A Grey-Based Nearest Neighbor Approach for Missing Attribute Value Prediction

This paper proposes a grey-based nearest neighbor approach to predict accurately missing attribute values. First, grey relational analysis is employed to determine the nearest neighbors of an instance with missing attribute values. Accordingly, the known attribute values derived from these nearest neighbors are used to infer those missing values. Two datasets were used to demonstrate the performance of the proposed method. Experimental results show that our method outperforms both multiple imputation and mean substitution. Moreover, the proposed method was evaluated using five classification problems with incomplete data. Experimental results indicate that the accuracy of classification is maintained or even increased when the proposed method is applied for missing attribute value prediction.     

MkNNI：基于相互最近邻的缺失值填充新方法

针对k最近邻填充算法（kNNI）在缺失数据的k个最近邻可能存在噪声,提出一种新的缺失值填充算法——相互k最近邻填充算法MkNNI（Mutualk-NearestNeighborImputa—tion）。用于填充缺失值的数据,不仅是缺失数据的k最近邻,而且它的k最近邻也包含该缺失数据．从而有效地防止kNNI算法选取的k个最近邻点可能存在噪声这一情况。实验结果表明．MkNNI算法的填充准确性总体上要优于kNNI算法。     

基于标准欧氏距离的燃油流量缺失数据填补算法

为减小数据缺失对飞机油耗统计推断精度带来的负面影响,针对基于传统欧氏距离、马氏距离以及精简关联度的最近邻填补算法的不足,提出了一种基于标准欧氏距离的填补算法来估计QAR(Quick Access Recorder)数据中部分燃油流量数值的缺失。该算法通过QAR数据样本之间的标准欧氏距离选择最近邻样本,并利用熵值赋权法计算最近邻的加权系数,基于最近邻样本中燃油流量的加权平均即可得到缺失燃油流量的估计值。实验结果表明,标准欧氏距离能够有效度量样本相似性,所提出的算法优于常规填补算法,是处理飞机油耗数据缺失的一种有效方法。     

基于马氏距离的缺失值填充算法

提出了一种基于马氏距离的填充算法来估计基因表达数据集中的缺失数据。该算法通过基因之间的马氏距离来选择最近邻居基因,并将已得到的估计值应用到后续的估计过程中,然后采用信息论中熵值的概念计算最近邻居的加权系数,得到缺失数据的填充值。实验结果证明了该算法具有有效性,其性能优于其他基于最近邻居法的缺失值处理算法。     

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.     

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.     

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。     

Benchmarking k-nearest neighbour imputation with homogeneous Likert data

Missing data are common in surveys regardless of research field, undermining statistical analyses and biasing results. One solution is to use an imputation method, which recovers missing data by estimating replacement values. Previously, we have evaluated the hot-deck k-Nearest Neighbour (k-NN) method with Likert data in a software engineering context. In this paper, we extend the evaluation by benchmarking the method against four other imputation methods: Random Draw Substitution, Random Imputation, Median Imputation and Mode Imputation. By simulating both non-response and imputation, we obtain comparable performance measures for all methods. We discuss the performance of k-NN in the light of the other methods, but also for different values of k, different proportions of missing data, different neighbour selection strategies and different numbers of data attributes. Our results show that the k-NN method performs well, even when much data are missing, but has strong competition from both Median Imputation and Mode Imputation for our particular data. However, unlike these methods, k-NN has better performance with more data attributes. We suggest that a suitable value of k is approximately the square root of the number of complete cases, and that letting certain incomplete cases qualify as neighbours boosts the imputation ability of the method.     

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.     

Missing data imputation for fuzzy rule-based classification systems

Fuzzy rule-based classification systems (FRBCSs) are known due to their ability to treat with low quality data and obtain good results in these scenarios. However, their application in problems with missing data are uncommon while in real-life data, information is frequently incomplete in data mining, caused by the presence of missing values in attributes. Several schemes have been studied to overcome the drawbacks produced by missing values in data mining tasks; one of the most well known is based on preprocessing, formerly known as imputation. In this work, we focus on FRBCSs considering 14 different approaches to missing attribute values treatment that are presented and analyzed. The analysis involves three different methods, in which we distinguish between Mamdani and TSK models. From the obtained results, the convenience of using imputation methods for FRBCSs with missing values is stated. The analysis suggests that each type behaves differently while the use of determined missing values imputation methods could improve the accuracy obtained for these methods. Thus, the use of particular imputation methods conditioned to the type of FRBCSs is required.     

基于局部加权重构的化工过程数据恢复算法

针对化工过程数据中存在缺失数据的问题,在保持局部数据结构特征的基础上提出了基于局部加权重构的化工过程数据恢复算法。通过定位缺失的数据点并以符号NaN(Not a Number)标记,将缺失的数据集分为完备数据集和不完备数据集。不完备的数据集按照完整性的大小依次找到它们在完备数据集中相应的k个近邻,根据误差平方和最小的原则,求出k个近邻相应的权值,用k个近邻及相应的权值重构出缺失的数据点。将该算法应用在不同缺失率下的两种化工过程数据中并与望最大化主成分分析(EM-PCA)法和平均值(MA)两种传统的数据恢复算法相比较,该算法的恢复数据误差最小,并且计算速度相比EM-PCA算法平均提高了2倍。实验结果表明,局部加权重构的化工过程数据恢复算法可以有效地对数据进行恢复,提高了数据的利用率,适用于非线性化工过程缺失数据的恢复。     

Imputation of missing links and attributes in longitudinal social surveys

The predictive analysis of longitudinal social surveys is highly sensitive to the effects of missing data in temporal observations. Such high sensitivity to missing values raises the need for accurate data imputation, because without it a large fraction of collected data could not be used properly. Previous studies focused on the treatment of missing data in longitudinal social networks due to non-respondents and dealt with the problem largely by imputing missing links in isolation or analyzing the imputation effects on network statistics. We propose to account for changing network topology and interdependence between actors’ links and attributes to construct a unified approach for imputation of links and attributes in longitudinal social surveys. The new method, based on an exponential random graph model, is evaluated experimentally for five scenarios of missing data models utilizing synthetic and real life datasets with 20 %–60 % of nodes missing. The obtained results outperformed all alternatives, four of which were link imputation methods and two node attribute imputation methods. We further discuss the applicability and scalability of our approach to real life problems and compare our model with the latest advancements in the field. Our findings suggest that the proposed method can be used as a viable imputation tool in longitudinal studies.     

Missing data imputation by utilizing information within incomplete instances

This paper proposes to utilize information within incomplete instances (instances with missing values) when estimating missing values. Accordingly, a simple and efficient nonparametric iterative imputation algorithm, called the NIIA method, is designed for iteratively imputing missing target values. The NIIA method imputes each missing value several times until the algorithm converges. In the first iteration, all the complete instances are used to estimate missing values. The information within incomplete instances is utilized since the second imputation iteration. We conduct some experiments for evaluating the efficiency, and demonstrate: (1) the utilization of information within incomplete instances is of benefit to easily capture the distribution of a dataset; and (2) the NIIA method outperforms the existing methods in accuracy, and this advantage is clearly highlighted when datasets have a high missing ratio.     

基于精简关联度的基因表达数据迭代填补算法

基因表达数据时常出现缺失,阻碍了对基因表达的研究。提出了一种新的相似性度量方案——精简关联度,在此基础上,又提出了基于精简关联度的缺失数据迭代填补算法(RKNNimpute)。精简关联度是对灰色关联度的一种改进,能达到与灰色关联度同样的效果,却显著降低了算法的时间复杂度。RKNNimpute算法以精简关联度作为相似度量,将填补后的基因扩充到近邻的候选基因集,通过迭代的方式填补其他缺失数据,提高了算法的填补效果和性能。选用时序、非时序、混合等不同类型的基因表达数据集进行了大量实验来评估RKNNimpute算法的性能。实验结果表明,精简关联度是一种高效的距离度量方法,所提出的RKNNimpute算法优于常规填补算法。     

基于属性相关度的缺失数据填补算法研究

针对不完备信息系统的数据缺失填补精度不够高问题,以水产养殖预警信息系统为背景,提出一种基于属性相关度的缺失数据填补算法。在有效保证预警信息系统确定性的前提下,通过研究限制容差关系知识和决策规则,根据新定义的限制相容关系求出缺失对象的限制相容类,同时将条件属性之间的相关度概念引入,构造出一种新的扩展矩阵进行数据填补,实现了系统的完备性。以鲈鱼养殖缺失数据填补为实例,以数据集进行填补验证,结果表明与其他方法相比该算法在填补准确度和时间性能上有明显提高。     

On the choice of the best imputation methods for missing values considering three groups of classification methods

In real-life data, information is frequently lost in data mining, caused by the presence of missing values in attributes. Several schemes have been studied to overcome the drawbacks produced by missing values in data mining tasks; one of the most well known is based on preprocessing, formerly known as imputation. In this work, we focus on a classification task with twenty-three classification methods and fourteen different imputation approaches to missing values treatment that are presented and analyzed. The analysis involves a group-based approach, in which we distinguish between three different categories of classification methods. Each category behaves differently, and the evidence obtained shows that the use of determined missing values imputation methods could improve the accuracy obtained for these methods. In this study, the convenience of using imputation methods for preprocessing data sets with missing values is stated. The analysis suggests that the use of particular imputation methods conditioned to the groups is required.     

POP algorithm: Kernel-based imputation to treat missing values in knowledge discovery from databases

To complete missing values a solution is to use correlations between the attributes of the data. The problem is that it is difficult to identify relations within data containing missing values. Accordingly, we develop a kernel-based missing data imputation in this paper. This approach aims at making an optimal inference on statistical parameters: mean, distribution function and quantile after missing data are imputed. And we refer this approach to parameter optimization method (POP algorithm). We experimentally evaluate our approach, and demonstrate that our POP algorithm (random regression imputation) is much better than deterministic regression imputation in efficiency and generating an inference on the above parameters.     

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.     

Instance variant nearest neighbor using particle swarm optimization for function approximation

In this paper, a new approach called ‘instance variant nearest neighbor’ approximates a regression surface of a function using the concept of k nearest neighbor. Instead of fixed k neighbors for the entire dataset, our assumption is that there are optimal k neighbors for each data instance that best approximates the original function by fitting the local regions. This approach can be beneficial to noisy datasets where local regions form data characteristics that are different from the major data clusters. We formulate the problem of finding such k neighbors for each data instance as a combinatorial optimization problem, which is solved by a particle swarm optimization. The particle swarm optimization is extended with a rounding scheme that rounds up or down continuous-valued candidate solutions to integers, a number of k neighbors. We apply our new approach to five real-world regression datasets and compare its prediction performance with other function approximation algorithms, including the standard k nearest neighbor, multi-layer perceptron, and support vector regression. We observed that the instance variant nearest neighbor outperforms these algorithms in several datasets. In addition, our new approach provides consistent outputs with five datasets where other algorithms perform poorly.     

Estimation of incomplete values in heterogeneous attribute large datasets using discretized Bayesian max–min ant colony optimization

The size of datasets is becoming larger nowadays and missing values in such datasets pose serious threat to data analysts. Although various techniques have been developed by researchers to handle missing values in different kinds of datasets, there is not much effort to deal with the missing values in mixed attributes in large datasets. This paper has proposed novel strategies for dealing with this issue. The significant attributes (covariates) required for imputation are first selected using gain ratio measure to decrease the computational complexity. Since analysis of continuous attributes in imputation process is complex, they are first discretized using a novel methodology called Bayesian classifier-based discretization. Then, missing values in them are imputed using Bayesian max–min ant colony optimization algorithm which hybridizes ACO with Bayesian principles. The local search technique is also introduced in ACO implementation to improve its exploitative capability. The proposed methodology is implemented in real datasets with different missing rates ranging from 5 to 50% and from the experimental results, it is observed that the proposed discretization and imputation algorithms produce better results than the existing methods.