Fuzzy clustering with the entropy of attribute weights

Non-stationary Bayesian spatial model for disease mapping based on sub-regions

This paper aims to extend the Besag model, a widely used Bayesian spatial model in disease mapping, to a non-stationary spatial model for irregular lattice-type data. The goal is to improve the model's ability to capture complex spatial dependence patterns and increase interpretability. The proposed model uses multiple precision parameters, accounting for different intensities of spatial dependence in different sub-regions. We derive a joint penalized complexity prior to the flexible local precision parameters to prevent overfitting and ensure contraction to the stationary model at a user-defined rate. The proposed methodology can be used as a basis for the development of various other non-stationary effects over other domains such as time. An accompanying R package fbesag equips the reader with the necessary tools for immediate use and application. We illustrate the novelty of the proposal by modeling the risk of dengue in Brazil, where the stationary spatial assumption fails and interesting risk profiles are estimated when accounting for spatial non-stationary. Additionally, we model different causes of death in Brazil, where we use the new model to investigate the spatial stationarity of these causes.

Improvement of Neural-Network Classifiers Using Fuzzy Floating Centroids

In this article, a fuzzy floating centroids method (FFCM) is proposed, which uses a fuzzy strategy and the concept of floating centroids to enhance the performance of the neural-network classifier. The decision boundaries in the traditional floating centroids neural-network (FCM) classifier are "hard." These hard boundaries force a point, such as noisy or boundary point, to be assigned to a class exclusively, thereby frequently resulting in misclassification and influencing the performance of optimization methods to train the neural network. A fuzzy strategy combined with floating centroids is introduced to produce "soft" boundaries to handle noisy and boundary points, which increases the chance of discovering the optimal neural network during optimization. In addition, the FFCM adopts a weighted target function to correct the preference to majority classes for imbalanced data. The performance of FFCM is compared with ten classification methods on 32 benchmark datasets by using indicators: average F -measure (Avg.FM) and generalization accuracy. Also, the proposed FFCM is applied to nondestructively estimate the strength grade of cement specimens based on microstructural images. In the experimental results, FFCM achieves the optimal generalization accuracy and Avg.FM on 17 datasets and 21 datasets, respectively; FFCM balances precision and recall better than its competitors for the estimation of cement strength grade.

A novel weighted fuzzy c-means based on feature weight learning

In feature weighted fuzzy c-means algorithms, there exist two challenges when the feature weighting techniques are used to improve their performances. On one hand, if the values of feature weights are learnt in advance, and then fixed in the process of clustering, the learnt weights might be lack of flexibility and might not fully reflect their relevance. On the other hand, if the feature weights are adaptively adjusted during the clustering process, the algorithms maybe suffer from bad initialization and lead to incorrect feature weight assignment, thus the performance of the algorithms may degrade the in some conditions. In order to ease these problems, a novel weighted fuzzy c-means based on feature weight learning (FWL-FWCM) is proposed. It is a hybrid of fuzzy weighted c-means (FWCM) algorithm with Improved FWCM (IFWCM) algorithm. FWL-FWCM algorithm first learns feature weights as priori knowledge from the data in advance by minimizing the feature evaluation function using the gradient descent technique, then iteratively optimizes the clustering objective function which integrates the within weighted cluster dispersion with a term of the discrepancy between the weights and the priori knowledge. Experiments conducted on an artificial dataset and real datasets demonstrate the proposed approach outperforms the-state-of-the-art feature weight clustering methods. The convergence property of FWL-FWCM is also presented.

A Feature Weighted Fuzzy Clustering Algorithm Based on Multistrategy Grey Wolf Optimization

Traditional fuzzy clustering is sensitive to initialization and ignores the importance difference between features, so the performance is not satisfactory. In order to improve clustering robustness and accuracy, in this paper, a feature-weighted fuzzy clustering algorithm based on multistrategy grey wolf optimization is proposed. This algorithm cannot only improve clustering accuracy by considering the different importance of features and assigning each feature different weight but also can easily obtain the global optimal solution and avoid the impact of the initialization process by implementing multistrategy grey wolf optimization. This multistrategy optimization includes three components, a population diversity initialization strategy, a nonlinear adjustment strategy of the convergence factor, and a generalized opposition-based learning strategy. They can enhance the population diversity, better balance exploration and exploitation, and further enhance the global search capability, respectively. In order to evaluate the clustering performance of our clustering algorithm, UCI datasets are selected for experiments. Experimental results show that this algorithm can achieve higher accuracy and stronger robustness.

A new weighted fuzzy C-means clustering approach considering between-cluster separability

Fuzzy C-means clustering algorithm (FCM) is an effective approach for clustering. However, in most existing FCM type frameworks, only in-cluster compactness is taken into account, whereas the between-cluster separability is overlooked. In this paper, to enhance the clustering, by incorporating the feature weighting and data weighting method, we put forward a new weighted fuzzy C-means clustering approach considering between-cluster separability, in which for achieving good compactness and separability, making the in-cluster distances as small as possible and making the between-cluster distances as large as possible, the in-cluster distances and between-cluster distances are taken into account; To achieve the optimal clustering result, the iterative formulas of the feature weights, membership degrees, data weights and cluster centers are obtained by maximizing the in-cluster compactness and the between-cluster separability. Experiments on real-world datasets were carried out, the results showed that the new approach could obtain promising performance.

Feature reduction fuzzy C-Means algorithm leveraging the marginal kurtosis measure

The feature reduction fuzzy c-means (FRFCM) algorithm has been proven to be effective for clustering data with redundant/unimportant feature(s). However, the FRFCM algorithm still has the following disadvantages. 1) The FRFCM uses the mean-to-variance-ratio (MVR) index to measure the feature importance of a dataset, but this index is affected by data normalization, i.e., a large MVR value of original feature(s) may become small if the data are normalized, and vice versa. Moreover, the MVR value(s) of the important feature(s) of a dataset may not necessarily be large. 2) The feature weights obtained by the FRFCM are sensitive to the initial cluster centers and initial feature weights. 3) The FRFCM algorithm may be unable to assign the proper weights to the features of a dataset. Thus, in the feature reduction learning process, important features may be discarded, but unimportant features may be retained. These disadvantages can cause the FRFCM algorithm to discard important feature components. In addition, the threshold for the selection of the important feature(s) of the FRFCM may not be easy to determine. To mitigate the disadvantages of the FRFCM algorithm, we first devise a new index, named the marginal kurtosis measure (MKM), to measure the importance of each feature in a dataset. Then, a novel and robust feature reduction fuzzy c-means clustering algorithm called the FRFCM-MKM, which incorporates the marginal kurtosis measure into the FRFCM, is proposed. Furthermore, an accurate threshold is introduced to select important feature(s) and discard unimportant feature(s). Experiments on synthetic and real-world datasets demonstrate that the FRFCM-MKM is effective and efficient.

Improved Overlap-based Undersampling for Imbalanced Dataset Classification with Application to Epilepsy and Parkinson’s Disease

Classification of imbalanced datasets has attracted substantial research interest over the past decades. Imbalanced datasets are common in several domains such as health, finance, security and others. A wide range of solutions to handle imbalanced datasets focus mainly on the class distribution problem and aim at providing more balanced datasets by means of resampling. However, existing literature shows that class overlap has a higher negative impact on the learning process than class distribution. In this paper, we propose overlap-based undersampling methods for maximizing the visibility of the minority class instances in the overlapping region. This is achieved by the use of soft clustering and the elimination threshold that is adaptable to the overlap degree to identify and eliminate negative instances in the overlapping region. For more accurate clustering and detection of overlapped negative instances, the presence of the minority class at the borderline areas is emphasized by means of oversampling. Extensive experiments using simulated and real-world datasets covering a wide range of imbalance and overlap scenarios including extreme cases were carried out. Results show significant improvement in sensitivity and competitive performance with well-established and state-of-the-art methods.

An Entropy Regularization k-Means Algorithm with a New Measure of between-Cluster Distance in Subspace Clustering

Although within-cluster information is commonly used in most clustering approaches, other important information such as between-cluster information is rarely considered in some cases. Hence, in this study, we propose a new novel measure of between-cluster distance in subspace, which is to maximize the distance between the center of a cluster and the points that do not belong to this cluster. Based on this idea, we firstly design an optimization objective function integrating the between-cluster distance and entropy regularization in this paper. Then, updating rules are given by theoretical analysis. In the following, the properties of our proposed algorithm are investigated, and the performance is evaluated experimentally using two synthetic and seven real-life datasets. Finally, the experimental studies demonstrate that the results of the proposed algorithm (ERKM) outperform most existing state-of-the-art k-means-type clustering algorithms in most cases.

Study on Development Sustainability of Atmospheric Environment in Northeast China by Rough Set and Entropy Weight Method

In order to evaluate the atmospheric environment sustainability in the provinces of Northeast China, this paper has constructed a comprehensive evaluation model based on the rough set and entropy weight methods. This paper first constructs a Pressure-State-Response (PSR) model with a pressure layer, state layer and response layer, as well as an atmospheric environment evaluation system consisting of 17 indicators. Then, this paper obtains the weight of different indicators by using the rough set method and conducts equal-width discrete analysis and clustering analysis by using SPSS software. This paper has found that different discrete methods will end up with different reduction sets and multiple indicators sharing the same weight. Therefore, this paper has further introduced the entropy weight method based on the weight solution determined by rough sets and solved the attribute reduction sets of different layers by using the Rosetta software. Finally, this paper has further proved the rationality of this evaluation model for atmospheric environment sustainability by comparing the results with those of the entropy weight method alone and those of the rough set method alone. The results show that the sustainability level of the atmospheric environment in Northeast China provinces has first improved, and then worsened, with the atmospheric environment sustainability level reaching the highest level of 0.9275 in 2014, while dropping to the lowest level of 0.6027 in 2017. Therefore, future efforts should focus on reducing the pressure layer and expanding the response layer. Based on analysis of the above evaluation results, this paper has further offered recommendations and solutions for the improvement of atmospheric environment sustainability in the three provinces of Northeast China.

Uncertain Data Clustering in Distributed Peer-to-Peer Networks

Uncertain data clustering has been recognized as an essential task in the research of data mining. Many centralized clustering algorithms are extended by defining new distance or similarity measurements to tackle this issue. With the fast development of network applications, these centralized methods show their limitations in conducting data clustering in a large dynamic distributed peer-to-peer network due to the privacy and security concerns or the technical constraints brought by distributive environments. In this paper, we propose a novel distributed uncertain data clustering algorithm, in which the centralized global clustering solution is approximated by performing distributed clustering. To shorten the execution time, the reduction technique is then applied to transform the proposed method into its deterministic form by replacing each uncertain data object with its expected centroid. Finally, the attribute-weight-entropy regularization technique enhances the proposed distributed clustering method to achieve better results in data clustering and extract the essential features for cluster identification. The experiments on both synthetic and real-world data have shown the efficiency and superiority of the presented algorithm.

Improving Neural-Network Classifiers Using Nearest Neighbor Partitioning

This paper presents a nearest neighbor partitioning method designed to improve the performance of a neural-network classifier. For neural-network classifiers, usually the number, positions, and labels of centroids are fixed in partition space before training. However, that approach limits the search for potential neural networks during optimization; the quality of a neural network classifier is based on how clear the decision boundaries are between classes. Although attempts have been made to generate floating centroids automatically, these methods still tend to generate sphere-like partitions and cannot produce flexible decision boundaries. We propose the use of nearest neighbor classification in conjunction with a neural-network classifier. Instead of being bound by sphere-like boundaries (such as the case with centroid-based methods), the flexibility of nearest neighbors increases the chance of finding potential neural networks that have arbitrarily shaped boundaries in partition space. Experimental results demonstrate that the proposed method exhibits superior performance on accuracy and average f-measure.

Sensor Fault and Delay Tolerant Control for Networked Control Systems Subject to External Disturbances

In this paper, the problem of sensor fault and delay tolerant control problem for a class of networked control systems under external disturbances is investigated. More precisely, the dynamic characteristics of the external disturbance and sensor fault are described as the output of exogenous systems first. The original sensor fault and delay tolerant control problem is reformulated as an equivalence problem with designed available system output and reformed performance index. The feedforward and feedback sensor fault tolerant controller (FFSFTC) can be obtained by utilizing the solutions of Riccati matrix equation and Stein matrix equation. Based on the designed fault diagnoser, the proposed FFSFTC is further reconstructed to compensate for the sensor fault and delayed measurement effects. Finally, numerical examples are provided to illustrate the effectiveness of our proposed FFSFTC with different cases with various types of sensor faults, measurement delays and external disturbances.