# A Review of the Development and Future Challenges of Case-Based Reasoning
## 3 Development of CBR Key Technologies
### Similarity Measure and Case Retrieval
#### 3.2.1 Similarity Measure  
In CBR, similarity is a bridge between case representation and retrieval. [PERSON] and [PERSON] [9] thoroughly introduced similarity evaluations, which are mainly divided into surface similarity, structural similarity, and a similarity framework. This method is mostly selected according to the case representation method; for example, feature representation often uses surface similarity calculation, and object-oriented case representation can use structural similarity calculation [31]. There are two mathematical methods for representing similarity: relationship description and function representation. Table 2 provides the details regarding similarity. The most commonly used method is to calculate the similarity between cases \(x\) and \(y\) by a distance metric function (taking Euclidean distance as an example):  
\[SIM(x,y)=1-DIST(x,y)=1-\sqrt{\sum_{i}w_{i}^{2}dist^{2}(x_{i},y_{i})} \tag{3}\]  
where \(x_{i}\) and \(y_{i}\) represent the same feature of the two cases, \(w_{i}\) is the corresponding weight, and \(SIM(x,y)\in[0,1]\). With the continuous expansion of CBR applications, there have been difficulties in obtaining similarity measurements based on complex or mixed data such as time series, images (or graph structure), or text in complex CBR tasks. However, since the metric function calculation is mainly applicable to the case of numerical attribute descriptions, it cannot be directly applied to cases containing multiple complex representations; therefore, improving retrieval performance by developing more effective similarity measurement methods has become the focus of research in the field of CBR, such as [32; 33; 34]. At present, many scholars have improved the measurement algorithm in the following three directions:  
1. An improved method based on a hybrid similarity measure [32; 35; 36; 37] mainly improves the calculation accuracy of similarity by processing attribute features, such as adding other information and setting multiple attribute value formats. This hybrid measurement method solves the similarity measurement problem of multi-attribute representation cases, but it often needs to combine the relevant knowledge of specific applications, which is a highly professional task and computationally complex. 2. Based on the weighted similarity measure of feature weight optimization [38; 39; 40; 41; 42], the measurement calculation is improved through the reasonable distribution of feature weight (i.e., \(w_{i}\) in Formula (3)). The emphasis is on the selection, optimization, and improvement of the weight distribution method. This kind of method has been studied for the longest amount of time, and the achievements are more fruitful. It combines information entropy, genetic algorithm, neural network, and other optimization algorithms. However, due to the different evaluation criteria in each article, how to choose the appropriate optimization algorithm in practical applications is a difficult problem. 3. Based on the (deep) metric learning algorithm [33; 43; 44], the learning of the similarity measure is achieved by training a (deep) neural network. This method has a shorter research time in CBR compared with that of other case similarity measurement algorithms. Its advantage is that it realizes similarity calculations in the form of a neural network, solves the nonlinear problem, and reduces the computational complexity of the similarity measurement process. In dealing with cases represented by text and images, etc., the network structure has better representation advantages in case data processing; however, problems such as the neural network design caused by this method also need to be considered and studied. In addition, there are some other intelligent methods combined with similarity measurement methods to improve the retrieval performance [45; 46; 47; 48]. However, due to the large number of AI methods, this article only lists several articles that the author believes have been more valuable in recent years for reference. [PERSON] et al.