# Comparative Analysis of Exemplar-Based Approaches for Students' Learning Style Diagnosis Purposes
## 2 Methods
### Case-Based Reasoning and Similarity-Based Retrieval  
Following [7], case-based reasoning describes a methodology for solving problems. The term consists of _case_--an experience of a solved problem that may be represented in different ways; _based_--meaning that the reasoning is based on cases stored in case base; _reasoning_--meaning that conclusions should be made using cases, given a new problem to be solved. Major types of experiences occur in classification, diagnosis, prediction, planning, and configuration [7]. Using these experiences, solutions to new problems may be found and represented in different ways: commenting, presenting illustrations, explanations, advising, seeing that effects occurred in previous analogous situations, etc. In their content, these representations are some kinds of exemplars of previous experiences. Reasoning by exemplars imitates the natural process of human thinking [8]; therefore, it should be used in machine learning and artificial intelligence. Applying case-based reasoning, we make an approximate reasoning using knowledge about previous experiences recorded as cases in a case base, which is also called memory. Knowledge can either be represented explicitly or be hidden (for example, in a latent variable, in an algorithm). The so-called \"4R\" process is performed in case-based reasoning: retrieve (search using index structure), reuse (adapt in various levels of granularity), revise (test in reality and modify), and retain (store/learn new case in case base in order to improve it) [7]. CBR divides an experience into two parts [7]: a problem part (description of a problem situation) and a solution part (description of the reaction to a situation). There are two major ways to formulate problems: standardized formulation (using mathematical models, formulas, etc.) and interactive formulation, using user's feedback or dialogue with the user. In CBR, a failed solution is also an important piece of information and should be stored in the memory. Experiences may be saved in various forms: visual, textual, and conversational. In a typical, most simple way, cases are represented as feature-value pairs (also called attribute-value pairs) that need to be identified for both the problem and solution [7]. The concept of a feature's importance (weight) also takes part. Authors of [7] describe the important attribute as one having a large influence on the choice of which case is the nearest neighbour. For case representation Case retrieval nets, the Dynamic Memory Model, and the Category and Exemplar Model may be used [9; 10]. Cases may also be combined with other knowledge. To reuse cases from the past, a recorded experience needs to be similar to the new problem. Thus, each attribute in a new case requires its own similarity function. In the similarity assessment, comparing new case with cases that already exist in the case base, the relative relevance of each attribute also has to be represented. The new case is most similar to the nearest neighbour's case; therefore, the global similarity can be computed as sum of local similarities [7]:  
\[\sum_{\text{i=1}}^{\text{n}}(\text{w}_{\text{i}}\text{*sim}(\text{x}_{\text{i }},\;\text{y}_{\text{i}}))|1\leq\text{i}\leq\text{n} \tag{1}\]  
Depending on a concrete task, similarity may be obtained in various ways: using the Euclidean distance, using a real-valued function, classification and clustering algorithms (fuzzy, nearest neighbour, etc. ), and modelling similarity as the result of a dot product over feature vectors [11]. To compare a new case with past cases from the case base by using the common space of attributes, existing models for similarity-based retrieval may also be applied: ARCS, MAC/FAC models, etc. For example, [11] presents an efficient two-stage similarity-based model MAC/FAC, which uses content vectors to inexpensively search the memory first (MAC phase), and then applies a more expensive literal similarity matcher (FAC phase) for obtaining structurally sound matches.