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In spite of some attempts at improving the quality of the clustering ensemble methods, it seems that little research has been devoted to the selection procedure within the fuzzy clustering ensemble. In addition, quality and local diversity of base-clusterings are two important factors in the selection of base-clusterings. Very few of the studies have considered these two factors together for selecting the best fuzzy base-clusterings in the ensemble. We propose a novel fuzzy clustering ensemble framework based on a new fuzzy diversity measure and a fuzzy quality measure to find the base-clusterings with the best performance. Diversity and quality are defined based on the fuzzy normalized mutual information between fuzzy base-clusterings. In our framework, the final clustering of selected base-clusterings is obtained by two types of consensus functions: (1) a fuzzy co-association matrix is constructed from the selected base-clusterings and then, a single traditional clustering such as hierarchical agglomerative clustering is applied as consensus function over the matrix to construct the final clustering. (2) a new graph based fuzzy consensus function. The time complexity of the proposed consensus function is linear in terms of the number of data-objects. Experimental results reveal the effectiveness of the proposed approach compared to the state-of-the-art methods in terms of evaluation criteria on various standard datasets.

Data partition with high confidence is one of the main concentration of researchers in Soft Computing for many years. It is known that there may be some data with less confidence (wrong values, incorrect attribute types, irrelevant domain ranges, etc.) existed in the whole dataset due to the data gathering process. This would degrade the performance of final clustering results because of noises and outliers being occurred. Safe semi-supervised fuzzy clustering has been used extensively in recent years to tackle with this problem by adding the concept of a local graph between labeled and unlabeled data so that wrong labeled data has small impact to the final clusters. However, this process often takes much computational time and sometimes produces unreasonable results. In this research, we propose a new algorithm for the Data partition with confidence problem named as Trusted Safe Semi-Supervised Fuzzy Clustering Method (TS3FCM). The key motivation behind TS3FCM is to handle the drawbacks of the related safe semi-supervised fuzzy clustering algorithms regarding huge computational time. The novelty of TS3FCM against the other safe semi-supervised fuzzy clustering algorithms lies at the isolated processes of finding trusted labeled data and performing semi-supervised fuzzy clustering. The key contributions of the paper are briefly summarized as follows. At first, a new objective function is proposed. This function is incorporated with new weights for each labeled data so that the system can check whether a labeled data point is corrected or not. This function is also optimized to find the cluster centers and the membership matrix. Indeed, the labeled data having small impact after clustering are either set up with very low membership values or removed from the set of labeled data. Furthermore, a new semi-supervised fuzzy clustering model is defined to partition the whole dataset with the additional information being a mixture of the prior membership degrees ( U ¯ ) and labeled data. The whole TS3FCM works through 3 main phases with the main aim to accelerate the computational time and to achieve reasonable clustering quality compared to the related algorithms. TS3FCM is implemented and experimentally compared against the related methods such as the standard Fuzzy C-Means (FCM), the Semi-supervised Fuzzy Clustering method (SSFCM), and the Confidence-weighted safe semi-supervised clustering (CS3FCM) algorithm by both the computational time and the quality of clustering results. The experimental results on the benchmark UCI Machine Learning datasets show that TS3FCM runs faster than the other algorithms while maintaining reasonable clustering quality. We also analyze the results statistically by ANOVA.

Picture fuzzy C-means clustering is a new computational intelligence method that has more significant potential advantages than fuzzy clustering in medical image interpretation. However, the practical application of picture fuzzy clustering in medical image segmentation is severely limited by its sensitivity to noise or outliers. Therefore, this paper proposes a medical image segmentation method called possibilistic picture fuzzy product partition C-means clustering with local information. This method combines picture fuzzy clustering with fuzzy possibilistic product partition C-means clustering to solve the segmentation problem of noisy medical image. Firstly, this paper extends picture fuzzy clustering to construct a possibilistic picture C-means clustering, enhancing the robustness of picture fuzzy clustering to noise or outliers. Secondly, by combining picture fuzzy clustering with possibilistic picture C-means clustering, a novel possibilistic picture fuzzy product partition C-means clustering is proposed, further enhancing the adaptability of picture fuzzy clustering in medical image analysis. Finally, a weighted squared Euclidean distance with complement spatial information and a novel possibilistic picture fuzzy local information factor are constructed, and they are introduced into the possibilistic picture fuzzy product partition clustering to enhance the robustness of this method in noisy image segmentation. The experimental results on medical images indicate that the proposed method not only has good segmentation performance and strong anti-noise robustness, but also improves segmentation accuracy by 1.66% to 17.39% compared with FRFCM method.

Data clustering is the process of dividing data elements into different clusters in which elements in one cluster have more similarity than those in other clusters. Semi-supervised fuzzy clustering methods are used in various applications. The available methods are based on fuzzy C-Mean, kernel function, weight function and adaptive function. The fuzzification coefficient is an important factor that affects to the performance in these methods. In this paper, we propose the improvements of semi-supervised standard fuzzy C-Mean clustering (SSFCM) by using multiple fuzzifiers to increase clusters quality. Two proposed models, named as MCSSFC-P and MCSSFC-C, use different fuzzifiers for each data point and for each cluster, respectively, which are established in a form of optimal problems. The values of fuzzifiers are updated to get the best values of objective functions. Evaluations on different datasets are performed. The numerical results show the higher performance of our model than some related models.

Spectral Clustering is a graph clustering algorithm that makes use of eigenvector obtained from a matrix describing pairwise similarity between data points. It provides a dimensionality reduction for clustering in lower dimensions. One example of spectral clustering application is the clustering of protein-protein interaction (PPI) network. PPI networks are usually represented as a graph network with proteins and interactions as vertices and edges respectively. However, this spectral clustering only produces a hard clustering of proteins, whereas there may be some relationship between each protein clusters, and possibly multiple functionality for each proteins that has not been detected before. Fuzzy Random Walk is a fuzzy clustering method based on transition probability from a random walk on a dataset. In this paper, we combine both Spectral Clustering and Fuzzy Random Walk to cluster PPI network of protein TP53, a protein thatplays an important role in managing cell cycle, especially in tumor cell suppression. Using PPI dataset of TP53 obtained from the STRING database, we found the combined algorithm is proven to produce both robust and fuzzy clusters with each cluster explains one of TP53 protein's functionality related to the tumor cell.

The study analyses the hidden relationship between transport and ICT use for an extensive sample of 26,500 EU citizens. To that aim, a fuzzy clustering Eco-extended apostle model is applied to both latent variables: interurban transport trips and ICT use. The interurban long-distance trip (LDT) latent variable is measured by four different indicators (long- and medium-distance trips for work and leisure in the past twelve months), and the ICT use is based on a ten-item scale that provides information on different transport modes. The fuzzy Eco-extended apostle model is compared with the classical apostle model, translating the satisfaction and loyalty dimensions to our case. The fuzzy clustering model shows that most EU citizens are similar to the representative citizen who moved and used ICT at very low rates (56.5 and 50.4 per cent, respectively). The classical apostle model shows that the quadrants low LDT–high ICT and low LDT–low ICT are more represented by 38.5 and 35.2 per cent, respectively. However, the Eco-extended apostle model reinforces the results of the quadrant of low LDT–low ICT (40.22%) but softens those obtained in the quadrant of low LDT–high ICT (21.01%). Interesting insights of the effects of gender, age, education, and employment status are discussed.

In this study, a new approach for novelty and anomaly detection, called HPFuzzNDA, is introduced. It is similar to the Possibilistic Fuzzy multi-class Novelty Detector (PFuzzND), which was originally developed for data streams. Both algorithms initially use a portion of labelled data from known classes to divide them into a given number of clusters, and then attempt to determine if the new instances, which may be unlabelled, belong to the known or novel classes or if they are anomalies, namely if they are extreme values that deviate from other observations, indicating noise or errors in measurement. However, for each class in HPFuzzNDA clusters are designed by using the new evolutionary algorithm NL-SHADE-RSP, the latter is a modification of the well-known L-SHADE approach. Additionally, the number of clusters for all classes is automatically adjusted in each step of HPFuzzNDA to improve its efficiency. The performance of the HPFuzzNDA approach was evaluated on a set of benchmark problems, specifically generated for novelty and anomaly detection. Experimental results demonstrated the workability and usefulness of the proposed approach as it was able to detect extensions of the known classes and to find new classes in addition to the anomalies. Moreover, numerical results showed that it outperformed PFuzzND. This was exhibited by the new mechanism proposed for cluster adjustments allowing HPFuzzNDA to achieve better classification accuracy in addition to better results in terms of macro F-score metric.

The present study proposes a music recommendation service in a mobile environment using the DASS-21 questionnaire to distinguish and measure certain psychological state instability symptoms—viz. anxiety, depression, and stress—that anyone can experience regardless of job or age. In general, the outcome of the DASS-21 from almost every participant did not reveal any single psychological state out of the abovementioned three states. Therefore, the weighted scores were calculated for each scale and fuzzy clustering was used to cluster users into groups with similar states. For the initial dataset’s generation, we used the DASS inventory collected from the Open-Source Psychometrics Project conducted from 2017 to 2019 on approximately 39,000 respondents, and the results of the survey showed that the average scores for each scale were 23.6 points for depression, 17.4 for anxiety, and 23.3 for stress. Based on the datasets collected from fuzzy clustering, the individuals were classified into three groups: Group 1 was recommended with music for “high” depression, “high” anxiety, and “low” stress; Group 2 was recommended with music for “normal” depression, “low” anxiety, and “normal” stress; and Group 3 was recommended with music for “high” depression, “high” anxiety, and “high” stress. Especially, the largest numbers of recommended music in the three groups were for Group 1 with “High” depressive (4.64), Group 2 for “Low” anxiety (4.54), and Group 3 for “High” anxiety (4.76). In addition, to compare the results of fuzzy clustering with other data, the silhouette coefficient of the samples extracted with the same severity ratio and those generated by simple random sampling were 0.641 and 0.586, respectively, which were greater than 0. The proposed service can recommend not only the music of users with similar trends at all psychological states, but also the music of users with similar psychological states in part.

In today's reality 'World Wide Web' is considered as the archive of extremely enormous measure of data. The substance and complexity of WWW are increasing day by day. Presently the circumstances are such that we are suffocating in data yet starving for knowledge. Because of these circumstances data mining is extremely important to get valuable data from WWW. Clustering data mining is the process of putting together meaning-full or use-full similar object into one group. It is a common technique for statistical data, machine learning and computer science analysis. Clustering is a kind of unsupervised data mining technique which describes general working behavior, pattern extraction and extracts useful information from time series data. In this paper we are discussing our new procedure for clustering called Fuzzy C-least median of squares algorithm which is an improvement to Fuzzy C-means (FCM) algorithm. As it is concerned with the least value among medians, it wipes out means squared error and eliminates the effect of outliers. We compared our clustering result got by applying FCM and FCLM by using Xie-Beni Index, Fukuyama-Sygeno Index and Partition Coefficient. The outcomes demonstrate a clear improvement of our algorithm than existing FCM algorithm.

Fuzzy clustering has been gaining prominence in medical image segmentation but challenges still exist. This paper proposes a novel Type-II Intuitionistic Fuzzy C Means clustering algorithm by introducing a new membership degree called Intuitionistic Type-II membership. Intuitionistic Type-II membership combines Type-II membership with hesitation degree. Using Intuitionistic Type-II membership, the proposed algorithm shows following advantages: (1) defining clusters clearly, (2) robustness to noise and outliers, and (3) improving desired position of centroids. These advantages make Type-II Intuitionistic Fuzzy C Means clustering algorithm a preferred choice for mammogram segmentation. On some mammograms from Mammographic Image Analysis Society database, performance of Type-II Intuitionistic Fuzzy C Means clustering algorithm is compared with the performance of other fuzzy clustering algorithms such as Fuzzy C-Means, Intuitionistic Fuzzy C-Means, Type-II Fuzzy C-Means, Interval Type-II Fuzzy C-Means, and Particle Swarm Optimization Based Interval Type-II Fuzzy C-Means using Intuitionistic Fuzzy Sets. By qualitative analysis, results of Type-II Intuitionistic Fuzzy C Means are found to be better than the results of discussed algorithms as the proposed algorithm identifies shape and size of lumps in mammograms more accurately. On experimenting with synthetic data sets, it is observed that Type-II Intuitionistic Fuzzy C Means produces robust and stable results as outliers increase and average error is reduced by 84% on D15 dataset.