Membership Vector Research Articles

Designing function-specific minimal microbiomes from large microbial communities

Microorganisms exist in large communities of diverse species, exhibiting various functionalities. The mammalian gut microbiome, for instance, has the functionality of digesting dietary fibre and producing different short-chain fatty acids. Not all microbes present in a community contribute to a given functionality; it is possible to find a minimal microbiome, which is a subset of the large microbiome, that is capable of performing the functionality while maintaining other community properties such as growth rate and metabolite production. Such a minimal microbiome will also contain keystone species for SCFA production in that community. In this work, we present a systematic constraint-based approach to identify a minimal microbiome from a large community for a user-proposed function. We employ a top-down approach with sequential deletion followed by solving a mixed-integer linear programming problem with the objective of minimising the L1-norm of the membership vector. Notably, we consider quantitative measures of community growth rate and metabolite production rates. We demonstrate the utility of our algorithm by identifying the minimal microbiomes corresponding to three model communities of the gut, and discuss their validity based on the presence of the keystone species in the community. Our approach is generic, flexible and finds application in studying a variety of microbial communities. The algorithm is available from https://github.com/RamanLab/minMicrobiome.

Enterprise Credit Risk Decision: Application Based on Improved AHP

The credit risk of Shouguang vegetable enterprises in China is the biggest obstacle to corporate loans. Building a credit risk assessment model for Shouguang vegetable enterprises and accurately rating the risk of loan enterprises is the key to successful loans. This article aims to construct an AHP evaluation model for the credit risk of Shouguang vegetable enterprises. The data is sourced from managers, bank credit personnel, university researchers, and enterprise related customers who are familiar with the enterprise, while considering four risk levels: impact degree(I), occurrence probability(P), risk manageability(M), and government support(S). This article uses AHP and risk index scores to evaluate the credit risk of Shouguang vegetable enterprises. This model calculates the risk index score based on survey data from 41 corporate credit risk professionals, constructs a pairwise comparison judgment matrix, and conducts consistency testing. It calculates the risk level membership vectors of impact degree, occurrence probability, risk manageability, and government support level at four risk levels, and then calculates the comprehensive evaluation membership vector of credit risk for Shouguang vegetable enterprise. The calculation results show that the comprehensive credit risk assessment level of Shouguang vegetable enterprise belongs to the general risk level, with a membership value of 0.5836. The results still show that the credit rating of Shouguang vegetable enterprises in the four risk levels of impact degree, occurrence probability, risk manageability, and government support are all average risk levels, but there are differences in membership values. The maximum membership value under the impact degree level is 0.6163, and the minimum membership value under the risk manageability level is 0.5572. This study provides a feasible and practical model for enterprise credit risk assessment and conducts a detailed evaluation of the credit risk of Shouguang vegetable enterprise, providing valuable reference for enterprise managers, bank credit personnel, and related researchers.

Shared style linear k nearest neighbor classification method

While previous linear k nearest neighbor methods have demonstrated strong generalization capability for ordinary datasets, they often fail to achieve comparable generalization capability when applied to stylistic datasets due to the unique characteristics of this type of datasets. Additionally, when multiple testing samples share a certain style characteristic, both the traditional k nearest neighbor method and evolved versions of the linear k nearest neighbor method tend to ignore the shared style in the testing sample set, leading to inefficient utilization of information resources. In order to address these issues, we propose a new classification method called Shared Style Linear kNearest Neighbor (SSL-KNN), which enhances the generalization capability of the linear k nearest neighbor method on stylistic datasets. The proposed method is motivated by the observation that one can better determine the class of a collection of homogeneous samples by evaluating their overall style, rather than simply aggregating individual sample judgments. The proposed method achieves this goal and two additional goals: a) we obtain the style membership vectors of the testing samples with different classes of the training samples in order to seek a guarantee of the generalization capability on the stylistic datasets; b) we introduce a Gaussian kernel distance metric constraining the linear expression weights in order to seek a guarantee of the generalization capability on the ordinary datasets. Furthermore, we propose an alternating optimization strategy implemented to optimize the proposed SSL-KNN method. Finally, we evaluate the proposed method and the comparative methods on 15 benchmark datasets containing both ordinary and stylistic datasets. The results show that the proposed SSL-KNN method guarantees good generalization capability on both ordinary and stylistic datasets.

Style linear k-nearest neighbor classification method

Most studies on linear k-nearest neighbor methods assume independent and identically distributed training and testing samples. However, this is not the case in many practical applications, particularly when each class shares a homogeneous style. We propose a novel style linear k-nearest neighbor method to achieve two goals: (a) the linear k-nearest neighbor method should mine the stylistic data for explicit or implicit stylistic features while obtaining linear expressions and effectively transfer them to the predictor through matrix expressions; (b) the similarity of stylistic features between testing and training samples should be numerically quantified to enhance the generalizability of the predictor. To this end, firstly we introduce style matrices to express the style information of each class. In order to prevent the style matrices from degenerating into identity matrices, we introduce enhanced nodes to separate the manifold structure of the original data. The dual representation of matrix and enhanced nodes makes it easy to extract stylistic features from data. Furthermore, we introduce the style membership vector for the first time in the linear k-nearest neighbor method to calculate the style similarity of testing samples to each class, and determine the labels of testing samples easily and accurately through the style membership vector. We also propose an implementable alternating optimization strategy for the proposed method, which decomposes the complex optimization problem into independent subproblems for easy implementation. The experimental results demonstrate that the proposed method keeps comparable generalization capability on the total 9 ordinary datasets. And it outperforms the comparative methods, and even achieving 9.76 % improvement of average testing accuracy over the state-of-the-art weighted locally linear k-nearest neighbor method on the total 6 stylistic datasets.

Sustainable development, eco-tourism carrying capacity and fuzzy algorithm-a study on Kanas in Belt and Road

In this paper, the method of fuzzy pattern recognition is adopted in more precisely evaluating the actual state of eco-tourism development regarding a given tourist destination in comparison with the three standard patterns (saturated/optimal/deficient) of development degree. The research process is as follows: Firstly, the indictors of carrying capacity of a tourist destination and the corresponding measuring factors are established; secondly, an assessment group is recruited to work out the most constraining factors among the measuring factors; thirdly, by means of field survey, numerical values of the actual state are acquired; fourthly, there comes out the membership vectors and the membership matrix of the standard patterns corresponding to the vectors of three standard patterns, threshold and the actual state; Finally, it could be identified which standard pattern that the actual state is closest to via the lattice degrees of proximity. An exemplary case study on Kanas National Nature Reserves is attached to the logic calculus. This paper is contributed to dynamically monitor the threshold of tourism carrying capacity and precisely identify which carrying capacity (spatial resource/ecological environment/economic resources/people’s psychology/socio-culture) with potential risks.

A risk source identification model for network security of power CPS system (CPS) based on fuzzy artificial neural network

In order to improve the effect and accuracy of risk source identification, this paper studied the network security risk source identification model of power CPS system based on fuzzy artificial neural network. The network security risk source index system of power CPS system was constructed, and the dimension of index data was reduced by principal component analysis. Fuzzy theory is used to process the index data after dimension reduction, and the comprehensive membership vector of each index is obtained. The dynamic clustering algorithm is used to determine the number of hidden layer units of radial basis function neural network, and the network security risk source identification model is established. Finally, the quantitative value of risk source identification is output. The experimental results show that the model can effectively reduce the dimension of the network security risk source index data of the power CPS system. The optimal distance threshold of the hidden layer is 4.2, and the optimal number of units is 6. In the final identification results, four severe risk sources and five moderate risk sources were obtained, and the quantitative values of risk source identification of each index were 63, 70, 71, 77, 65, 89 and 96, respectively, indicating that the model can effectively identify network security risk sources of power CPS systems. With the increase of the proportion of communication nodes removed, when there are various types of security vulnerability information, the mean square error value of the model is always lower than the set threshold, indicating that the model has high recognition accuracy.

Device Health Status Assessment Under the Influence of Multiple Exception Modes

Equipment reliability is the key feature to ensure the equipment operation for a long time. It is difficult to determine the overall reliability of industrial equipment due to the different reliability states of different subsystems. A device abnormality identification method based on JS (Jenson's Shannon) divergence and a health status assessment technology based on FMECA (failure mode, effect and criticality analysis) are proposed. This method enables an accurate assessment of the current health status of the device. First, the historical operation data is preprocessed according to the characteristics of the equipment to improve the data quality. The JS divergence method is reused to extract the similarity between the key feature data distribution and the benchmark data distribution. Then, the FMECA report is established using the real running data of the device combined with expert experience. Gray theory was used to determine the degree of association between one-way health state membership vector and different health state rank vector. Finally, the health status level was comprehensively evaluated by the fuzzy membership method. Taking the mechanical arm component of a 100-ton crane as an example, the results show that this method can effectively evaluate the current health state of the equipment, and provide power for the abnormal advance disposal and auxiliary management decisions.

Power enhancement and phase transitions for global testing of the mixed membership stochastic block model

The mixed-membership stochastic block model (MMSBM) is a common model for social networks. Given an n-node symmetric network generated from a K-community MMSBM, we would like to test K=1 versus K>1. We first study the degree-based χ2 test and the orthodox Signed Quadrilateral (oSQ) test. These two statistics estimate an order-2 polynomial and an order-4 polynomial of a “signal” matrix, respectively. We derive the asymptotic null distribution and power for both tests. However, for each test, there exists a parameter regime where its power is unsatisfactory. It motivates us to propose a power enhancement (PE) test to combine the strengths of both tests. We show that the PE test has a tractable null distribution and improves the power of both tests. To assess the optimality of PE, we consider a randomized setting, where the n membership vectors are independently drawn from a distribution on the standard simplex. We show that the success of global testing is governed by a quantity βn(K,P,h), which depends on the community structure matrix P and the mean vector h of memberships. For each given (K,P,h), a test is called optimal if it distinguishes two hypotheses when βn(K,P,h)→∞. A test is called optimally adaptive if it is optimal for all (K,P,h). We show that the PE test is optimally adaptive, while many existing tests are only optimal for some particular (K,P,h), hence, not optimally adaptive.

Regularized spectral clustering under the mixed membership stochastic block model

Mixed membership community detection is a challenging problem in network analysis. Previous spectral clustering algorithms for this problem are developed based on the adjacency matrix instead of regularized Laplacian matrix. To close this gap, under the popular mixed membership stochastic blockmodels (MMSB), this article proposes two efficient spectral clustering algorithms based on an application of the regularized Laplacian matrix, the Simplex Regularized Spectral Clustering (SRSC) algorithm, and the Cone Regularized Spectral Clustering (CRSC) algorithm. SRSC and CRSC are developed based on the simplex structure and the cone structure in the variants of the eigendecomposition of the regularized Laplacian matrix. We show that these two approaches SRSC and CRSC are asymptotically consistent under mild conditions by providing error bounds for the estimated membership vector of each node under MMSB. These two proposed approaches are successfully applied to synthetic and empirical networks with encouraging results compared with some benchmark methods.

Mixed membership estimation for social networks

In economics and social science, network data are regularly observed, and a thorough understanding of the network community structure facilitates the comprehension of economic patterns and activities. Consider an undirected network with n nodes and K communities. We model the network using the Degree-Corrected Mixed-Membership (DCMM) model, where for each node i=1,2,…,n, there exists a membership vector πi=(πi(1),πi(2),…,πi(K))′, where πi(k) is the weight that node i puts on community k, 1≤k≤K. In comparison to the well-known stochastic block model (SBM), the DCMM permits both severe degree heterogeneity and mixed memberships, making it more realistic and general. We present an efficient approach, Mixed-SCORE, for estimating the mixed membership vectors of all nodes and the other DCMM parameters. This approach is inspired by the discovery of a delicate simplex structure in the spectral domain. We derive explicit error rates for the Mixed-SCORE algorithm and demonstrate that it is rate-optimal over a broad parameter space. Our findings provide a novel statistical tool for network community analysis, which can be used to understand network formations, extract nodal features, identify unobserved covariates in dyadic regressions, and estimate peer effects. We applied Mixed-SCORE to a political blog network, two trade networks, a co-authorship network, and a citee network, and obtained interpretable results.

Uncertainty Based Optimal Sample Selection for Big Data

In Machine learning and pattern recognition, building a better predictive model is one of the key problems in the presence of big or massive data; especially, if that data contains noisy and unrepresentative data samples. These types of samples adversely affect the learning model and may degrade its performance. To alleviate this problem, sometimes, it becomes necessary to sample the data after eliminating unnecessary instances by maintaining the underlying distribution intact. This process is called sampling or instance selection (IS). However, in this process, a substantial computational cost is involved. This paper discusses an uncertainty based optimal sample selection (UBOSS) method which can select a subset of optimal samples efficiently. Our proposed work comprises three main steps; initially, it uses an IS method to identify the patterns of representative and unrepresentative samples from the original data set; then, an uncertainty-based selector is designed to obtain fuzziness (i.e., a type of uncertainty) of those samples using a classifier whose output is a membership or fuzzy vector; this process further utilizes the divide-and-conquer strategy to obtain a subset of representative samples. Experiments are conducted on six datasets to evaluate the performance of the proposed IS method. Results show that our proposed methodology outperforms when compared with the selection performance (i.e., optimum samples) of the baseline methods (i.e., CNN, IB3, and DROP3).

A Method of Power Supply Health State Estimation Based on Grey Clustering and Fuzzy Comprehensive Evaluation

Health state estimation can evaluate the current degradation state of equipment, and the evaluation results can provide a basis for formulating equipment maintenance strategies. At present, in the research on health state estimation, only one level of indicators of the equipment is usually considered, meaning incomplete estimation results. In addition, the current evaluation methods rarely consider the impact of data noise on the evaluation results, which can easily lead to abnormal evaluation results. To solve the above two problems, this paper first introduces the state indicators such as ripple voltage and output voltage, as well as the ratio of theoretical use time into the evaluation indicators. Furthermore, a health state estimation method combining grey clustering and fuzzy comprehensive evaluation methods is established. This method can consider the characteristics of multiple data groups at the same time, thus the impact of data noise on the evaluation results can be reduced. During the evaluation, the grey clustering method is used to evaluate the clustering coefficient vector of the power supply under a single group of data. After that, the clustering coefficient vector of multiple groups of data is used as the membership vector of fuzzy comprehensive evaluation, and the fuzzy comprehensive evaluation method is used to evaluate the health state of a power supply under multiple groups of data. An example shows that this method is effective in estimating the health state of a normally degraded power supply.

Characterization of Nested Lattice Codes Through Quotient Groups Relative to Normal Fuzzy Subgroups for Channel Quantization

Interference is in general, an undesirable obstacle to communication in wireless communication networks. Therefore, in order to realize interference alignment, this work intends to characterize classical codes through the framework of fuzzy set theory for quantizing real-valued channel coefficients. Thenceforward, from the classical framework nested real lattice codes are constructed by using construction A of nested real ideal lattices and, therefore, through normal fuzzy subgroups this work shows that the constructed quotient groups of the nested real ideal lattices relative to normal fuzzy subgroups of these nested real ideal lattices are nested vector spaces and, consequently, such nested quotient groups have the structure of a linear code, are isomorphic to the nested real lattice codes and defined by linear fuzzy codes. Through such an isomorphism and the construction of the nested quotient groups relative to normal fuzzy subgroups, it is possible to conclude that the codewords of these nested linear fuzzy codes are in a one-to-one correspondence to membership vectors. Through the constructed nested quotient groups, that is, nested linear fuzzy codes, this work supplies how to quantize real-valued channel coefficients onto these nested quotient groups in order to realize interference alignment and, consequently, it is possible to encode an arbitrary real-valued channel coefficient by a codeword from a linear fuzzy code.

Geometric consistent fuzzy cluster ensemble with membership reconstruction for image segmentation

In recent years, to handle the ubiquitous uncertainty and unknown noise, different fuzzy clustering methods have been introduced to solve image segmentation problem for various applications, such as natural image, satellite image, multichannel (typically remote sensing) image. In fact, it is hard to know which one is the best for specified task. Cluster ensemble method is proposed to solve the problem of choosing a particular fuzzy clustering algorithm, or a special image processing before clustering, that best suits the given image segmentation task. In fuzzy cluster ensemble, membership vectors generated from different fuzzy clustering methods are merged into one vector as an input object, which is also a combination of data partitions. However, this kind of input object may lose detail information from original target image and may cause inaccurate edges in segmentation results. Moreover, by means of treating it as a new representation of original data, the membership vector of fuzzy cluster ensemble should be intuitively geometric consistent with the original target image. In this paper, by holding this view, we develop a geometric consistent fuzzy cluster ensemble model for spatial data, which involves a constraint between the membership and its reconstruction, to improve the clustering performance on image segmentation. In the proposed model, a pre-determined gradient-preserving weight is used in the membership reconstruction item to make the membership matrix be geometric consistent with the original target image. A semi-implicit optimization iterative algorithm is adopted to solve the proposed geometric consistent model. Experimental results demonstrate the effectiveness of proposed model in synthetic and real-world image segmentation problems over several state-of-the-art methods.

Risk Assessment of an Existing Metro Tunnel in Close Proximity to New Shield Tunnels following Construction

The construction of a new shield tunnel near an existing operating tunnel poses a great risk to the existing tunnel structure due to the continuous encryption of the rail transit network. This study investigated the safety status of an existing metro tunnel in close proximity to new shield tunnels following construction. A fuzzy comprehensive assessment model (hierarchical fuzzy comprehensive evaluation model) based on an analytic hierarchy process was proposed to assess the risks of the existing tunnel structure. The threshold of indicators in the existing tunnel structure risk assessment system was determined based on the tunnel function and structure security. Then, we described the membership vector determination method, weight vector determination method, and comprehensive evaluation vector processing method. Taking a project case in China as the research object, the quantitative analysis of the established evaluation system was carried out, and the intuitive risk assessment results were obtained. The hierarchical fuzzy comprehensive evaluation model can be employed as a decision-making tool for newly built shield tunnels passing through the existing tunnels, which can provide guidance for tunnel maintenance and guarantee.

FSTruct: An FST -based tool for measuring ancestry variation in inference of population structure.

In model‐based inference of population structure from individual‐level genetic data, individuals are assigned membership coefficients in a series of statistical clusters generated by clustering algorithms. Distinct patterns of variability in membership coefficients can be produced for different groups of individuals, for example, representing different predefined populations, sampling sites or time periods. Such variability can be difficult to capture in a single numerical value; membership coefficient vectors are multivariate and potentially incommensurable across predefined groups, as the number of clusters over which individuals are distributed can vary among groups of interest. Further, two groups might share few clusters in common, so that membership coefficient vectors are concentrated on different clusters. We introduce a method for measuring the variability of membership coefficients of individuals in a predefined group, making use of an analogy between variability across individuals in membership coefficient vectors and variation across populations in allele frequency vectors. We show that in a model in which membership coefficient vectors in a population follow a Dirichlet distribution, the measure increases linearly with a parameter describing the variance of a specified component of the membership vector and does not depend on its mean. We apply the approach, which makes use of a normalized F ST statistic, to data on inferred population structure in three example scenarios. We also introduce a bootstrap test for equivalence of two or more predefined groups in their level of membership coefficient variability. Our methods are implemented in the r package FSTruct.

Spatial Assessment of Water River Pollution Using the Stochastic Block Model: Application in Different Station in the Litani River, Lebanon

Water pollution is a major global environmental problem. In Lebanon, water pollution threatens public health and biological diversity. In this work, a non-classical classification method was used to assess water pollution in a Mediterranean River. A clustering proposal method based on the stochastic block model (SBM) was used as an application on physicochemical parameters in three stations of the Litani River to regroup these parameters in different clusters and identify the evolution of the physicochemical parameters between the stations. Results showed that the used method gave advanced findings on the distribution of parameters between inter and intra stations. This was achieved by calculating the estimated connection matrices between the obtained clusters and the probability vector of belonging of the physicochemical parameters to each cluster in the different stations. In each of the three stations, the same two clusters were obtained, the difference between them was in the estimated connection matrices and the estimated cluster membership vectors. The power of SBM proposed methods is demonstrated in simulation studies and a new real application to the sampling physicochemical parameters in Litani River. First, we compare the proposed method to the classical principal component analysis (PCA) method then to the Hierarchical and the K-means clustering methods. Results showed that these classical methods gave the same two clusters as the proposed method. However, unlike the proposed SBM method, classical approaches are not able to show the blocks structure of the three stations.

Risk Management of Prefabricated Building Construction Based on Fuzzy Neural Network

With the rapid development of society, the risk management of personal health and assets has become an important content that cannot be ignored in all walks of life. With the in-depth advancement of risk management, most of the construction risks of prefabricated buildings adopt qualitative research based on experience and intuitive judgment and quantitative research on quantitative mathematical statistics, but there are few models for risk assessment of prefabricated buildings with dynamic characteristics to adapt to the rapid development of prefabricated buildings and the lack of prefabricated construction in various stages and complex environments, with risk prediction and effective response capabilities. Based on this, this paper attempts to propose a fuzzy neural network risk research method for prefabricated building construction, making full use of the fuzzy neural network’s qualitative knowledge expression and quantitative numerical computing advantages, to establish a set of strong fault tolerance and better adaptive ability: fuzzy neural network evaluation model for extensive prefabricated building construction risk. Through the design of the fuzzy network model structure, the membership vector of the qualitative and quantitative indicators of the fuzzy comprehensive evaluation of the risk of prefabricated building construction is used as the input vector of the neural network, and the evaluation result is used as the output of the neural network. The samples were trained, programmed, and debugged, and it was found that the training results of the samples were in good agreement with the expected output results, which further verified the feasibility and applicability of the fuzzy neural network in the risk assessment process of prefabricated buildings. It is of good guiding significance to conduct continuous observation and formulate effective risk aversion and response plans.

Regression-based heterogeneity analysis to identify overlapping subgroup structure in high-dimensional data.

Heterogeneity is a hallmark of complex diseases. Regression-based heterogeneity analysis, which is directly concerned with outcome-feature relationships, has led to a deeper understanding of disease biology. Such an analysis identifies the underlying subgroup structure and estimates the subgroup-specific regression coefficients. However, most of the existing regression-based heterogeneity analyses can only address disjoint subgroups; that is, each sample is assigned to only one subgroup. In reality, some samples have multiple labels, for example, many genes have several biological functions, and some cells of pure cell types transition into other types over time, which suggest that their outcome-feature relationships (regression coefficients) can be a mixture of relationships in more than one subgroups, and as a result, the disjoint subgrouping results can be unsatisfactory. To this end, we develop a novel approach to regression-based heterogeneity analysis, which takes into account possible overlaps between subgroups and high data dimensions. A subgroup membership vector is introduced for each sample, which is combined with a loss function. Considering the lack of information arising from small sample sizes, an norm penalty is developed for each membership vector to encourage similarity in its elements. A sparse penalization is also applied for regularized estimation and feature selection. Extensive simulations demonstrate its superiority over direct competitors. The analysis of Cancer Cell Line Encyclopedia data and lung cancer data from The Cancer Genome Atlas show that the proposed approach can identify an overlapping subgroup structure with favorable performance in prediction andstability.

Semantic-Based Multi-Keyword Ranked Search Schemes over Encrypted Cloud Data

Traditional searchable encryption schemes construct document vectors based on the term frequency-inverse document frequency (TF-IDF) model. Such vectors are not only high-dimensional and sparse but also ignore the semantic information of the documents. The Sentence Bidirectional Encoder Representations from Transformers (SBERT) model can be used to train vectors containing document semantic information to realize semantic-aware multi-keyword search. In this paper, we propose a privacy-preserving searchable encryption scheme based on the SBERT model. The SBERT model is used to train vectors containing the semantic information of documents, and these document vectors are then used as input to the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) clustering algorithm. The HDBSCAN algorithm generates a soft cluster membership vector for each document. We treat each cluster as a topic, and the vector represents the probability that the document belongs to each topic. According to the clustering process in the schemes, the topic-term frequency-inverse topic frequency (TTF-ITF) model is proposed to generate keyword topic vectors. Through the SBERT model, searchable encryption scheme can achieve more precise semantic-aware keyword search. At the same time, the special index tree is used to improve search efficiency. The experimental results on real datasets prove the effectiveness of our scheme.