## 4 Discussion  
The research presented in this paper evaluates the efficacy of different machine learning models--SVM, LSTM, and boosting ensemble decision trees--in the context of tool condition monitoring in the milling processes. Support vector machines (SVMs) are particularly renowned for their ability to handle high-dimensional data efficiently. They work by finding a hyperplane that best divides a dataset into classes, which is particularly useful in complex classification problems where the decision boundaries are not readily apparent. The major challenges with SVM involve its sensitivity to the choice of kernel and the scaling of features; the right choice of kernel and proper feature scaling can significantly influence the model's performance. Despite these challenges, SVM's effectiveness in high-dimensional spaces makes it an excellent choice for classification tasks where the number of features exceeds the number of samples. The superiority of SVM in our experiments can be theoretically attributed to its structural risk minimization principle, which effectively handles the high-dimensional space of the features extracted from the milling data. The SVM's ability to construct a hyperplane in a high-dimensional space provides an optimal separation boundary between the classes, which is critical given the subtle variations in the tool's wear condition. On the other hand, the LSTM model underperformed, which could be due to its reliance on large datasets to capture complex dependencies in sequence data observed, while in our study it had limited data size and lacked a pre-trained network for times series data. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Classifier**} & **Sequential Data Required** & **Challenges** & **Advantages** \\ \hline \multirow{2}{*}{SVM} & \multirow{2}{*}{No} & Sensitive to feature scaling, kernel choice critical & Effective in high dimensional spaces \\ \hline \multirow{2}{*}{Boosting Ensemble DT} & \multirow{2}{*}{No} & Prone to overfitting; requires careful tuning & Good performance with non-linear data \\ \hline \multirow{2}{*}{LSTM} & \multirow{2}{*}{Yes} & Requires large dataset, complex model tuning & Excellent with sequential data \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparative analysis of algorithms, denoting requirements for sequential data, key challenges that each of them faces, and the main advantages. Boosting ensemble decision trees, such as those used in gradient-boosting machines (GBMs), harness the power of many weak decision trees to create a robust classifier. By focusing on correcting the errors of previous trees in a sequence, boosting methods can dramatically improve model accuracy. However, these models are susceptible to overfitting, especially when the data are noisy or when the trees are too complex. They also require careful tuning of parameters such as the number of trees and learning rate to balance bias and variance effectively. Nevertheless, their strength in handling non-linear data makes them suitable for complex data sets where the relationships between variables are nonlinear. Boosting ensemble decision trees showed a balanced performance, leveraging the strengths of multiple weak learners to improve classification accuracy. The ensemble approach is particularly effective for non-linear and complex decision boundaries that characterize tool wear data. A long short-term memory (LSTM) network, a type of recurrent neural network, is uniquely capable of analyzing sequential data. This makes this network ideal for applications such as time-series analysis, natural language processing, and other tasks where the order of data points is crucial. LSTMs can capture long-term dependencies in data sequences, a feature that traditional methods may fail to encapsulate. However, LSTMs come with their own set of challenges, including the need for large amounts of data to train effectively and the complexity involved in tuning multiple hyperparameters such as the number of layers and the size of the LSTM units.