## 5 Behavioral Demonstration of RANs
### Experiment with IRIS Dataset  
There are two objectives of this probe, first is to demonstrate flexibility in choosing an appropriate methodology for concept Identification operation in RANs modeling (see Section 4.2). The second is to show how RANs modeling can be used to build a deep hierarchy of convex abstract concepts dynamically. This experiment uses affinity propagation [58] clustering algorithm as a concept identifier to support the claim of independence in selecting a suitable clustering method for CI process in RANs modeling. Unlike the K-means algorithm (used to describe the RANs methodology in Section 4), with the affinity propagation algorithm, the number of clusters within the data need not be known beforehand. Furthermore, affinity propagation conforms to the basic requirements (see Section 4.2) for being a concept identifier in RANs modeling. The second prospect of this experiment is to illustrate the dynamic topology of the RAN's approach where the network grows to form several layers representing convex abstract concepts. For this demonstration, an algorithm is developed, named Concept Hierarchy Creation (CHC) algorithm (see Algorithm 2). The CHC algorithm streamlines all four steps of RANs modeling (i.e., CI, CC, ILL and UAP) and uses these steps iteratively to build a hierarchy of convex abstract concepts as described through Algorithm 2. This experiment was also conducted using the IRIS dataset obtained from the UCI machine learning repository [60]. In the CHC algorithm the affinity propagation clustering algorithm was initialized with the following parameters: (1) damping_factor (DF) = 0.94 for layers below level 3, DF = 0.9679 for the layers at level 3 and above; (2) convergence_iteration = 15; (3) max_iteration = 1000. ```
Input: Multi-variate data with values between [0,1]. Output: Set of layers of concepts--concept hierarchy. Initialization: Create input layer layer-0 having dimension equal to that of input data. Set Current-layer-size \(CLS\) = \(i\), dimension of input-data vector. Set Layer-count \(L\) = 0. Set Desired-depth = 6. Select Clustering algorithm and initialize. Set current-data = input-data. repeat Run clustering algorithm on current-data to identify set of cluster centers \(C\). Create a new-layer above current-layer, with no nodes. for each cluster center \(C_{j}\in C\)do Create new node \(j\) in new layer \(l\) + 1. for each node \(i\) in current-layerdo Create a new weighted connection \(W_{c_{j},i}\) between \(c_{j}\) and \(i\) such that \(W_{c_{i},i}\) is the coordinate of \(c\) along the \(i\) dimension. endfor endfor Set new-data = empty data set. for each datum in current-datado Inject datum in current-layer  Propagate activation from current-layer to new-layer using algorithm 1. Add activation pattern produced in new-layer to new-data. endfor Set \(L\) = \(L\) + 1. Set \(CLS\) = number of clusters in current-layer. Set current-data = new-data. Set current-layer = new-layer. until\(CLS\) = 1 OR Desired-depth = \(L\). ```  
**Algorithm 2** Concept Hierarchy Creation algorithm  
Input layer-0 was created, with four nodes (equal to the dimension of IRIS data), and the RANs hierarchy generation was carried out according to Algorithm 2. The model obtained from the CHC process is depicted by Figure 7, the model was initialized to grow six layers deep. Therefore, hierarchy augmentation terminates at Layer-5, with Layer-5 identified as most abstract layer consisting of three nodes acting as abstract representatives of three categories of flowers of IRIS dataset. To evaluate the obtained RANs model, True-labels, and Test-labels were retrieved using an abstract concept labeling procedure (see Appendix A.3). A confusion matrix (see Figure 8a) was generated using the True and Test labels. With the aid of the confusion matrix, Precision, Recall, F1-Score, and Accuracy were calculated to evaluate the model. The model performed quite recently with an observed accuracy of 93.33 (ca.