Fuzzy Partition Research Articles

Functional dimension reduction based on fuzzy partition and transformation

SummaryFunctional sliced inverse regression (FSIR) is the among most popular methods for the functional dimension reduction. However, FSIR has two evident shortcomings. On the one hand, the number of samples in each slice must not be too small and selecting a suitable S is difficult, particularly for data with small sample size, where S indicates the number of slices. On the other hand, FSIR and its related methods are well‐known for their poor performance when the link function is an even (or symmetric) dependency. To solve these two problems, we propose three new types of estimation methods. First, we propose the functional fuzzy inverse regression (FFIR) method based on a fuzzy partition. Compared with FSIR that uses a hard partition, the fuzzy partition uses all samples with different weights to estimate the mean in each slice. Therefore, FFIR exhibits good performance even for data with small sample size. Second, we suggest two transformation approaches, namely, FSIRR and FSIRP, avoiding the symmetric dependency between the response and the predictor. FSIRR eliminates the symmetric dependency by transforming the response variable, while FSIRP overcomes the symmetric dependency by transforming the functional predictor. Third, we propose the FFIRR and FFIRP methods by combining the advantages of FFIR and two transformation methods. FFIRR and FFIRP replace the FSIR method on the transformation data via FFIR. Simulation and real data analysis show that three types of proposed methods exhibit better performance than FSIR in terms of the estimation accuracy and stability.

Optimal experiment design for locally adaptive regression models

The problem of reconstruction of dependencies using locally adaptive linear regression models is considered. The problem of a priori optimal design of experiments during identification of locally adaptive linear regression models is solved. In this case, the region of determining the active factors is divided into 2 or 3 fuzzy partitions. The problem of constructing D-optimal designs of experiment is formulated and solved

On Assessments of Agreement Between Fuzzy Partitions

On Assessments of Agreement Between Fuzzy Partitions

A fuzzy partition-based method to classify social messages assessing their emotional relevance

With the surge of the large volume of data availability, Machine Learning and mainly Deep Learning techniques are the leading solutions in classification and predictive tasks, targeted at data-efficient learning. These models learn by training on many diversified samples in a process that is computationally expensive or time-consuming. Moreover, in many real-world scenarios, the amount of available data for training is unsuitable, because it is unlabeled or covers only portions of the whole reference domain cases.This paper proposes an alternative approach for document classification that leverages the distribution of the data projected in the multi-dimensional feature space to assess the weight of features in the final classification. The approach does not rely on traditional iterative methods for classification but builds a relevance measure to assess the relevance/importance of the features describing the domain of interest. The idea is to harness this metric to select relevant features and then express the values calculated by these metrics in natural language by exploiting fuzzy variables and linguistic labels to make human comprehension more immediate. The approach has been employed for emotion extraction from social media messages. The novelty of this approach is twofold: first, the well-known TF-IDF measure was reinterpreted as a relevance measure of emotions discovered in text content. Then, the discovered emotion relevance was described by fuzzy linguistic labels, defined on an ad-hoc-designed fuzzy partition, to express the data classification in natural language, more suitable to human understanding.

Locally weighted factorization machine with fuzzy partition for elderly readmission prediction

The mitigation of preventable readmissions is the key to enhance the quality and efficiency of healthcare services in Hong Kong’s aging society. A general predictor like factorization machine (FM) can efficiently capture non-linear interactions among patient characteristics for readmission prediction. However, FM cannot formulate local patient heterogeneity that commonly exists due to different demographics and hospitalization characteristics. This study proposes a locally weighted factorization machine (WFM) by developing a locally weighting scheme that assigns differentiated weights for training instances in accordance with their local similarities with high-readmission-risk ones. Io account for global heterogeneity among patient groups, we further extend WFM and propose a fuzzy partition enhanced WFM model (i.e., WFMFP), which (I) splits the dataset into multiple training subsets with fuzzy partition approach, (II) fits the WFM model on the basis of each training subset, and (III) combines the sub-prediction WFM models by using Takagi–Sugeno–Kang fuzzy weighting mechanism. We collected a territory-wide cohort with electronic health records in Hong Kong during 2008 to 2017. We demonstrated that the proposed WFMFP model outperforms several baselines, including standard FM, XGBoost, Lightgbm, Catboost, Gradient boosting machine, random forests, SVMs with different kernels, and multilayer perceptron. Comparative analysis results demonstrate the effectiveness of applying the locally weighting notion into FM to improve readmission prediction for clinical resource management.

Aggregation Operators with Undefined Inputs or Outputs

We consider a generalization of aggregation and fusion functions when some of their inputs or outputs are undefined. For simplicity, we represent undefined values by a single NaN (not-a-number) value. We define four main methods of treating undefined values, observe some of their properties, and compare them with several mainstream implementations and norms for handling NaN values. Finally, as a case study demonstrating the apparatus's usefulness, the formalism is applied to the discrete fuzzy transform technique. The formalism allows us to prove a generalized approximation theorem for fuzzy transforms, which removes previously required restrictions on fuzzy partitions for sparse input data.

A fuzzy entropy, Contourlet based automatic fault detection

Seismic fault interpretation has great importance in characterising subsurface geology. However, it is in general a manual and time-consuming task, thus, adaptive methods to achieve good fault detection results would be valuable. In this paper, we present a new method using combination of Contourlet transform and fuzzy entropy definition to adaptively detect and extract faults from seismic data. Contourlet is a multiscale and multidirectional filter that has high directionality which decomposes an image to various subscales. Our proposed scheme has 3 phases: first, employing Contourlet to pull out fault information using multidirectional and multiscale property of contourlet (feature extraction), second, using differentiation to boost fault information and calculating the correlation coefficient between the input image and subscales, fault information can be isolated from reflectors adaptively (feature selection) and third, applying a multi-level thresholding approach built on fuzzy partition of the histogram and entropy theory to classify image pixels into fault and non-fault (classification). The adaptive hybrid technique was applied to one synthetic and two real datasets containing fault data, reflectors and random noise. According to the results and their assessments, the proposed scheme has desirably located fault features in the data. We also examined the effect of random noise (Signal to Noise Ratio (SNR) = 2) on our adaptive algorithm which showed the success of our designed technique in the presence of noise.

Improved Wavelet Packet Noise Reduction for Microseismic Data via Fuzzy Partition

It is crucial to retain as many signal components as possible, while noise is eliminated for wavelet packet noise reduction algorithms. Conventional thresholding functions take coefficients smaller than a given threshold as the noise component and get them removed in many ways. In this letter, considering the potential probability of being the signal-related component of coefficients whose value is smaller than the given threshold and the nonnegligible fact that microseismic (MS) event is sparse compared with the noise, we proposed a new wavelet packet-based denoising method via fuzzy partition. First, instead of a hard partition from a given threshold, wavelet packet coefficients get reduced by a fuzzy partition to retain more potential signal elements and suppress the noise. Second, we employ fuzzy c-means (FCM) clustering to identify the interval period of the MS event further to remove the residual noise and additional resonance in processed time series. We tested our method on synthetic datasets and real-field data from an MS monitoring experiment in a coal mine in Sichuan Basin, China. We utilize Pearson correlation coefficient and root-mean-square error between ideal signal and denoised data as performance indicators in synthetic tests, while sample entropy and kurtosis of denoised data are involved in the real field dataset. Test results from synthetic datasets and the real field dataset demonstrate that the proposed noise reduction method is superior to traditional hard-, soft-, and garrote-thresholding and is more applicable and effective in MS data processing.

Study on food safety risk based on LightGBM model: a review

Accurately detecting risk points is crucial to food safety risk assessment and prewarning in food safety risk management because it helps solve food safety problems at their source. With the advancement of informationization in the food industry, a vast quantity of food safety data generated throughout sample inspection, transportation, storage, food processing, and raw material production has become urgently necessary to develop and use. Nevertheless, the existing food safety risk warning system has several flaws, including a high personnel cost, a low data utilization rate, and a crude risk measurement system. As a result, we described the data attributes for further analysis and sorted the food safety data in this study. In the meantime, to fully exploit the high dimension and the data's large amount, a mixture of fuzzy hierarchy partition and prior risk probability could be used to calculate fuzzy comprehensive risk values depending on multiple traits as the predicted outcome of a predictive model which can forecast and confirm risk levels, created with the use of a light gradient boosting machine (LightGBM) and skilled adjustment procedures. Finally, the outcomes of the multiple methods are compared using the same training and test data in order to verify the efficiency of LightGBM. The risk analysis results presented in this study, including attribute importance distribution and the risk values, can be useful to decision-makers.

Information Classification Algorithm based on Project-based Learning Data-driven and Stochastic Grid

The adaptive partitioning algorithm of information set in simulation laboratory based on project-based learning data-driven and random grid is studied to effectively preprocess the information set and improve the adaptive partitioning effect of the information set. Using the improved fuzzy C-means clustering algorithm driven by project-based learning data, the fuzzy partition of information set in simulation laboratory is carried out to complete preprocessing of information set; The pre-processing information set space is roughly divided by the grid partitioning algorithm based on the data histogram; A random mesh generation algorithm based on uniformity is used to finely divide the coarse mesh cells; Taking the representative points of grid cells as the clustering center, the pre-processing information set is clustered by the density peak clustering algorithm to complete the adaptive partitioning of the information set in simulation laboratory. Experimental results show that this algorithm can effectively preprocess and adaptively partition the information set of simulation laboratory; For different dimension information sets, the evaluation index values of Rand index, Purity, standard mutual information, interval and Dunn index of the algorithm are all high, and the evaluation index values of compactness and Davidson's banding index are all low, so the algorithm has a high accuracy of adaptive partitioning of information sets.

Fuzzy Isolation Forest for Anomaly Detection

Anomaly detection is nowadays a key data mining task. Anomaly detection methods generally look for patterns of ”normal” profile and then identify data points that do not match that profile. One outstanding method, Isolation Forest, showed high detection performance and computational efficiency. This method does not profile normal instances. Instead, it seeks to separate ”abnormal” data points that are ”few and different”, from the others. This method builds a forest of trees to define a model for classifying data points as normal or abnormal. Building trees involve recursive random partitioning of data. Instances resulting in shorter path lengths are considered anomalies because they are located in sparse regions whereas instances ending deeper in tree path are normal points. Most outlier detection approaches, including Isolation Forest, have been used on precise, crisp data. However, in real life, data may be imprecise, incomplete, ambiguous, or uncertain. In this paper, we propose a new approach, called Fuzzy Isolation Forest, which adapts the Isolation Forest method to fuzzy data to handle the ”vagueness” of data. We use a fuzzy partitioning strategy based on the alpha-cut approach in which data instances will be assigned to tree nodes by comparing their membership value to an alpha-cut threshold. Fuzzy Isolation Forest is as efficient as Isolation Forest in detecting anomalies on fuzzy data without significantly increasing processing time.

An Information Based Fuzzy Partitioning Approach (IBFP) for “Bad” Credit Detection

Credit cardholder behavior analysis is a very important issue for credit risk control. And classification method, which is an important topic in data mining, is usually used here for "Bad" credit detection. Data pre-processing may affect classification accuracy. In this paper, an information-based fuzzy partition approach is proposed for bad credit detection. In this approach, the membership function based on domain knowledge is constructed. And the approach has based the information both supervised data transferring method and domain knowledge. The experiments show its performance for "Bad" credit detection.

Hybrid approach for adaptive fuzzy grid partitioning and rule generation using rough set theory

This research proposes a hybrid approach for adaptive fuzzy grid partitioning and rule generation using rough set theory to address the problem of customer segmentation based on purchasing behavior. The objective is to minimize the fuzziness of the partitioning while maximizing the accuracy and interpretability of the generated rules. The research utilizes a dataset consisting of customer transactions, including demographics, purchase details, and satisfaction ratings. The fuzzy grid partitioning process divides the customer space into grid cells, representing different segments. Fuzzy membership values are assigned to data points based on their association with each grid cell. Rough set theory is employed for attribute reduction, identifying the most relevant attributes for customer segmentation. Rule induction algorithms generate rules that capture the patterns and dependencies among customer attributes and their association with specific grid cells. The hybrid approach combines the advantages of adaptive fuzzy grid partitioning and rough set-based rule generation. The optimization process adjusts fuzzy membership values and refines the generated rules to improve accuracy and interpretability. A numerical example and a case study in the retail industry are presented to demonstrate the effectiveness of the proposed approach. Results show successful customer segmentation and generation of actionable rules for marketing strategies. The research contributes to the field of customer segmentation by providing a comprehensive methodology that integrates adaptive fuzzy grid partitioning and rule generation using rough set theory. The hybrid approach offers valuable insights into customer behavior, enabling targeted marketing campaigns, personalized recommendations, and enhanced customer satisfaction.

An approach to Fuzzy clustering of the iris petals by using Ac-means Analysis

This paper proposes a definition of a fuzzy partition element based on the homomorphism between type-1 fuzzy sets and the three-valued Kleene algebra. A new clustering method based on the C-means algorithm, using the defined partition, is presented in this paper, which will be validated with the traditional iris clustering problem by measuring its petals.

A novel hybrid forecasting system based on data augmentation and deep learning neural network for short-term wind speed forecasting

As a clean, economical, and renewable energy source, wind energy plays a very important role in easing the shortage of fossil energy, environmental population, and climate change. However, due to the strong intermittency, volatility, and randomness of wind speed, the large-scale connection of wind energy into the power grid is restricted. Therefore, constructing a reliable prediction model to achieve high-accuracy wind speed prediction is necessary. For this purpose, a novel hybrid model for short-term wind speed prediction is proposed in this paper. First, empirical mode decomposition is employed to decompose the raw wind speed time series into a set of subseries. Then, a data augmentation technique is first used to generate more training data to avoid overfitting of the prediction model. Furthermore, a new predictor based on a convolutional neural network (CNN), a long short-term memory (LSTM) network, and an extreme learning machine (ELM) is proposed for deterministic wind speed prediction, where a fuzzy entropy-based partition strategy is implemented to assign subseries to the CNN-LSTM and ELM. To improve the prediction performance, a synchronous optimization method based on an improved hybrid particle swarm optimization/gray wolf optimizer is proposed for feature selection and parameter optimization. Afterward, kernel density estimation is used to estimate the wind speed probability density function for probabilistic prediction. Finally, the performance of the proposed model is compared with seven other models by using three wind speed datasets from four aspects: point prediction, interval prediction, probability prediction comprehensive performance, and prediction reliability. The experimental results show that the proposed method achieves excellent performance on wind speed time series prediction.

Realizing Deep High-Order TSK Fuzzy Classifier by Ensembling Interpretable Zero-Order TSK Fuzzy Subclassifiers

Although high-order Takagi–Sugeno–Kang (TSK) fuzzy systems have demonstrated their computational advantages and simultaneously circumvent the weakness that the number of rules with the number of input variables and membership functions grows exponentially in both zero-order and first-order TSK fuzzy systems for complex modeling tasks, they still face two serious issues: incapability for a changing environment and no interpretability of the coefficients in high-order polynomial used in the consequent part of each fuzzy rule. In order to circumvent these two challenges, a novel stacked architecture of an interpretable deep higher order TSK fuzzy classifier called DHO-TSK and its deep learning method are proposed by proving the equivalence between a high-order TSK fuzzy classifier and a deep ensemble of interpretable zero-order TSK fuzzy classifiers in this article. DHO-TSK can be built by assembling interpretable zero-order TSK fuzzy classifiers in a special stacked way. Each zero-order TSK fuzzy classifier can be learnt by randomly selecting input features, randomly assigning an antecedent fuzzy subset from a fixed fuzzy partition to each of the selected input features, and then multiplying the output of each TSK fuzzy classifier by a randomly selected feature. Except for the abovementioned solid theoretical equivalence, DHO-TSK is featured in the following aspects: first, the consequent part of each fuzzy rule in DHO-TSK becomes interpretable and the output expression of each layer in DHO-TSK becomes comprehensible due to the adopted stacked ensemble; second, its enhanced classification performance can be achieved in a stacked deep learning way; third, DHO-TSK has its adoptability for changing environments owing to random selection of both features and fuzzy membership functions. Our experimental results on the benchmarking UCI and KEEL datasets and a real dataset indicate the effectiveness of DHO-TSK and its learning method in the sense of both classification performance and interpretability.

Reliable Distributed Fuzzy Discretizer for Associative Classification of Big Data

Data Mining is an essential task because the digital world creates huge data daily. Associative classification is one of the data mining task which is used to carry out classification of data, based on the demand of knowledge users. Most of the associative classification algorithms are not able to analyze the big data which are mostly continuous in nature. This leads to the interest of analyzing the existing discretization algorithms which converts continuous data into discrete values and the development of novel discretizer Reliable Distributed Fuzzy Discretizer for big data set. Many discretizers suffer the problem of over splitting the partitions. Our proposed method is implemented in distributed fuzzy environment and aims to avoid over splitting of partitions by introducing a novel stopping criteria. Proposed discretization method is compared with existing distributed fuzzy partitioning method and achieved good accuracy in the performance of associative classifiers.

Continuous Fuzzy Transform as Integral Operator

The fuzzy transform (F-transform) is ubiquitous in different research fields and applications, such as image and data compression, data mining, knowledge discovery, and the analysis of linguistic expressions. As a generalization of the F-transform, in this article, we introduce the continuous F-transform and its inverse, as an integral operator induced by a kernel function. Through the relation between membership functions and integral kernels, we show that the main properties (e.g., continuity and symmetry) of the membership functions are inherited by the continuous F-transform. Then, the relation between the continuous F-transform and integral operators is used to introduce a data-driven F-transform, which encodes intrinsic information (e.g., structure, geometry, and sampling density) about the input data. In this way, we avoid coarse fuzzy partitions, which group data into large clusters that do not adapt to their local behavior, or a too dense fuzzy partition, which generally has cells that are not covered by the data, thus being redundant and resulting in a higher computational cost. To this end, the data-driven membership functions are defined by properly filtering the spectrum of the Laplace–Beltrami operator associated with the input data. Finally, we introduce the space of continuous F-transforms, which is useful for the comparison of different continuous F-transforms and for their efficient computation.

Fuzzy clustering algorithms with distance metric learning and entropy regularization

Clustering has been used in various fields, such as image processing, data mining, pattern recognition, and statistical analysis. Generally, clustering algorithms consider all variables equally relevant or not correlated. Nevertheless, the pattern of data samples in the multidimensional space can be geometrically complicated, e.g., clusters may exist in different subsets of features. In this regard, new soft subspace clustering algorithms have been proposed, in which the correlation and relevance of variables are considered to improve their performance. Since regularization-based methods are robust for initializations, the approaches proposed introduce an entropy regularization term for controlling the membership degree of the objects. Such regularizations are popular due to high performance in large-scale data clustering and low computational complexity. These three-step iterative algorithms provide a fuzzy partition, a representative for each cluster, and the relevance weight of the variables or their correlation by minimizing a suitable objective function. Several experiments on synthetic and real datasets, including their application to the segmentation of noisy image textures, demonstrate the usefulness of the proposed clustering methods.

An evolving concept in the identification of an interval fuzzy model of Wiener-Hammerstein nonlinear dynamic systems

This paper presents a new approach for identifying interval fuzzy models, which enables estimating fuzzy model structures, parameters, and upper and lower bounds simultaneously and online. It is based on a filtered recursive least squares method combined with an incrementally evolving Gaussian clustering. The proposed method generates interval fuzzy models online, on the fly, and in an evolving manner. This means that the algorithm starts with no a priori information, evolves the structure of the model, adjusts the model parameters simultaneously, and computes the upper and lower intervals simultaneously. The fuzzy partitioning of the input–output data space is based on the eGauss + method; the parameters of the local linear models, which together form the fuzzy model, are determined using a recursive least squares method. The interval fuzzy model, used in a predictive manner as a single or multi-level predictor, can be successfully applied in on-line monitoring, fault detection, and the control of dynamic systems. The proposed identification procedure was used to identify the fuzzy interval model of two different processes: a simplified Hammerstein-type nonlinear dynamic process and a realistic industrial continuously stirred tank reactor.The main contribution and advantage of the proposed new method is the identification of an interval fuzzy model in an online manner, which means that the structural and parametric identification of nonlinear systems is done simultaneously and from the data stream. The structural and parametric uncertainties are modeled and integrated into the upper and lower fuzzy models, which form the fuzzy interval in which the measured data samples of the process output are located with a certain probability. The approach is limited to processes that have Wiener-Hammerstein structures.