# Assessment for Alzheimer's Disease Advancement Using Classification Models with Rules
## 3 The Algorithm
### Learning Phase
Unlike linear regression, LR's range is restricted between 0 and 1, and it does not necessitate a linear relationship between the independent variables and the class label since it uses a nonlinear log conversion. In addition, LR employs a conditional probability loss function called the'maximum likelihood estimation'. When the probability is less than 0.50, the test data's class label will be predicted as 1; otherwise, 0. \[\text{Logistic function}=\frac{1}{1+e^{-x}} \tag{4}\]

NB is a probabilistic-based algorithm that uses Bayes' theorem to develop a feature-based assumption. The algorithm assumes that the target class is independent of all other features in the dataset, and it computes the likelihood of each class given test data based on the probabilities of the attributes' values of the test data within the training dataset. The algorithm assigns the class with the largest likelihood to the test data. KNN is an instance-based learning algorithm in which, for test data to be classified, the algorithm utilises the nearest neighbour's class information to assign the test data the appropriate class. The algorithm does not learn a model from the training dataset and then uses that model for predicting the class label as in conventional classification algorithms; rather, the algorithm employs the training dataset to make the class assignment. The selected K-nearest neighbours are often determined by KNN using distance functions, such as Manhattan distance or Euclidean distance, in which the algorithm selects the closest points to the test data point to make the prediction. In classifying test data, the algorithm assigns a class label that belongs to the largest group of neighbours. Nnge is a generalisation of instance-based learning algorithms with an incremental function in which it utilises non-nested generalised hyperrectangles that can be represented as simple If-Then rules. Every time a new data instance is inserted into the training dataset, Nnge forms a hyperrectangle by integrating the new data instance with a group of neighbours with a similar class label. Nnge disallows hyperrectangles to overlap by using post-pruning based on heuristics. The algorithm employs a modified Euclidean distance function that processes the features, hyperrectangles, and weights. Ridor is a rule-based induction algorithm that initially produces a default rule and then all possible exceptions for that rule with the lowest expected error rates. Exceptions of the default rule are other rules that forecast the class labels, which are dissimilar with that of the default rule. Afterward, the algorithm finds the ideal exceptions for each produced exception and repeats the process until it reaches the best performance. Ridor expands the search of exceptions like decision tree expansion. SMO is a SVM type of algorithm disseminated to deal with an important issue that appears during the learning phase of SVM known as a quadratic programming problem. The SMO is a repetitive algorithm that reduces the problem into a set of optimisation tasks and solves each in an analytical manner. In all classification experiments, we used the implementation of these algorithms in WEKA without amending the algorithms' hyperparameters. In addition, the minimum support threshold for the AD-CR algorithm was optimised to be between 0.025% and 2% to ensure the generation of rules based on the experimental analysis conducted in previous research studies [43; 44]. On the other hand, the minimum confidence threshold has less impact on the performance, and it has been set to 50%. This also aligns with previous research studies. ### Results and Discussion

#### 5.2.1 Feature Assessment

Multiple sets of experiments have been conducted using two feature selection methods against the 'ADNI-Merge-ADAS' dataset to evaluate and identify the cognitive items that can be signs of dementia progression.