## 4 Self-Healing Approaches
### Machine-Learning Algorithms
#### 4.3.12 Naive Bayes  
The naive Bayes machine-learning algorithm is described by [39] as a classification algorithm based on Bayes theorems. It is also described in Rani in [28] as a classifier that applies the Bayes theorem to solve various classification problems such as detecting systems vulnerability, disease diagnosis, spam prevention, document filtering, etcetera. It is a simple but effective ML algorithm that is particularly useful when dealing with high-dimensional data. The participation features involved in naive Bayes classification are usually independent as a fundamental principle that guides the algorithm. The naive Bayes algorithm applies to self-healing systems functionality because it applies to classifying datasets into models that can aid the detection of system vulnerability, providing the first step towards realising a self-healing functionality. The algorithm utilises conditional, and class probability, and the class probability can be the probability of a random dataset belonging to a particular class, which is calculated as:  
\[\text{P(C)}=\frac{\text{Number of Samples in the Class}}{\text{Total Number of Samples}}\]The conditional probability, on the other hand, as [39] noted, is the probability of a feature value of a class and is calculated as:  
\[\mathrm{P(F|C)}=\frac{\mathrm{Number\ of\ Frequencies\ of\ each\ Attributes}}{\mathrm{Number\ of\ Frequencies\ of\ Samples}}\]  
All the samples belonging to the classes are compared with each other from the calculated probabilities, and the classes with the most significant probabilities are chosen as the output [39] further argued that the naive Bayes algorithm performs well on datasets with trivial features because of the probability of the trivial features contributing less to the output. It performs well when making predictions, as it involves only probabilities of features and classes.  
Naive Bayes assumes that each feature is independent of all other features. The algorithm can effectively scale to large datasets by simplifying the computation of probabilities. It can be trained on historical data to identify patterns and accurately predict future behaviour. For example, a naive Bayes classifier could be used to predict the likelihood of a particular system component failing based on the factors such as CPU usage, memory usage, network traffic, and disk I/O. The classifier could be trained on historical data to learn the relationship between these variables and their impact on the system performance. Once a classifier has been trained, it can diagnose faults or failures in real time. For example, if CPU usage suddenly spikes, the naive Bayes classifier could predict that a particular component will soon fail. In response to anomalies, this can trigger an automated response, such as workload migration to another server or service restart, facilitating effective self-healing. Naive Bayes is a valuable tool for self-healing systems, enabling them to detect and respond to faults or failures quickly and accurately. However, it is essential to note that the \"naive\" assumption of independence may not always hold in practice; more sophisticated models may be required for complex systems.