer from some difficulties such as determination of the optimal number of clusters which is a key factor for clustering quality. A common approach for overcoming this difficulty is to use the trial-and-validation strategy, i.e., traversing every integer from large number like $\sqrt{n}$ to 2 until finding the optimal number corresponding to the peak value of some cluster vali…
Huazhong University of Science and Technology（华中科技大学）
This paper presents PyTSK, a Python toolbox for developing Takagi-Sugeno-Kang (TSK) fuzzy systems. Based on scikit-learn and PyTorch, PyTSK allows users to optimize TSK fuzzy systems using fuzzy clustering or mini-batch gradient descent (MBGD) based algorithms. Several state-of-the-art MBGD-based optimization algorithms are implemented in the toolbox, which can improve the generalization performance of TSK fuzzy systems, especially for big data applications. PyTSK can also be easily extended and customized for more complicated algorithms, such as modifying the structure of TSK fuzzy systems, d…
Université de Lyon（里昂大学）；ERIC EA 3083；ArAr UMR 5138
Clustering is an extensive research area in data science. The aim of clustering is to discover groups and to identify interesting patterns in datasets. Crisp (hard) clustering considers that each data point belongs to one and only one cluster. However, it is inadequate as some data points may belong to several clusters, as is the case in text categorization. Thus, we need more flexible clustering. Fuzzy clustering methods, where each data point can belong to several clusters, are an interesting alternative. Yet, seeding iterative fuzzy algorithms to achieve high quality clustering is an issue.…
The identification of co-regulated genes and their transcription-factor binding sites (TFBS) are the key steps toward understanding transcription regulation. In addition to effective laboratory assays, various bi-clustering algorithms for detection of the co-expressed genes have been developed. Bi-clustering methods are used to discover subgroups of genes with similar expression patterns under to-be-identified subsets of experimental conditions when applied to gene expression data. By building two fuzzy partition matrices of the gene expression data with the Axiomatic Fuzzy Set (AFS) theory, t…
Pemalang District Government（北加浪安区政府）；Universitas Muhammadiyah Semarang（三宝垄穆罕默迪亚大学）
Clustering is one of the major roles in data mining that is widely application in pattern recognition and image segmentation. Fuzzy C-means (FCM) is the most used clustering algorithm that proven efficient, fast and easy to implement, however, FCM uses the Euclidean distance that often leads to clustering errors, especially when handling multidimensional and noisy data. In the last few years, many distances metric have been proposed by researchers to improve the performance of the FCM algorithms, and the majority of researchers propose weighted distance. In this paper, we proposed Canberra Wei…
