fuzzy clustering
در نشریات گروه ریاضی-
Semi-supervised clustering, utilizing the supervision information to guide the clustering process, could improve the clustering effect of the models. Most of existing semi-supervised clustering models only consider pairwise constraints or pointwise constraints. In this paper, the semi-supervised method is applied to the fuzzy clustering algorithm, and a robust semi-supervised fuzzy clustering algorithm is proposed. Firstly, fully considering prior knowledge, our models integrate pointwise constraints and pairwise constraints into a unified framework to improve the clustering performance of the fuzzy clustering algorithm. Secondly, in order to alleviate the impact of outliers, the robust performance of the models is considered by introducing an adaptive loss function into the models. Thirdly, our models can capture the global structures and the local manifold structures of data sets. Finally, a simple and efficient algorithm is proposed to solve the models, which ensures that the obtained solution is sparse and satisfies the constraint conditions in our models. Compared with five representative methods, experimental results on public datasets, such as text dataset (dbworld), voice dataset (Isolet), image datasets (YALE, Umist), chemical dataset (wine) and biological datasets (colon, TOX-171), show the effectiveness of the proposed models.
Keywords: Semi-Supervised Clustering, Adaptive Loss, Pairwise Constraints, Fuzzy Clustering, Label Information -
International Journal Of Nonlinear Analysis And Applications, Volume:15 Issue: 5, May 2024, PP 177 -187Today, computer network fault diagnosis is one of the key challenges experts are facing in the field of computer networks. Therefore, achieving an automatic diagnosis system which is based on artificial intelligence methods and is able to diagnose faults with maximum accuracy and speed is of high importance. One of the methods which is studied and utilized up to now is artificial neural networks with a back propagation algorithm while using neural networks with a back propagation algorithm has two main challenges in front. The first challenge is related to the backpropagation learning type as it is a supervised learning requiring inductive knowledge driven from previous conditions. The second challenge is the long time required for training such a neural network. In this work, combining neural networks with a backpropagation algorithm and fuzzy logic is applied as a method for confronting these challenges. The result of this study shows that fuzzy clustering is able to provide the inductive knowledge required for backpropagation learning by determining the membership degree of training samples to different clusters of network faults. Also, according to the simulations taken place, implementing a fuzzy controller in determining the learning rate in each backpropagation iteration has resulted in successful outcomes. Thus, the learning speed of this algorithm has been increased in comparison to the constant learning rate mode resulted in reducing the training time duration of this neural networks.Keywords: Computer Networks Fault Diagnosis, Artificial Neural Networks, Back Propagation Algorithm, Fuzzy Clustering, Fuzzy Controller
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Iranian Journal of Numerical Analysis and Optimization, Volume:13 Issue: 4, Autumn 2023, PP 763 -774The fuzzy-C-means (FCM) algorithm is one of the most famous fuzzy clus-tering algorithms, but it gets stuck in local optima. In addition, this algo-rithm requires the number of clusters. Also, the density-based spatial of the application with noise (DBSCAN) algorithm, which is a density-based clus-tering algorithm, unlike the FCM algorithm, should not be pre-numbered. If the clusters are specific and depend on the number of clusters, then it can determine the number of clusters. Another advantage of the DBSCAN clus-tering algorithm over FCM is its ability to cluster data of different shapes. In this paper, in order to overcome these limitations, a hybrid approach for clustering is proposed, which uses FCM and DBSCAN algorithms. In this method, the optimal number of clusters and the optimal location for the centers of the clusters are determined based on the changes that take place according to the data set in three phases by predicting the possibility of the problems stated in the FCM algorithm. With this improvement, the values of none of the initial parameters of the FCM algorithm are random, and in the first phase, it has been tried to replace these random values to the optimal in the FCM algorithm, which has a significant effect on the convergence of the algorithm because it helps to reduce iterations. The proposed method has been examined on the Iris flower and compared the results with basic FCM algorithm and another algorithm. Results shows the better performance of the proposed method.Keywords: Clustering, Fuzzy clustering, DBSCAN
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This study proposes an automatic genetic algorithm in fuzzy cluster analysis for numerical data. In this algorithm, a new measure called the FB index is used as the objective function of the genetic algorithm. In addition, the algorithm not only determines the appropriate number of groups but also improves the steps of traditional genetic algorithm as crossover, mutation and selection operators. The proposed algorithm is shown the step by step throughout the numerical example, and can perform fast by the established Matlab procedure. The result from experiments show the superiority of the proposed algorithm when it overcomes the existing algorithms. Moreover, it has been applied in recognizing the image data, and building the fuzzy time series model. These show the potential of this study for many real applications of the different fields.
Keywords: Fuzzy clustering, genetic algorithm, image recognition, time series -
یکی از پرکاربردترین مدل ها برای رده بندی یا کلاس بندی داده ها که در سال های اخیر مورد توجه بسیاری از پژوهشگران قرار گرفته است، مدل های مخلوط متناهی است. بطور کلی رده بندی به فرایندی گفته می شود که در آن هر یک از مشاهدات به یکی از گروه های مشخص شده تعلق گرفته می شود. گرچه ایده اصلی در مدل های مخلوط بر اساس توزیع نرمال بوده است، اما در سال های اخیر با معرفی توزیع های دیگر مدل های مخلوط بر اساس این توزیع ها مورد توجه بسیاری از محققین بوده است. در مقالات از الگوریتم EM و گسترش های آن برای برآوردیابی استفاده شده است. با این حال این امکان وجود دارد که الگوریتم EM نتایج مناسبی برای کلاس بندی ارایه ندهد، زیرا در این روش هر عضو مشاهدات متعلق به یک کلاس است. این محدودیت باعث استفاده از رویکرد کلاس بندی فازی در این نوع مسایل شد. در این مقاله یک الگوریتم کلاس بندی براساس توزیع مخلوط متناهی آمیخته مقیاسی نرمال ارایه شده است. در این الگوریتم برای کلاس بندی از روش یادگیری فازی $-c$میانگین استفاده شده است. برای بررسی تاثیر مقادیر گمشده بر کلاس بندی داده ها، داده گمشده نیز در نظر گرفته شده است. از ساختار توزیع مخلوط متناهی آمیخته مقیاسی نرمال برای بررسی داده های گمشده و کلاس بندی داده ها استفاده می شود. در انتها نیز با استفاده از مثال واقعی و داده های شبیه سازی شده، مقایسه بین الگوریتم $\text{LB-FCM}$ و $\text{EM}$ صورت می گیرد. از این مقایسه نتیجه شده است که استفاده از این الگوریتم برای کلاس بندی داده ها مناسبتر است.کلید واژگان: بازسازی تصویر، کلاس بندی فازی، توزیع مخلوط متناهی، توزیع مخلوط متناهی امیخته مقیاسی نرمال، داده گمشدهOne of the most widely used models for data clustering, which has been considered by many researchers in recent years, is finite mixture models. Clustering is generally a process in which each observation is assigned to one of the specified groups. Although the main idea in mixture models is based on normal distribution, but in recent years with the introduction of other distributions of mixture models based on these distributions has been considered by many researchers. In the articles, the EM algorithm and its extensions are used for estimation. However, it is possible that the EM algorithm does not provide good results for clustering because in this method each member of the observation belongs to one class. This limitation led to the use of the fuzzy clustering approach in this type of problem. In this paper is proposed a clustering algorithm, based on a fuzzy treatment of finite mixtures of multivariate scale mixture of normal distribution, using Learning-based fuzzy c-means (LB-FCM) algorithm as well as missing data. We construct a robust LB-FCM framework for handling missing data assuming the finite mixture of multivariate scale mixture of normal distribution. Comparisons between LB-FCM and EM-type algorithms are made. Experimental results and comparisons actually demonstrate the advantage of the proposed LB-FCM.Keywords: IMAGE RECONSTRUCTION, Fuzzy Clustering, Finite mixture distribution. Finite mixture of scale mixture normal distribution, Missing data
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. دراین مقاله، الگوریتم خوشه بندی بهبود یافته PCM-Type2 مبتنی بر بهینه سازی ازدحام ذرات سازگار به نام IAPSO-PCM-Type2 پیشنهاد شده است. ابتدا، الگوریتم خوشه بندی جدید به نام PCM-Type پیشنهاد شده است. الگوریتم PCM-Type2 میتواند مشکلاتی را که الگوریتم PCM احتمالی C-means الگوریتم ، G-K) Gustafson-Kessel الگوریتم) ، FCM NPCM حساسیت به نویز یا نقاط انحراف و حداقل حساسیت محلی... و غیره با آن روبرو میشوند، حل کند. در مرحله دوم، ما الگوریتم PCM-Type2 خود را با الگوریتم بهینه سازی ازدحام ذرات سازگار بهبود یافته IAPSO ادغام کردیم تا از همگرایی مناسب با مینیمم موضعی تابع هدف اطمینان حاصل کنیم. اثربخشی دو الگوریتم پیشنهادی PCM-Type2 و IAPSO-PCM-Type2 بر روی سیستمی که توسط یک معادله مختلف، کوره گاز، Jenkins-Box ،سیستم خشک کن و سیستم همرفت توصیف شده است، آزمایش شد. آزمونهای اعتبارسنجی استفاده شده عملکرد خوبی از این الگوریتمها را نشان داد. با این حال آزمون خطای مربع میانگین آنها MSE رفتار بهتری از FCM- ،PCM ،G-K ، FCM الگوریتم های با مقایسه در Type2-PCM-IAPSO الگوریتم .RKPFCM-PSO و RKPFCM ،Type2-PCM-PSO ،PSO نشان می هد.
In this paper, an improved Type2-PCM clustering algorithm based on improved adaptive particle swarm optimization called Type2-PCM-IAPSO is proposed. Firstly, a new clustering algorithm called Type2-PCM is proposed. The Type2-PCM algorithm can solve the problems encountered by fuzzy c-means algorithm (FCM), Gustafson-Kessel algorithm (G-K), possibilistic c-means algorithm (PCM) and NPCM (sensitivity to noise or aberrant points and local minimal sensitivity). . . etc. Secondly, we combined our Type2-PCM algorithm with the improved adaptive particle swarm optimization algorithm (IAPSO) to ensure proper convergence to a local minimum of the objective function. The effectiveness of the two proposed algorithms Type2-PCM and Type2-PCM-IAPSO was tested on a system described by a different equation, Box-Jenkins gas furnace, dryer system and the convection system. The validation tests used showed good performance of these algorithms. However, their average square error test (MSE) shows a better behaviour of the Type2-PCM-IAPSO algorithm compared to the FCM, G-K, PCM, FCM-PSO, Type2-PCM-PSO, RKPFCM and RKPFCM-PSO algorithms.
Keywords: Improved adaptive particle swarm optimization (IAPSO), Type2-PCM algorithm, Type2-PCM-IAPSO algorithm, fuzzy identification, Fuzzy clustering -
Fuzzy C-mean (FCM) is the most well-known and widely-used fuzzy clustering algorithm. However, one of the weaknesses of the FCM is the way it assigns membership degrees to data which is based on the distance to the cluster centers. Unfortunately, the membership degrees are determined without considering the shape and density of the clusters. In this paper, we propose an algorithm which takes the FCM clustering results and re-fuzzifies them by taking into account the shape and density of the clusters. The algorithm first defuzzifies the FCM clustering results. Then the crisp result is fuzzified again. Re-fuzzification in our algorithm has some advantages. The main advantage is that the fuzzy membership degrees of data points are obtained based on the shape and density of clusters. Adding the ability to eliminate noise and outlier data is the other advantage of our algorithm. Finally, our proposed re-fuzzification algorithm can slightly improve the FCM clustering quality, because the data points change their clusters according to similarity to the shape and density of their respective clusters. These advantages are supported by simulations on real and synthetic datasets.
Keywords: Fuzzy c-means, FCM, re-fuzzification, F3CM, fuzzified FCM, Fuzzy clustering, KFCM -
In this paper, we propose a new method to analyze the difference and similarity of biological sequences, based on the fuzzy sets theory. Considering the sequence order and some chemical and structural properties, we present a computational method to cluster the biological sequences. By some examples, we show that the new method is relatively easy and we are able to compare the sequences of arbitrary lengths.
Keywords: Similarity of biological sequences, Fuzzy polynucleotide space, Fuzzy clustering, Unit hypercube, Fuzzy similarity matrix -
تحلیل خوشه ایاز مهم ترین روش های طبقه بندی محسوب می شود. در تحلیل خوشه بندی تلاش می شود تا مشاهدات واقع در هر خوشه بیشترین تشابه را از نظر متغیرهای موردنظر باهم داشته باشند. به طورکلی روش های خوشه بندی به دو دسته قطعی و فازی تقسیم می شوند. در روش های متداول خوشه بندی، هر مشاهده تنها در یک خوشه قرار می گیرد، اما در خوشه بندی فازی، یک مشاهده هم زمان در دو یا چند خوشه جای می گیرد. در سال 1966، یانگ[1] و کو[2]]16[ یک روش خوشه بندی فازی را ارائه کردند. روش آن ها، تعمیمی از روش متداول خوشه بندی میانگین معمولی برای حالتی است که داده ها به صورت فازی مشاهده شده اند. یک مدل رگرسیون فازی، برای رابطه ی بین متغیرهای مستقل و متغیر وابسته به کار می رود؛ اما در برخی از موارد پراکندگی و ناهمگنی برخی از مشاهدات باعث می شود که یک معادله رگرسیونی نتواند به داده ها برازش خوبی داشته باشد. برای رفع این مشکل یانگ و کو]16 [داده ها را خوشه بندی نموده و برای هر خوشه یک معادله رگرسیونی بر اساس داده های فازی، برازش نموده است. در این مقاله، ابتدا معادله رگرسیون نیمه پارامتری که توسط حسامیان و همکاران ]8[ معرفی شده را بیان نموده و سپس با استفاده از آن نویسندگان برای اولین بار از این معادله در خوشه بندی با داده های فازی استفاده نموده اند. لازم به ذکر است که نتایج حاصل از این روش با روش یانگ و کو بر اساس معیارهای نیکویی برازش پیشنهادی، مقایسه می کنیم.
[1]-Yang
[2]-Koکلید واژگان: عدد فازی، آلفا، شک، خوشه بندی فازی، رگرسیون تعمیم یافته ی یک مرحله ای، رگرسیون نیمه پارامتریCluster analysis is one of the most important methods in classification in which the observations of each cluster has maximum similarity in terms of some desirable variables. In general the clustering methods are divided into two parts, crisp and fuzzy. In usual clustering methods an observation is in only one cluster whereas in fuzzy clustering it may fall into two or more clusters simultaneously. Yang and Ko (1996) introduced a fuzzy clustering method. Their method is an extension of the usual k-means clustering method as they assumed that the observations are fuzzy. A fuzzy regression model is used for studying the relationship between the explanatory variables and dependent variable. In some situations when some observations are dispersed and are heterogeneous, the regression model may not have a goodness of fit for data. To solve this problem Yang and Ko classified data and then based on fuzzy observations fitted a regression model to each cluster. In this paper we first explain the semi-parametric regression model introduced by Hesamian et al. [2017] and then use their model to perform our clustering method for fuzzy observations. Finally, based on some suggested goodness of fit criterions. We compare our results with those of Yang and Ko.Keywords: Fuzzy number, α-pessimistic, Fuzzy clustering, One-stage generalized regression, Semi-parametric regression -
In this paper we have applied Genetic-DEA modelling to help decision makers improve national economic performance through enhancing intellectual property rights indices. We categorized countries applying a novel classification approach and applied genetic algorithm and data envelopment analysis for modelling the relativity of property rights behavior of nations to their economic productivity. We also present a new concept as the uncertainty factor for priority suggestions to have a confidence factor tailored for each specific country for priority recommendations. The results of our research indicate that rich countries shall let people easy access to loans and fight copyright piracy afterwards. Middle income countries have to first enhance the independency of their judicial system and thenceforth respect intellectual property rights. Subsequently, they need to enhance their political stability. Countries that pay few respects to property rights shall boost judicial independence as the first priority and then advance the protection of physical property rights. Poor countries are advised to enhance registering properties and then focus on the rule of law.
Keywords: Property Rights, DEA, Genetic Algorithm, Fuzzy Clustering, IPRI, Maslow, Economic Performance
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