## 2 Related Works  
### TF-IDF (Term Frequency-Inverse Document Frequency)  
With the rapid advancement of information technology and the exponential growth of data volume, efficient and accurate processing of large-scale unstructured data has become essential [10; 11; 12]. In this context, Term Frequency-Inverse Document Frequency (TF-IDF) is widely utilized as a fundamental feature extraction technique for representing textual data numerically. It plays a crucial role in text mining and information retrieval [13; 14; 15]. textTF-IDF calculates the importance of a word by considering two key factors:  
* textTerm Frequency (TF): measures the frequency of a term within a document. * Inverse Document Frequency (IDF): evaluates how rare a term is across all documents. The TF-IDF score is obtained by multiplying these two values: \[TF\text{-}IDF(t,d,D)=TF(t,d)\times IDF(t,D)\] (1)  
This scoring method ensures that terms frequently appearing in a document but rarely in the entire dataset receive higher importance, allowing effective differentiation of key terms. The definitions of Term Frequency (TF) and Inverse Document Frequency (IDF) are as follows:  
* Term Frequency (TF) quantifies how often a term \(t\) appears in a document \(d\): \[TF(t,d)=\frac{f_{t,d}}{\sum_{t^{\prime}\in d}f_{t^{\prime},d}}\] (2) where \(f_{t,d}\) represents the raw count of term \(t\) in document \(d\). * Inverse Document Frequency (IDF) measures the importance of a term by considering its occurrence across all documents in the collection \(D\): \[IDF(t,D)=\text{log}\bigg{(}\frac{N}{1+|\{d\in D:t\in d\}|}\bigg{)}\] (3) where \(N\) is the total number of documents, and \(|\{d\in D:t\in d\}|\) is the number of documents containing term \(t\). The \(+1\) in the denominator prevents division by zero when a term does not appear in any document. This smoothing technique ensures numerical stability. TF emphasizes frequently appearing words in a document, while IDF reduces the influence of common words that appear in many documents. The multiplication of these two values results in a higher TF-IDF score for terms that are frequent in a specific document but rare in the overall corpus. This mechanism enables effective text representation, allowing the proposed system to capture key error patterns in student diagnostic assessment data. By effectively converting textual data into numerical representations, TF-IDF provided a solid foundation for analyzing student learning errors. This transformation played a crucial role in our research, as it enabled the classification model (XGBoost) to extract meaningful insights from diagnostic assessments. The combination of TF-IDF and XGBoost not only addressed the limitations of previous studies but also expanded the applicability of text-based educational data analysis. These findings highlight the effectiveness of the proposed method in providing automated, scalable, and interpretable feedback for students. Due to its effectiveness, TF-IDF has become a core technology in modern search engines [16; 17]. Traditional data analysis methods often required manual interpretation, which introduced the risk of subjective bias and posed difficulties in processing large datasets efficiently. TF-IDF overcomes these limitations and offers several advantages. First, it converts textual data into numerical vectors, enhancing both processing speed and analytical accuracy. Second, it extracts critical patterns by identifying terms that appear frequently but are unique to specific documents. Finally, TF-IDF is applicable in a variety of fields, including information retrieval, document classification, and keyword extraction [18; 19]. The versatility of TF-IDF has led to its application in various domains. It has been used to extract key terms from large document collections and to evaluate important patterns in textual data. Additionally, TF-IDF has been applied in social media analytics to identify customer demands and analyze user sentiment fluctuations [20; 21; 22; 23].