Missing Value Estimation Methods Research Articles

Opinion evolution and dynamic trust-driven consensus model in large-scale group decision-making under incomplete information

The shift to a new era of dealing with big data has driven continuous progress and development in computer science, artificial intelligence and machine learning. This change has led to the application of advanced techniques in the realm of decision science, particularly in the area of large-scale group decision-making (LSGDM). However, although these existing techniques have become the core of LSGDM methods, they are still limited in solving problems facing incomplete data. In addition, due to the rise of social media platforms such as Weibo, WeChat and Twitter, which build bridges for communication between decision makers (DMs), this brings new opportunities and challenges for consensus research. To address this set of issues, this study develops a consensus architecture that combines dynamic social network and opinion evolution in the context of an incomplete multi-attribute LSGDM. It is worth mentioning that the proposed consensus framework is a novel decision-making system that can be used to complete the estimation of the missing values and the consensus reaching process (CRP) by simulating the realistic decision-making scenarios. Firstly, considering the size of the trust value and the length of the path, a new trust propagation method is designed to achieve a more reliable estimation of the unknown trust value. Secondly, this paper establishes a missing value estimation method by virtue of the improved DeGroot model, which is able to obtain complete evaluation information by simulating the opinion formation process of DMs. Next, a hierarchical clustering algorithm with stronger robustness is constructed, which not only can adaptively complete the clustering process, but also integrally considers two attributes of trust and opinion similarity. In light of the above research, this study designs an opinion evolution and dynamic trust-driven consensus model, referred to as the DSN-DG-LSGDM model. Finally, the sensitivity analysis and experiments on a real dataset verify the significant superiority of the constructed DSN-DG-LSGDM model compared with the extant LSGDM consensus models.

Quantum mechanics-based missing value estimation framework for industrial data

As the importance of data-based predictive maintenance frameworks is rising, one of the emerging issues is the missing values in industrial data. Data with various missing values due to measurement sensor faults and power change issues can not only cause errors in future analyses but also lead to data shortages. Although various missing value estimation methods have been proposed to address this issue, correction methods that consider the fine uncertainty and noise of the missing values themselves have been relatively unexplored. Therefore, this study modeled missing values estimated using Gaussian progress regression by considering the fine movements and noises of data using a quantum mechanics-based stochastic differential equation and corrected them using Ito’s lemma. Estimating the missing data in this manner more closely simulates the attributes of data compared to existing estimation methods, enabling more accurate analysis. To demonstrate the excellence of the proposed framework, missing values were estimated using vehicle operation data and semiconductor manufacturing data with multiple missing values, and the estimation results were compared with those of existing algorithms.

Unit consensus cost-based approach for group decision-making with incomplete probabilistic linguistic preference relations

In group decision-making, the incomplete probabilistic linguistic preference relation (InPLPR) has been widely studied because it can flexibly reflect the decision psychology of decision makers (DMs). In addition, to help DMs revise their opinions and reach a consensus, a large number of scholars have conducted research on the consensus reaching process. Therefore, this study proposes a group consensus decision approach based on InPLPR, considering consistency, the social trust network (STN), and unit cost consensus adjustment. First, an InPLPR consistency measure formula is proposed, based on which a multi-stage missing value estimation method based on optimal consistency and STN is offered for the missing information problem in InPLPR. Thereafter, the hesitation index and unit consensus cost measurement formulas are presented for incomplete probabilistic linguistic term set. Subsequently, consensus reaching and ranking selection are performed based on the proposed unit minimum cost consensus model. Finally, a numerical example of the future development choice problem for new energy vehicle enterprises is provided to demonstrate the applicability of the decision process, and the advantages of the method are derived through comparative analysis.

A process monitoring and fault isolation framework based on variational autoencoders and branch and bound method

Nonlinear characteristic widely exists in industrial processes. Many approaches based on kernel methods and machine learning have been developed for nonlinear process monitoring. However, the fault isolation for nonlinear processes has rarely been studied in previous works. In this paper, a process monitoring and fault isolation framework is proposed for nonlinear processes using variational autoencoder (VAE) model. First, based on the probability graph model of VAE, a uniform monitoring index can be calculated by the probability density of observation variables. Then, the fault variables are estimated with normal variables by a missing value estimation method. The optimal fault variable set can be searched by branch and bound (BAB) algorithm. The proposed method can resolve the ”smearing effects” problem existing in traditional fault isolation methods. Finally, a numerical case and a hot strip mill process case are used to verified the proposed method.

Efficiency Comparison of Missing Value Estimation Methods of Response Variable for Three Factor Factorial Experiment in Randomized Complete Block Design

Efficiency Comparison of Missing Value Estimation Methods of Response Variable for Three Factor Factorial Experiment in Randomized Complete Block Design

Motif identification in vital signs of chronic patients

With the development of remote medicine, more and more programs are being opened for the remote monitoring of chronic patients. The purpose of this research is to provide maximum understanding of the patient’s condition using their vital signs collected remotely. The vital signs are presented as irregular time series. Firstly, five missing value estimation methods are used to fill gaps in data. One of the best methods is to predict missing values with an artificial neural network trained on available data. Then, we use the exact method based on the matrix profile to search for motifs in one-dimensional and two-dimensional time series. The obtained motifs can be used to monitor the patient’s condition, to assess the effectiveness of therapy or to assess the physician’s actions.

Missing Value Estimation in a Nested-Factorial Design with Three Factors

When faced with unbalanced data, it is often necessary to estimate the necessary missing values before the application of the analysis of variance technique. Previous studies have shown that different designs require different missing value estimators. With the introduction of some relatively new statistical designs, it has become expedient to derive missing value estimators for such designs. In this study, least squares estimators of missing values in a three-factor nested-factorial design are derived. Properties of the estimators are equally determined. A numerical example is given to show the application of the theoretical results obtained in this paper. Our empirical results establish the appropriateness of the missing value estimation method presented in this study.

Missing Value Estimation Methods for Data in Linear Functional Relationship Model

Missing value problem is common when analysing quantitative data. With the rapid growth of computing capabilities, advanced methods in particular those based on maximum likelihood estimation has been suggested to best handle the missing values problem. In this paper, two modern imputing approaches namely expectation-maximization (EM) and expectation-maximization with bootstrapping (EMB) are proposed in this paper for two kinds of linear functional relationship (LFRM) models, namely LFRM1 for full model and LFRM2 for linear functional relationship model when slope parameter is estimated using a nonparametric approach. The performance of EM and EMB are measured using mean absolute error, root-mean-square error and estimated bias. The results of the simulation study suggested that both EM and EMB methods are applicable to the LFRM with EMB algorithm outperforms the standard EM algorithm. Illustration using a practical example and a real data set is provided.

Automatic instance selection via locality constrained sparse representation for missing value estimation

Missing values in real application can significantly disturb the result of knowledge discovery, and it is thus vital to estimate this unknown data accurately. This paper focuses on applying sparse representation to improve the quality of estimation of the absent values. Firstly, a novel sparse representation scheme called locality constrained sparse representation (LCSR) is presented, introducing locality l1-norm and l2-norm regularization. Taking the advantage of sparsity, smoothness and locality structure, LCSR is capable of automatically selecting instance and avoiding overfitting. Then LCSR-based missing value estimation (LCSR-MVE) is proposed to estimate the unobserved values through the linear combination of automatically selected atoms from dictionary due to the sparsity in reconstruction coefficient vector, while three dictionary constructions are also developed respectively. The proposed LCSR-MVE is evaluated on 6 datasets from UCI and gene expression databases, compared with other instance-based missing value estimation methods. Results show that the proposed LCSR-MVE outperforms other state-of-arts methods in terms of normalized root mean squared error (NRMSE), and is not much sensitive to the dictionary size and regularization parameters.

A Bicluster-Based Bayesian Principal Component Analysis Method for Microarray Missing Value Estimation

Data generated from microarray experiments often suffer from missing values. As most downstream analyses need full matrices as input, these missing values have to be estimated. Bayesian principal component analysis (BPCA) is a well-known microarray missing value estimation method, but its performance is not satisfactory on datasets with strong local similarity structure. A bicluster-based BPCA (bi-BPCA) method is proposed in this paper to fully exploit local structure of the matrix. In a bicluster, the most correlated genes and experimental conditions with the missing entry are identified, and BPCA is conducted on these biclusters to estimate the missing values. An automatic parameter learning scheme is also developed to obtain optimal parameters. Experimental results on four real microarray matrices indicate that bi-BPCA obtains the lowest normalized root-mean-square error on 82.14% of all missing rates.

Syntheses and characterizations of aluminophosphate molecular sieves AFI guided by missing value estimation on database of aluminophosphate syntheses

Several experiments have been performed based on the results of four missing value estimation methods on the database of AlPO syntheses. The target products, aluminophosphate molecular sieves with AFI topology, have been prepared by using triethylamine (TEA), N,N-dimethylbenzylamine (BDMA) and N-(2-aminoethyl)-piperazine (AEP) as the structure-directing agents, and their structures have been characterized by PXRD, SEM, TG, CHN, ICP and NMR. The experimental results show that BP impute method is the most effective approach for estimation of missing data of microporous aluminophosphates. This work further indicates that data mining provides a useful guidance for the rational synthesis of inorganic microporous materials.

Missing Value Estimation for Microarray Data by Bayesian Principal Component Analysis and Iterative Local Least Squares

Missing values are prevalent in microarray data, they course negative influence on downstream microarray analyses, and thus they should be estimated from known values. We propose a BPCA-iLLS method, which is an integration of two commonly used missing value estimation methods—Bayesian principal component analysis (BPCA) and local least squares (LLS). The inferior row-average procedure in LLS is replaced with BPCA, and the least squares method is put into an iterative framework. Comparative result shows that the proposed method has obtained the highest estimation accuracy across all missing rates on different types of testing datasets.

WIMP: Web server tool for missing data imputation

The imputation of unknown or missing data is a crucial task on the analysis of biomedical datasets. There are several situations where it is necessary to classify or identify instances given incomplete vectors, and the existence of missing values can much degrade the performance of the algorithms used for the classification/recognition. The task of learning accurately from incomplete data raises a number of issues some of which have not been completely solved in machine learning applications. In this sense, effective missing value estimation methods are required. Different methods for missing data imputations exist but most of the times the selection of the appropriate technique involves testing several methods, comparing them and choosing the right one. Furthermore, applying these methods, in most cases, is not straightforward, as they involve several technical details, and in particular in cases such as when dealing with microarray datasets, the application of the methods requires huge computational resources. As far as we know, there is not a public software application that can provide the computing capabilities required for carrying the task of data imputation. This paper presents a new public tool for missing data imputation that is attached to a computer cluster in order to execute high computational tasks. The software WIMP (Web IMPutation) is a public available web site where registered users can create, execute, analyze and store their simulations related to missing data imputation.

Missing value estimation for database of aluminophosphate (AlPO) syntheses

Database of AlPO syntheses will serve as useful guidance for the rational synthesis of microporous functional materials. But the database contains missing values about 29% of total. In this paper, to deal with the problem of missing values, four missing value estimation methods (back-propagation neural networks imputes, K-nearest neighbor imputes, singular value decomposition imputes and least square imputes) are employed on database of AlPO syntheses for the first time. The efficiency and revise of estimation methods are demonstrated by normalized root mean squared error (NRMSE) and prediction accuracy. A large number of experimental results show that the estimation methods are competent for microporous aluminophosphates and the BPimpute is recommended.

Towards better accuracy for missing value estimation of epistatic miniarray profiling data by a novel ensemble approach

Epistatic miniarray profiling (E-MAP) is a powerful tool for analyzing gene functions and their biological relevance. However, E-MAP data suffers from large proportion of missing values, which often results in misleading and biased analysis results. It is urgent to develop effective missing value estimation methods for E-MAP. Although several independent algorithms can be applied to achieve this goal, their performance varies significantly on different datasets, indicating different algorithms having their own advantages and disadvantages. In this paper, we propose a novel ensemble approach EMDI based on the high-level diversity to impute missing values that consists of two global and four local base estimators. Experimental results on five E-MAP datasets show that EMDI outperforms all single base algorithms, demonstrating an appropriate combination providing complementarity among different methods. Comparison results between several fusion strategies also demonstrate that the proposed high-level diversity scheme is superior to others. EMDI is freely available at www.csbio.sjtu.edu.cn/bioinf/EMDI/.

Approximation of Missing Values in DNA Microarray Gene Expression Data

In the past few years, there has been a detonation of data in the field of biotechnology. Gene expression microarray experiments produce datasets with numerous missing expression values due to various reasons, e.g. insufficient resolution, image corruption, dust or scratches on the slides, or experimental error during the laboratory process.. To improve these missing values, many algorithms for gene expression analysis oblige a complete matrix of gene array values as input, such as K nearest neighbor impute method, Bayesian principal components analysis impute method, etc. Accurate estimation of missing values is an important requirement for efficient data analysis. Main problem of existing methods for microarray data is that there is no external information but the estimation is based exclusively on the expression data. We conjectured that utilizing a priori information on functional similarities available from public databases facilitates the missing value estimation. Robust missing value estimation methods are required since many algorithms for gene expression analysis entail a complete matrix of gene array values. Either genes with missing values can be removed, or the missing values can be replaced using prediction. Current methods for estimating the missing values include sample mean and K-nearest neighbors (KNN). Whether the accuracy of estimation methods depends on the actual gene expression has not been thoroughly investigated. Under this setting, we examine how the accuracy depends on the actual expression level and propose new method that provides improvements in accuracy relative to the current methods in certain ranges of gene expression.

Predicting incomplete gene microarray data with the use of supervised learning algorithms

Motivation With the wealth of sequence data and the huge amount of data generated from molecular technologies, the issue of gene classification/prediction has become a central challenge in the field of microarray data analysis. This has led to the application of many well-established supervised learning (SL) algorithms in an attempt to provide more accurate and automatic diagnosis class (cancer/non cancer) prediction. Virtually all research on SL addresses the task of learning to classify complete domain instances. However, in some research situations we often have to classify instances given incomplete vectors, which can affect the predictive accuracy of learned classifiers. The task of learning an accurate incomplete data classifier from instances raises a number of new issues some of which have not been properly addressed by bioinformatics research. Thus, an effective missing value estimation method is required for improving predictive accuracy. Results The essence of the approach is the proposal that prediction using supervised learning can be improved in probabilistic terms given incomplete microarray data. This imputation approach is based on the a priori probability of each value determined from the instances at that node of a decision tree (PDT) that have specified values. The proposed approach exploits the total probability and Bayes’ theorems and it has three versions. We evaluate our approach with other supervised learning techniques including C5.0, classification and regression trees (CART), k-nearest neighbour ( k-NN), linear discrimination (LD) naïve Bayes classifier (NBC), Repeated Incremental Pruning to Produce Error Reduction (RIPPER) and support vector machines (SVMs), from the point of view of their effect or tolerance of incomplete test data. Eight cancer related gene expression datasets are utilized for this task. Experimental results are provided to illustrate the efficiency and the robustness of the proposed algorithm.

Autoregressive-Model-Based Missing Value Estimation for DNA Microarray Time Series Data

Missing value estimation is important in DNA microarray data analysis. A number of algorithms have been developed to solve this problem, but they have several limitations. Most existing algorithms are not able to deal with the situation where a particular time point (column) of the data is missing entirely. In this paper, we present an autoregressive-model-based missing value estimation method (ARLSimpute) that takes into account the dynamic property of microarray temporal data and the local similarity structures in the data. ARLSimpute is especially effective for the situation where a particular time point contains many missing values or where the entire time point is missing. Experiment results suggest that our proposed algorithm is an accurate missing value estimator in comparison with other imputation methods on simulated as well as real microarray time series datasets.

Microarray missing values imputation methods: Critical analysis review

Gene expression data often contain missing expression values. For the purpose of conducting an effective clustering analysis and since many algorithms for gene expression data analysis require a complete matrix of gene array values, choosing the most effective missing value estimation method is necessary. In this paper, the most commonly used imputation methods from literature are critically reviewed and analyzed to explain the proper use, weakness and point the observations on each published method. From the conducted analysis, we conclude that the Local Least Square (LLS) and Support Vector Regression (SVR) algorithms have achieved the best performances. SVR can be considered as a complement algorithm for LLS especially when applied to noisy data. However, both algorithms suffer from some deficiencies presented in choosing the value of Number of Selected Genes (K) and the appropriate kernel function. To overcome these drawbacks, the need for new method that automatically chooses the parameters of the function and it also has an appropriate computational complexity is imperative.

Integrative missing value estimation for microarray data.

BackgroundMissing value estimation is an important preprocessing step in microarray analysis. Although several methods have been developed to solve this problem, their performance is unsatisfactory for datasets with high rates of missing data, high measurement noise, or limited numbers of samples. In fact, more than 80% of the time-series datasets in Stanford Microarray Database contain less than eight samples.ResultsWe present the integrative Missing Value Estimation method (iMISS) by incorporating information from multiple reference microarray datasets to improve missing value estimation. For each gene with missing data, we derive a consistent neighbor-gene list by taking reference data sets into consideration. To determine whether the given reference data sets are sufficiently informative for integration, we use a submatrix imputation approach. Our experiments showed that iMISS can significantly and consistently improve the accuracy of the state-of-the-art Local Least Square (LLS) imputation algorithm by up to 15% improvement in our benchmark tests.ConclusionWe demonstrated that the order-statistics-based integrative imputation algorithms can achieve significant improvements over the state-of-the-art missing value estimation approaches such as LLS and is especially good for imputing microarray datasets with a limited number of samples, high rates of missing data, or very noisy measurements. With the rapid accumulation of microarray datasets, the performance of our approach can be further improved by incorporating larger and more appropriate reference datasets.