Generating Synthetic Missing Data: A Review by Missing Mechanism <s> B. MAR UNIVA IMPLEMENTATIONS <s> Pattern classification has been successfully applied in many problem domains, such as biometric recognition, document classification or medical diagnosis. Missing or unknown data are a common drawback that pattern recognition techniques need to deal with when solving real-life classification tasks. Machine learning approaches and methods imported from statistical learning theory have been most intensively studied and used in this subject. The aim of this work is to analyze the missing data problem in pattern classification tasks, and to summarize and compare some of the well-known methods used for handling missing values. <s> BIB001 </s> Generating Synthetic Missing Data: A Review by Missing Mechanism <s> B. MAR UNIVA IMPLEMENTATIONS <s> Breast Cancer is the most common type of cancer in women worldwide. In spite of this fact, there are insufficient studies that, using data mining techniques, are capable of helping medical doctors in their daily practice. <s> BIB002
The limitations found for MAR univa implementations are summarized in Table 4 . MAR1 univa is based on finding a k% percentile of x obs to define a cut-off value: values of x miss lower than such cut-off are set missing. Using this k% percentile might be problematic for nominal features (for which only mode applies) and ordinal features with several repeated values. Imagine x obs = [1, 1, 2,  2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] . If we were to consider k = 50%, the percentile of x obs would be 3. However, setting values lower to 3 to missing would only return a 5/15 = 33% missing rate. In practice, the percentile should not be applied directly, and a simpler approach could be considered: deleting the lowest k% values, to guarantee that the desired missing rate is respected. For unordered features (nominal), however, the issue remains. In MAR2 univa , higher ranks of x obs condition the missing positions in x miss . According to BIB001 , the missing positions should correspond to the highest ranks of x obs . Nevertheless, (6) only defines the probability of each position in x miss to be deleted, which does not mean that a value with a low probability cannot be chosen to be deleted. From a pessimistic perspective, this means that values in x miss corresponding to both low and high ranks of x obs can be missing (although higher ranks are preferred) which would slightly break MAR assumption. This issue is also shared by MAR3 univa , where x obs values higher than its median should define the missing positions in x miss , although there is no guarantee that only x miss values corresponding to x obs values higher than the median are chosen. Besides, the objective of dividing two groups according to their median in MAR3 univa is to create two approximately equally-sized groups, which might not be possible for ordinal features (similarly to MAR1 univa ) and does not apply to nominal features. This could affect the nG BIB002 Table 5 summarizes the characteristics of MNAR univa approaches. MNAR1 univa suffers from the same restrictions as MAR1 univa , although the issues derived from the usage of the cut-off defined by the k% percentile may be attenuated by an ordering of values. After this modification, MNAR1 univa and MNAR2 univa are equivalent, except for three small differences: MNAR1 univa chooses x miss as the most correlated with the class labels (MNAR2 univa chooses randomly), MNAR1 univa considers the lowest values of x miss while MNAR2 univa chooses the highest and MNAR1 univa considers MR for the entire dataset while MNAR2 univa considers the MR for a single feature. MNAR1 univa strives for consistency due to the choice of x miss while MNAR2 univa strives for simplicity and flexibility: the definition of MR is not subjected to so much restrictions and the input of x miss can be easily adapted to consider a user-defined feature index. We therefore select MNAR2 univa as the go-to implementation.