Generating Synthetic Missing Data: A Review by Missing Mechanism <s> C. MULTIVARIATE MNAR IMPLEMENTATIONS <s> Increasing the awareness of how incomplete data affects learning and classification accuracy has led to increasing numbers of missing data techniques. This article investigates the robustness and accuracy of seven popular techniques for tolerating incomplete training and test data for different patterns of missing data—different proportions and mechanisms of missing data on resulting tree-based models. The seven missing data techniques were compared by artificially simulating different proportions, patterns, and mechanisms of missing data using 21 complete datasets (i.e., with no missing values) obtained from the University of California, Irvine repository of machine-learning databases (Blake and Merz, 1998). A four-way repeated measures design was employed to analyze the data. The simulation results suggest important differences. All methods have their strengths and weaknesses. However, listwise deletion is substantially inferior to the other six techniques, while multiple imputation, that utilizes the expectation maximization algorithm, represents a superior approach to handling incomplete data. Decision tree single imputation and surrogate variables splitting are more severely impacted by missing values distributed among all attributes compared to when they are only on a single attribute. Otherwise, the imputation—versus model-based imputation procedures gave—reasonably good results although some discrepancies remained. Different techniques for addressing missing values when using decision trees can give substantially diverse results, and must be carefully considered to protect against biases and spurious findings. Multiple imputation should always be used, especially if the data contain many missing values. If few values are missing, any of the missing data techniques might be considered. The choice of technique should be guided by the proportion, pattern, and mechanisms of missing data, especially the latter two. However, the use of older techniques like listwise deletion and mean or mode single imputation is no longer justifiable given the accessibility and ease of use of more advanced techniques, such as multiple imputation and supervised learning imputation. <s> BIB001 </s> Generating Synthetic Missing Data: A Review by Missing Mechanism <s> C. MULTIVARIATE MNAR IMPLEMENTATIONS <s> Missing data imputation is an important research topic in data mining. The impact of noise is seldom considered in previous works while real-world data often contain much noise. In this paper, we systematically investigate the impact of noise on imputation methods and propose a new imputation approach by introducing the mechanism of Group Method of Data Handling (GMDH) to deal with incomplete data with noise. The performance of four commonly used imputation methods is compared with ours, called RIBG (robust imputation based on GMDH), on nine benchmark datasets. The experimental result demonstrates that noise has a great impact on the effectiveness of imputation techniques and our method RIBG is more robust to noise than the other four imputation methods used as benchmark. <s> BIB002 </s> Generating Synthetic Missing Data: A Review by Missing Mechanism <s> C. MULTIVARIATE MNAR IMPLEMENTATIONS <s> Treatment of missing data has become increasingly significant in scientific research and engineering applications. The classic imputation strategy based on the K nearest neighbours (KNN) has been widely used to solve the plague problem. However, former studies do not give much attention to feature relevance, which has a significant impact on the selection of nearest neighbours. As a result, biased results may appear in similarity measurements. In this paper, we propose a novel method to impute missing data, named feature weighted grey KNN (FWGKNN) imputation algorithm. This approach employs mutual information (MI) to measure feature relevance. We present an experimental evaluation for five UCI datasets in three missingness mechanisms with various missing rates. Experimental results show that feature relevance has a non-ignorable influence on missing data estimation based on grey theory, and our method is considered superior to the other four estimation strategies. Moreover, the classification bias can be significantly reduced by using our approach in classification tasks. <s> BIB003 </s> Generating Synthetic Missing Data: A Review by Missing Mechanism <s> C. MULTIVARIATE MNAR IMPLEMENTATIONS <s> Abstract When applying data-mining techniques to real-world data, we often find ourselves facing observations that have no value recorded for some attributes. This can be caused by several phenomena, such as a machine’s incapability to record certain characteristics or a person refusing to answer a question in a poll. Depending on that motivation, values gone missing may follow one kind of pattern or another, or describe no regularity at all. One approach to palliate the effect of missing data on machine learning tasks is to replace the missing observations. Imputation algorithms attempt to calculate a value for a missing gap, using information associated with it, i.e., the attribute and/or other values in the same observation. While several imputation methods have been proposed in the literature, few works have addressed the question of the relationship between the type of missing data, the choice of the imputation method, and the effectiveness of classification algorithms that used the imputed data. In this paper we address the relationship among these three factors. By constructing a benchmark of hundreds of databases containing different types of missing data, and applying several imputation methods and classification algorithms, we empirically show that an interaction between imputation methods and supervised classification can be deduced. Besides, differences in terms of classification performance for the same imputation method in different missing data patterns have been found. This points to the convenience of considering the combined choice of the imputation method and the classifier algorithm according to the missing data type. <s> BIB004 </s> Generating Synthetic Missing Data: A Review by Missing Mechanism <s> C. MULTIVARIATE MNAR IMPLEMENTATIONS <s> In fact, raw data in the real world is dirty. Each large data repository contains various types of anomalous values that influence the result of the analysis, since in data mining, good models usually need good data, databases in the world are not always clean and includes noise, incomplete data, duplicate records, inconsistent data and missing values. Missing data is a common drawback in many real-world data sets. In this paper, we proposed an algorithm depending on improving (MIGEC) algorithm in the way of imputation for dealing missing values. We implement grey relational analysis (GRA) on attribute values instead of instance values, and the missing data were initially imputed by mean imputation and then estimated by our proposed algorithm (PA) used as a complete value for imputing next missing value.We compare our proposed algorithm with several other algorithms such as MMS, HDI, KNNMI, FCMOCS, CRI, CMI, NIIA and MIGEC under different missing mechanisms. Experimental results demonstrate that the proposed algorithm has less RMSE values than other algorithms under all missingness mechanisms. <s> BIB005
MNAR unifo implementations follow from the MAR unifo implementations discussed in the previous section, proposed in the same research works -Twala BIB001 , Garciarena and Santana BIB004 , Zhu et al. BIB002 , Pan et al. BIB003 , and Ali and Omer BIB005 . Similarly, we start by the approach presented in Garciarena and Santana BIB004 , herein referred to as MNAR1 unifo . Garciarena and Santana BIB004 propose two MNAR approaches designated MIV and MuOv in the original paper. MIV stands for Missingness depending on its Value Itself and directly illustrates the mechanism explained in Section III, where the probability of a value to be missing depends on the value itself. MuOv (Missing depending on unobserved Variables) is somewhat a domain-based MNAR approach, and therefore we will illustrate it in Section VII. MIV approach (herein designated MNAR1 unifo ) is an extension of MAR1 unifo , where x obs = x miss . In other words, there is not a determining feature x obs that affects the missingness of x miss . Instead, the probability of a value to be missing in each feature x miss is determined by the values of each x miss itself. In MNAR1 unifo , as illustrated in Figure 10 , the lowest values of each x miss are found and deleted, according to the specified MR. Similarly to MAR1 unifo , MR is specified for the entire dataset and the number of features losing their values can be chosen by the researcher. The MNAR unifo approach proposed by Twala BIB001 , MNAR2 unifo , follows the same pairing logic as MAR unifo . However, the values that are set missing in feature x miss of each pair/triple are defined by the values of x miss itself: lower values of x miss are deleted. Contrariwise, the MNAR unifo approaches by Ali and Omer BIB005 (MNAR3 unifo ), Zhu et al. BIB002 , and Pan et al. BIB003 (MNAR4 unifo ) do not require the creation of pairs/triples since the missing values are generated directly in all features, according to their respective medians. In MNAR3 unifo , two groups are defined for each feature, one with values lower or equal to its median and the other with values higher than its median. Then, one group is randomly chosen to have 2 × MR% of missing values, so that the overall MR% over the entire dataset is kept. Similarly, in MNAR4 unifo , missing values are inserted directly in each feature, without the need of creating pairs/triples of features. As performed for MAR4 unifo , if the feature is continuous or ordinal, two groups are created using its median; if the feature is nominal, the existing categories are divided into two equally-sized groups. Then, for each feature, one of those groups is selected to have 2 × MR% of missing values.