# WREB Mechanism: Web Search Results Exploration Mechanism for Blind Users
## 3 WSEB Mechanism
### Approach Formal Algorithm Definitions  
**Definition 1**.: _Query:_  
_The BU-based query \(q\) retrieves a set of documents \(D=\{d_{1},d_{2}\ldots,d_{n}\}\), which contains relevant textual information. During the information-seeking journey, the user may issue multiple queries and may refer to the previously issued query. Hence, multiple issued queries can be encapsulated in a set \(Q=\{q_{1},q_{2}\ldots,q_{n}\}\)._  
**Definition 2**.: _Multimodal Queries:_  
_The \(Q\) may comprise Textual query \(Q_{t}\) and Acoustic Query \(Q_{a}\). Both \(Q_{t}\) and \(Q_{a}\) accept multiple keywords as a set \(K=k_{1},k_{2}\ldots,k_{n}\). Moreover, the query may also incorporate Boolean operators (AND, OR, NOT). Hence, the formation of a query may take the form of \(k=k_{1}(AND\parallel OR\parallel NOT)k_{n}\)._  
**Definition 3**.: _Retrieved Documents:_  
_The \(d\) is considered as a tuple containing associated information \(d=t_{d},d_{d},d_{i}\), where \(t_{d}\) is the title of a document, \(u_{d}\) is the URL of the document and \(d_{i}\) is the document description. This can be formalized as \(\{t_{d},u_{d},d_{i}\}\in d\in D\)._  
**Definition 4**.: _Document Groupings:_  
_In \(D\), each unordered pair i.e., \(\{d_{n-1},d_{n}\}\) underpasses through statistical methods to form multiple groups \(g\) considering a threshold \(\gamma\). Let a set of groups \(G=\{g_{1},g_{2},\ldots,g_{n}\}\) and each \(g_{n}\) is a tuple-containing document \(g_{n}=\{d_{1},d_{2},\ldots,d_{n}\}\). However, all \(g_{n}\) documents contains unique \(d_{n}\); therefore, \(g_{n-1}\
eq g_{n}\)._  
**Definition 5**.: _Tree Data Model:_  
_Formally, a document tree DT is a pair containing nodes \(N\) and edges \(E\) given as \(T=(N,E)\). In the set of nodes \(N=\{n_{1},n_{2}\ldots,n_{n}\}\), each \(n\) represents the title of documents. For the set of edges \(E=\{e_{1},e_{2}\ldots,e_{n}\}\), each \(e\) represents weighted edges between nodes._  
**Definition 6**.: _Categorical Data Model:_  
_The categorical data model interacts with the k-array tree data model to generate hierarchies \(H=\{T_{1},T_{2}\ldots,T_{n}\}\). A similarity measure \(SM^{y}\) is applied on each \(T_{n}\) to arrange the hierarchies in descending order of similarity to \(Q\). This can be formalized as \(H^{\prime}=\{\forall(Q,T_{n})||SM^{y}(Q,T_{n})>SM^{y}(Q,T_{n-1})\}\), where \(y\) is a similarity threshold value._  
The notable distinction in the proposed categorical model is the prevention of overlapping hierarchies since the existing literature criticizes overlapping as being difficult to interpret, especially when documents belong to multiple branches or categories within the hierarchy [31]. This can make it challenging for users to understand the structure and locate relevant documents [32]. Furthermore, as the hierarchy grows, navigation and management become more challenging [33]. Hence, the decisive hierarchical structure was chosen to ensure that the form hierarchies are easier to interpret, able to handle high-dimensional data, demonstrate simplicity and high speed, good accuracy, and the capability to produce rules for clear and understandable human classification. To further enhance navigation within the proposed model, the cognitive rule is applied to display several categories where \(\{\forall T\in H^{\prime}\rightarrow|T|=7\mp 2\}\).  
```
Input: User Query \(Q\) Output: Retrieved Documents \(D\) Function Query (\(Q\)): ifmodality(\(Q\))!= Stringthen Q = MultimodalQueries(Q);  end if query = extract_keywords(Q); documents = fetch_results(query) return documents Function Multimodal Queries (\(Q\)): \(Q_{i}\) = extract_keywords(\(Q_{i}\)); return\(Q_{i}\) FunctionRetrieved Documents (_documents_): D = []; for document in documentsdo  D.append((title, URL, description = extract_metadata (_document_) D.append(tuple(title, URL, description)));  end for return D
```  
**Algorithm 1** Algorithm for querying and retrieving documents.