# Missing Data Imputation in the Internet of Things Sensor Networks
## 3 Related Works  
The classification of missing data mechanisms is important as it assists in the selection of suitable strategies for handling different missing data problems. According to [25], three important mechanisms of missing data exists namely; Missing at Random (MAR), Missing Completely at Random (MCAR) and Not Missing at Random (NMAR). In the _MAR_ mechanism, the probability of a missing value on an attribute Y depends on the value of another attribute X but not on the value of Y itself [26]. The _MCAR_ mechanismcan be noticed when the value of an attribute with missing data neither depends on the missing data nor observed data. _MCAR_ is a mechanism that is considered in most fields to be \"totally and randomly\" missing. Here, the probability of an attribute Y to have missing values is not directly associated with the output of the variable X or the output value of Y itself [25]. Contrary to previous missing data mechanisms described, assuming we have an organised data matrix, when the chances of missing values on a given attribute Y depends on Y itself, and not the value of another attribute X, data is said to be not missing at random (_NMAR_) [27]. The Expectation Maximization (EM) algorithm for missing data imputation was proposed by [28]. This is a well known missing data imputation strategy identified in the literature. When imputing missing continuous data, the EM algorithm first evaluates the mean and covariance matrix from the values that are present in the dataset. The algorithm then iterates until there is no significant change to the mean value and covariance matrix as the algorithm moves from one iteration to another. Research has shown that the EM algorithm only works best when data is missing at random. A disadvantage however, is that the EM technique largely depends on information obtained from other variables in a dataset. Therefore, more reliable missing data estimates can only be obtained from highly correlated data using the EM algorithm [23]. In [29], [PERSON] et al. approached missing data imputation by splitting a dataset into \(k\) distinct clusters in the first step. This method results in the generation of membership values for all the points that fall within a specific cluster or centroid. After that, all the missing instances are assessed using the membership measure of other points that fall within the boundary of the same cluster centroid. This technique constitutes an advantage due to its simplicity. However, the predictive accuracy of imputation results from FCM may be influenced by unusual clustering circumstances where the selection of an optimal number of \(k\) clusters is a challenge for data miners. An iterative imputation method was also developed by [17], based on the random forest (missForest) method. The idea behind this method involved averaging several regression and classification trees that were unpruned. Their Analyses were conducted on multiple datasets obtained from biological fields, and artificial missing values were simulated on their datasets in order to test the accuracy of their imputation method against different rates of missing values. Their work showed the ability of the missForest method to handle continuous and categorical missing data. Comparatively, after analysing the performance of missForest against some other methods such as KNN, their results showed that missForest outperformed other imputation methods, especially in settings where non-linear relationships and complex interactions were suspected in the dataset. [PERSON] et al. [30] approached missing data imputation using Neural Networks (NN) to solve classification problems. The researchers proposed a solution to rebuild missing values using a backpropagation algorithm. Results showed that reconstructing missing values using NN yielded better results than statistical methods. Further analysis also showed that reconstructing missing values using NN improved classification accuracy. Ref.