构造性覆盖下不完整数据修正填充方法

不完整数据处理是数据挖掘、机器学习等领域中的重要问题,缺失值填充是处理不完整数据的主流方法。当前已有的缺失值填充方法大多运用统计学和机器学习领域的相关技术来分析原始数据中的剩余信息,从而得到较为合理的值来替代缺失部分。缺失值填充大致可以分为单一填充和多重填充,这些填充方法在不同的场景下有着各自的优势。但是,很少有方法能进一步考虑样本空间分布中的邻域信息,并以此对缺失值的填充结果进行修正。鉴于此,本文提出了一种可广泛应用于诸多现有填充方法的框架用以提升现有方法的填充效果,该框架由预填充、空间邻域信息挖掘和修正填充三部分构成。本文对7种填充方法在8个UCI数据集上进行了实验,实验结果验证了本文所提框架的有效性和鲁棒性。     

基于EM和贝叶斯网络的丢失数据填充算法

实际应用中存在大量的丢失数据的数据集,对丢失数据的处理已成为目前分类领域的研究热点。分析和比较了几种通用的丢失数据填充算法,并提出一种新的基于EM和贝叶斯网络的丢失数据填充算法。算法利用朴素贝叶斯估计出EM算法初值,然后将EM和贝叶斯网络结合进行迭代确定最终更新器,同时得到填充后的完整数据集。实验结果表明,与经典填充算法相比,新算法具有更高的分类准确率,且节省了大量开销。     

异常信息的智能分类算法研究

信息处理过程中对异常信息的智能化处理是一个前沿的且富有挑战性的研究方向;针对所获取的信息由于噪声干扰等因素存在缺失这一异常现象,提出了一种不完整(缺失)数据的智能分类算法;对于某一个不完整样本,该方法首先根据找到的近邻类别信息得到单个或多个版本的估计样本,这样在保证插补的准确性的同时能够有效地表征由于缺失引起的不精确性,然后用分类器分类带有估计值的样本;最后,在证据推理框架下提出一种新的信任分类方法,将难以划分类别的样本分配到对应的复合类来描述由于缺失值引起的样本类别的不确定性,同时降低错误分类的风险;用UCI数据库的真实数据集来验证算法的有效性,实验结果表明该算法能够有效地处理不完整数据分类问题.     

An embedded imputation method via Attribute-based Decision Graphs

The performance of classification algorithms is highly dependent on the quality of training data. Missing attribute values are quite common in many real world applications, thus, in such cases, a complementary method to improve the quality of the data and, consequently, promote enhancements of the classifier performance, is necessary. To deal with this problem, two strategies are commonly employed in practice, 1) multiple imputation, which often maintains the statistical properties of the original data and, usually, has good performance, at the expense of high computational costs; 2) single imputation, which, in general, provides a suitable solution for data sets with a few missing attribute values, but hardly achieve good results when the number of missing values is high. This paper proposes a new single imputation method which uses Attribute-based Decision Graphs (AbDG) to estimate the missing values. AbDGs are a new type of data graphs which embed the information contained in the training set into a graph structure, built over pre-defined intervals of values from different attributes. As a consequence, similar data instances induce similar subgraphs when projected onto the AbDG, resulting in distinct patterns of connections. The main contribution of the paper is the proposal of a well-defined procedure to perform imputation, by partially matching instances with missing values against the AbDG. The proposed imputation method can effectively deal with data sets having high rates of missing attribute values while presenting low computational cost; a significant result towards the development of robust expert and intelligent systems. The obtained results show evidences that the proposed method is sound and promote qualitative imputation for classification purposes.     

基于AP聚类的不完整大数据填充

不完整数据的分析与填充一直是大数据处理的热点研究课题,传统的分析方法无法对不完整数据直接聚类,大部分方法先填充缺失值,然后对数据聚类。这些方法一般利用整个数据集对缺失数据进行填充,使得填充值容易受到噪声的干扰,导致填充结果不精确,进而造成聚类精度很低。提出一种不完整数据聚类算法,对不完全信息系统的相似度公式进行重新定义,给出不完整数据对象间的相似度度量方式,进而直接对不完整数据聚类。根据聚类结果将同一类对象划分到相同的簇中,通过同一类对象的属性值对缺失值进行填充,避免噪声对填充值的干扰,提高填充结果的精确性。实验结果表明,提出的方法能够对不完整数据进行聚类,并有效提高缺失数据的填充精度。     

顺序敏感的多源感知数据填补技术

近年来,随着感知网络的广泛应用,感知数据呈爆炸式增长.但是由于受到硬件设备的固有限制、部署环境的随机性以及数据处理过程中的人为失误等多方面因素的影响,感知数据中通常包含大量的缺失值.而大多数现有的上层应用分析工具无法处理包含缺失值的数据集,因此对缺失数据进行填补是不可或缺的.目前也有很多缺失数据填补算法,但在缺失数据较为密集的情况下,已有算法的填补准确性很难保证,同时未考虑填补顺序对填补精度的影响.基于此,提出了一种面向多源感知数据且顺序敏感的缺失值填补框架OMSMVI（order-sensitive missing value imputation framework for multi-source sensory data）.该框架充分利用感知数据特有的多维度相关性：时间相关性、空间相关性、属性相关性,对不同数据源间的相似度进行衡量;进而,基于多维度相似性构建以缺失数据源为中心的相似图,并将已填补的缺失值作为观测值用于后续填补过程中.同时考虑缺失数据源的整体分布,提出对缺失值进行顺序敏感的填补,即：首先对缺失值的填补顺序进行决策,再对缺失值进行填补.对缺失值进行顺序填补能够有效缓解在缺失数据较为密集的情况下,由于缺失数据源的完整近邻与其相似度较低引起的填补精度下降问题;最后,对KNN填补算法进行改进,提出一种新的基于近邻节点的缺失值填补算法NI（neighborhood-based imputation）,该算法利用感知数据的多维度相似性对缺失数据源的所有近邻节点进行查找,解决了KNN填补算法K值难以确定的问题,也进一步提高了填补准确性.利用两个真实数据集,并与基本填补算法进行对比,验证了算法的准确性及有效性.     

Data preprocessing issues for incomplete medical datasets

While there is an ample amount of medical information available for data mining, many of the datasets are unfortunately incomplete – missing relevant values needed by many machine learning algorithms. Several approaches have been proposed for the imputation of missing values, using various reasoning steps to provide estimations from the observed data. One of the important steps in data mining is data preprocessing, where unrepresentative data is filtered out of the data to be mined. However, none of the related studies about missing value imputation consider performing a data preprocessing step before imputation. Therefore, the aim of this study is to examine the effect of two preprocessing steps, feature and instance selection, on missing value imputation. Specifically, eight different medical‐related datasets are used, containing categorical, numerical and mixed types of data. Our experimental results show that imputation after instance selection can produce better classification performance than imputation alone. In addition, we will demonstrate that imputation after feature selection does not have a positive impact on the imputation result.     

Can k-NN imputation improve the performance of C4.5 with small software project data sets? A comparative evaluation

Missing data is a widespread problem that can affect the ability to use data to construct effective prediction systems. We investigate a common machine learning technique that can tolerate missing values, namely C4.5, to predict cost using six real world software project databases. We analyze the predictive performance after using the k-NN missing data imputation technique to see if it is better to tolerate missing data or to try to impute missing values and then apply the C4.5 algorithm. For the investigation, we simulated three missingness mechanisms, three missing data patterns, and five missing data percentages. We found that the k-NN imputation can improve the prediction accuracy of C4.5. At the same time, both C4.5 and k-NN are little affected by the missingness mechanism, but that the missing data pattern and the missing data percentage have a strong negative impact upon prediction (or imputation) accuracy particularly if the missing data percentage exceeds 40%.     

基于灰色关联分析的缺失值重复填补方法

缺失填补是机器学习与数据挖掘领域中极富有挑战性的工作。数据源中的缺失值会对学习算法的性能与学习的质量产生较大的负面影响。目前存在的缺失值填补方法还不能满足用户的需要。提出了一种基于灰色系统理论的缺失值填补方法,该方法采用了基于实例学习的非参拟合和灰色理论技术,对缺失数据进行重复填补,直至填补结果收敛或者满足用户的需要。实验结果表明,该方法在填补效果与效率方面都比现有的KNN填补法和普通的均值替代法要好。     

Missing data analyses: a hybrid multiple imputation algorithm using Gray System Theory and entropy based on clustering

Researchers and practitioners who use databases usually feel that it is cumbersome in knowledge discovery or application development due to the issue of missing data. Though some approaches can work with a certain rate of incomplete data, a large portion of them demands high data quality with completeness. Therefore, a great number of strategies have been designed to process missingness particularly in the way of imputation. Single imputation methods initially succeeded in predicting the missing values for specific types of distributions. Yet, the multiple imputation algorithms have maintained prevalent because of the further promotion of validity by minimizing the bias iteratively and less requirement on prior knowledge to the distributions. This article carefully reviews the state of the art and proposes a hybrid missing data completion method named Multiple Imputation using Gray-system-theory and Entropy based on Clustering (MIGEC). Firstly, the non-missing data instances are separated into several clusters. Then, the imputed value is obtained after multiple calculations by utilizing the information entropy of the proximal category for each incomplete instance in terms of the similarity metric based on Gray System Theory (GST). Experimental results on University of California Irvine (UCI) datasets illustrate the superiority of MIGEC to other current achievements on accuracy for either numeric or categorical attributes under different missing mechanisms. Further discussion on real aerospace datasets states MIGEC is also applicable for the specific area with both more precise inference and faster convergence than other multiple imputation methods in general.     

A machine learning approach for imputation and anomaly detection in IoT environment

The problem of anomaly and attack detection in IoT environment is one of the prime challenges in the domain of internet of things that requires an immediate concern. For example, anomalies and attacks in IoT environment such as scan, malicious operation, denial of service, spying, data type probing, wrong setup, malicious control can lead to failure of an IoT system. Datasets generated in an IoT environment usually have missing values. The presence of missing values makes the classifier unsuitable for classification task. This article introduces (a) a novel imputation technique for imputation of missing data values (b) a classifier which is based on feature transformation to perform classification (c) imputation measure for similarity computation between any two instances that can also be used as similarity measure. The performance of proposed classifier is studied by using imputed datasets obtained through applying Kmeans, F-Kmeans and proposed imputation methods. Experiments are also conducted by applying existing and proposed classifiers on the imputed dataset obtained using proposed imputation technique. For experimental study in this article, we have used an open source dataset named distributed smart space orchestration system publicly available from Kaggle. Experiment results obtained are also validated using Wilcoxon non-parametric statistical test. It is proved that the performance of proposed approach is better when compared to existing classifiers when the imputation process is performed using F-Kmeans and K-Means imputation techniques. It is also observed that accuracies for attack classes scan, malicious operation, denial of service, spying, data type probing, wrong setup are 100% while it is 99% for malicious control attack class when the proposed imputation and classification technique are applied.     

一种无参数的微阵列缺失值填补方法

微阵列数据中的缺失值会对随后的数据分析造成影响。因此,正确地估计这些缺失值是很必要的。将一个k值选取算法结合到有序的局部最小二乘填补算法中,提出了一种无参数的缺失值填补方法(SLLSkimpute)。该方法的三个特点是:第一,无需事先确定参数;第二,针对不同的目标基因使用不同数目的邻居基因;第三,有序地估计缺失值,并有选择地将已得到的估计值应用到后续的估计过程中。实验结果证实了该算法的有效性,其估计性能优于其它一些常用的填补方法。     

Single imputation with multilayer perceptron and multiple imputation combining multilayer perceptron and k-nearest neighbours for monotone patterns

The knowledge discovery process is supported by data files information gathered from collected data sets, which often contain errors in the form of missing values. Data imputation is the activity aimed at estimating values for missing data items. This study focuses on the development of automated data imputation models, based on artificial neural networks for monotone patterns of missing values. The present work proposes a single imputation approach relying on a multilayer perceptron whose training is conducted with different learning rules, and a multiple imputation approach based on the combination of multilayer perceptron and k-nearest neighbours. Eighteen real and simulated databases were exposed to a perturbation experiment with random generation of monotone missing data pattern. An empirical test was accomplished on these data sets, including both approaches (single and multiple imputations), and three classical single imputation procedures – mean/mode imputation, regression and hot-deck – were also considered. Therefore, the experiments involved five imputation methods. The results, considering different performance measures, demonstrated that, in comparison with traditional tools, both proposals improve the automation level and data quality offering a satisfactory performance.     

Using Bayesian regression and EM algorithm with missing handling for software effort prediction

ContextAlthough independent imputation techniques are comprehensively studied in software effort prediction, there are few studies on embedded methods in dealing with missing data in software effort prediction.ObjectiveWe propose BREM (Bayesian Regression and Expectation Maximization) algorithm for software effort prediction and two embedded strategies to handle missing data.MethodThe MDT (Missing Data Toleration) strategy ignores the missing data when using BREM for software effort prediction and the MDI (Missing Data Imputation) strategy uses observed data to impute missing data in an iterative manner while elaborating the predictive model.ResultsExperiments on the ISBSG and CSBSG datasets demonstrate that when there are no missing values in historical dataset, BREM outperforms LR (Linear Regression), BR (Bayesian Regression), SVR (Support Vector Regression) and M5′ regression tree in software effort prediction on the condition that the test set is not greater than 30% of the whole historical dataset for ISBSG dataset and 25% of the whole historical dataset for CSBSG dataset. When there are missing values in historical datasets, BREM with the MDT and MDI strategies significantly outperforms those independent imputation techniques, including MI, BMI, CMI, MINI and M5′. Moreover, the MDI strategy provides BREM with more accurate imputation for the missing values than those given by the independent missing imputation techniques on the condition that the level of missing data in training set is not larger than 10% for both ISBSG and CSBSG datasets.ConclusionThe experimental results suggest that BREM is promising in software effort prediction. When there are missing values, the MDI strategy is preferred to be embedded with BREM.     

Impact of imputation of missing values on classification error for discrete data

Numerous industrial and research databases include missing values. It is not uncommon to encounter databases that have up to a half of the entries missing, making it very difficult to mine them using data analysis methods that can work only with complete data. A common way of dealing with this problem is to impute (fill-in) the missing values. This paper evaluates how the choice of different imputation methods affects the performance of classifiers that are subsequently used with the imputed data. The experiments here focus on discrete data. This paper studies the effect of missing data imputation using five single imputation methods (a mean method, a Hot deck method, a Na?¨ve-Bayes method, and the latter two methods with a recently proposed imputation framework) and one multiple imputation method (a polytomous regression based method) on classification accuracy for six popular classifiers (RIPPER, C4.5, K-nearest-neighbor, support vector machine with polynomial and RBF kernels, and Na?¨ve-Bayes) on 15 datasets. This experimental study shows that imputation with the tested methods on average improves classification accuracy when compared to classification without imputation. Although the results show that there is no universally best imputation method, Na?¨ve-Bayes imputation is shown to give the best results for the RIPPER classifier for datasets with high amount (i.e., 40% and 50%) of missing data, polytomous regression imputation is shown to be the best for support vector machine classifier with polynomial kernel, and the application of the imputation framework is shown to be superior for the support vector machine with RBF kernel and K-nearest-neighbor. The analysis of the quality of the imputation with respect to varying amounts of missing data (i.e., between 5% and 50%) shows that all imputation methods, except for the mean imputation, improve classification error for data with more than 10% of missing data. Finally, some classifiers such as C4.5 and Na?¨ve-Bayes were found to be missing data resistant, i.e., they can produce accurate classification in the presence of missing data, while other classifiers such as K-nearest-neighbor, SVMs and RIPPER benefit from the imputation.     

A comprehensive empirical evaluation of missing value imputation in noisy software measurement data

The handling of missing values is a topic of growing interest in the software quality modeling domain. Data values may be absent from a dataset for numerous reasons, for example, the inability to measure certain attributes. As software engineering datasets are sometimes small in size, discarding observations (or program modules) with incomplete data is usually not desirable. Deleting data from a dataset can result in a significant loss of potentially valuable information. This is especially true when the missing data is located in an attribute that measures the quality of the program module, such as the number of faults observed in the program module during testing and after release. We present a comprehensive experimental analysis of five commonly used imputation techniques. This work also considers three different mechanisms governing the distribution of missing values in a dataset, and examines the impact of noise on the imputation process. To our knowledge, this is the first study to thoroughly evaluate the relationship between data quality and imputation. Further, our work is unique in that it employs a software engineering expert to oversee the evaluation of all of the procedures and to ensure that the results are not inadvertently influenced by poor quality data. Based on a comprehensive set of carefully controlled experiments, we conclude that Bayesian multiple imputation and regression imputation are the most effective techniques, while mean imputation performs extremely poorly. Although a preliminary evaluation has been conducted using Bayesian multiple imputation in the empirical software engineering domain, this is the first work to provide a thorough and detailed analysis of this technique. Our studies also demonstrate conclusively that the presence of noisy data has a dramatic impact on the effectiveness of imputation techniques.     

Granular data imputation: A framework of Granular Computing

Data imputation is a common practice encountered when dealing with incomplete data. Irrespectively of the existing spectrum of techniques, the results of imputation are commonly numeric meaning that once the data have been imputed they are not distinguishable from the original data being initially available prior to imputation. In this study, the crux of the proposed approach is to develop a way of representing imputed (missing) entries as information granules and in this manner quantify the quality of the imputation process and the quality of the ensuing data. We establish a two-stage imputation mechanism in which we start with any method of numeric imputation and then form a granular representative of missing value. In this sense, the approach could be regarded as an enhancement of the existing imputation techniques.Proceeding with the detailed imputation schemes, we discuss two ways of imputation. In the first one, imputation is realized for individual variables of data sets and afterwards enhanced by the buildup of information granules. In the second approach, we are concerned with the use of fuzzy clustering, Fuzzy C-Means (FCM), which helps establish a structure in the data and then use this information in the imputation process.The design of information granules invokes the fundamentals of Granular Computing, namely a principle of justifiable granularity and an allocation of information granularity. Numeric experiments concerned with a suite of publicly available data sets offer detailed insights into the main facets of the overall design process and deliver a parametric analysis of the methods.     

New methods for imputation of missing genotype using linkage disequilibrium and haplotype information

In this paper, we propose new missing imputation methods for the missing genotype data of single nucleotide polymorphism (SNP). The common objective of imputation methods is to minimize the loss of information caused by experimental missing elements. In general, imputation of missing genotype data has used a major allele method, but this approach is not far from the objective of the imputation - minimizing the loss of information. This method generally produces high error rates of missing value estimation, since the characteristics of the genotype data are not considered over the structure of given genotype data. In our methods, we use the linkage disequilibrium and haplotype information for the missing SNP genotype. As a result, we provide the results of the comparative evaluation of our methods and major allele imputation method according to the various randomized missing rates.     

Energy Consumption Prediction of a CNC Machining Process With Incomplete Data

Energy consumption prediction of a CNC machining process is important for energy efficiency optimization strategies.To improve the generalization abilities,more and more parameters are acquired for energy prediction modeling.While the data collected from workshops may be incomplete because of misoperation,unstable network connections,and frequent transfers,etc.This work proposes a framework for energy modeling based on incomplete data to address this issue.First,some necessary preliminary operations are used for incomplete data sets.Then,missing values are estimated to generate a new complete data set based on generative adversarial imputation nets(GAIN).Next,the gene expression programming(GEP)algorithm is utilized to train the energy model based on the generated data sets.Finally,we test the predictive accuracy of the obtained model.Computational experiments are designed to investigate the performance of the proposed framework with different rates of missing data.Experimental results demonstrate that even when the missing data rate increases to 30%,the proposed framework can still make efficient predictions,with the corresponding RMSE and MAE 0.903 k J and 0.739 k J,respectively.     

A simulation study comparing weighted estimating equations with multiple imputation based estimating equations for longitudinal binary data

Missingness frequently complicates the analysis of longitudinal data. A popular solution for dealing with incomplete longitudinal data is the use of likelihood-based methods, when, for example, linear, generalized linear, or non-linear mixed models are considered, due to their validity under the assumption of missing at random (MAR). Semi-parametric methods such as generalized estimating equations (GEEs) offer another attractive approach but require the assumption of missing completely at random (MCAR). Weighted GEE (WGEE) has been proposed as an elegant way to ensure validity under MAR. Alternatively, multiple imputation (MI) can be used to pre-process incomplete data, after which GEE is applied (MI-GEE). Focusing on incomplete binary repeated measures, both methods are compared using the so-called asymptotic, as well as small-sample, simulations, in a variety of correctly specified as well as incorrectly specified models. In spite of the asymptotic unbiasedness of WGEE, results provide striking evidence that MI-GEE is both less biased and more accurate in the small to moderate sample sizes which typically arise in clinical trials.