## 1 Introduction
introduced a contrastive domain-difference adversarial autoencoder (CDD-AAE) framework, achieving balanced multi-lithology classification performance through extensive experimentation on LWD datasets [35]. [PERSON] et al. proposed a real-time lithology identification approach using functional networks, RF, and SVM models basedon drilling parameters such as ROP, WOB, and torque [36]. Existing lithology identification studies predominantly utilize supervised algorithms such as XGBoost, SVM, and RF, which achieve strong performance in scenarios with sufficient labeled data. XGBoost excels in structured logging data classification through gradient-boosted trees, while SVM leverages kernel-based optimization for high-dimensional feature separation, and RF provides noise-resistant interpretations via ensemble decision trees. However, these methods face inherent limitations in real-time LWD applications, particularly under conditions of label scarcity and dynamic downhole heterogeneity. To address these challenges, an increasing number of studies have focused on semi-supervised learning approaches [37; 38]. Semi-supervised learning extracts patterns and structures from data using a limited set of labeled samples, thereby mitigating the label dependency inherent in traditional supervised learning methods [39; 40]. Clustering algorithms, such as K-means and DBSCAN, effectively manage unlabeled data by capturing the intrinsic distribution and structure of the dataset, thus uncovering potential lithological information [41]. For example, [PERSON] et al. (2020) introduced a clustering-based lithology identification technique that achieved automatic classification of complex formation lithologies through the cluster analysis of logging data, eliminating the need for costly and time-intensive core sampling [42]. By combining clustering outcomes with auxiliary calibration, it is possible to integrate semi-quantitative interpretation of geophysical data with qualitative geological information. Nevertheless, numerous challenges remain in applying multi-source logging-while-drilling data within complex geological settings. Achieving efficient semi-supervised learning in multi-source logging-while-drilling data and effectively extracting the dynamic characteristics of reservoir geology and engineering during directional drilling continues to be a critical area for future research. LWD and drilling engineering data contain abundant information about formation characteristics but are inherently high dimensional. By integrating gamma ray, resistivity, and other petrophysical responses with dynamic drilling parameters--such as rate of penetration (ROP), weight on bit (WOB), and torque, which reflect rock-breaking efficiency--a composite feature space can be constructed that incorporates both geomechanical and petrophysical properties. To effectively extract meaningful patterns from this high-dimensional, multi-source dataset, dimensionality reduction techniques are essential. Both linear and nonlinear dimensionality reduction algorithms are widely employed in geoscientific data analysis. Among linear methods, Principal Component Analysis (PCA) has been extensively applied to well logging data to reduce the dimensionality of highly correlated lithological variables. PCA transforms the data into a set of uncorrelated principal components, which can then be directly or indirectly used as input for lithology identification models [43]. Nonlinear methods, such as t-Distributed Stochastic Neighbor Embedding (t-SNE), have also been utilized to explore spatial distributions within geological data and to visualize complex subsurface structures [44]. Uniform Manifold Approximation and Projection (UMAP), a more recent nonlinear technique, offers distinct advantages over earlier algorithms. UMAP preserves both local and global data structure, captures nonlinear relationships, and enhances class separability in feature space. It is particularly sensitive to subtle variations in drilling dynamics, such as those observed at the interfaces of thin reservoirs.