The high-performance identification of insulating materials is crucial for reducing resource waste, minimizing pollution, and promoting resource recycling. To achieve this, a novel method based on laser-induced breakdown spectroscopy (LIBS), named the generalized spectrum method (GSM-LIBS), was proposed in this study. Compared to traditional dimensionality reduction methods such as PCA, GSM-LIBS outperforms by integrating multiple spectral features, preserving both global and local information that may be lost in PCA-based methods. GSM-LIBS not only effectively reduces the spectral dimensions but also extracts more key features, such as peak intensity, integral intensity, intensity ratio, radiation background, and spectral shape. These features help retain important information from the spectrum, providing more precise details such as plasma state, element concentration, and spectral characteristics, thereby significantly improving analysis performance. To verify the effectiveness of GSM-LIBS, this method was applied to the classification study of seven types of insulating materials and compared with principal component analysis (PCA-LIBS). To ensure the general applicability of this study, two traditional machine learning models, k-nearest neighbor (KNN) and support vector machine (SVM), and one deep learning model, neural network (NN), were used. For the machine learning models, the accuracy of the KNN and SVM classification models on the prediction set improved from 0.935 and 0.965 to 0.979 and 0.996, respectively. For the deep learning model, the performance of the NN classification model was also significantly improved, with accuracy increasing from 0.984 to 0.994. These experimental results strongly demonstrate the feasibility and effectiveness of GSM-LIBS in effectively reducing the spectral dimensions while retaining key information.