## 1 Introduction  
Porphyry deposits are globally significant sources of copper, molybdenum, and gold. Among them, porphyry copper deposits contribute approximately 55% of the world's copper reserves, while porphyry molybdenum deposits account for approximately 90% of global molybdenum reserves. Additionally, porphyry gold deposits make up around 20% of the world's gold reserves. Notably, China possesses a significant proportion of porphyry deposits [1; 2; 3; 4]. In recent years, extensive exploration and research efforts have been conducted on large-scale porphyry copper mines such as Qulong, Jiama, Xiongcun, Duolong, and Tiegelongnan. These endeavors have revealed the Qinghai-Tibet Plateau as a region of utmost importance and potential for copper production in China [5]. Mineralization is a process that leads to the concentration and accumulation of valuable materials within a relatively limited temporal and spatial range, as compared to normal regional geological processes [6]. The complexity of the metallogenic process stems from the intricate dynamics of multi-component and multi-geological interactions, coupled with overlay and other complex processes [7]. Relying solely on the exploration of single elements through geochemical analysis is insufficient for the porphyry copper mine prospecting work. Therefore, the identification of combination elements plays a crucial role in geochemical data processing. Currently, methods such as principal component analysis (PCA), robust principal component analysis (RPCA), factor analysis (FA), and robust factor analysis (RFA) are employed for combination element identification [8; 9; 10; 11; 12; 13]. These methods often require logarithmic transformations or logratio transformations (such as alr: additive logratio, clr: centered logratio, _ilr_: isometric logratio, etc.) to eliminate the closure effect of compositional data. However, they encounter challenges during the analysis process, such as difficulties in interpretation and singularity effects, which are difficult to resolve. To address these issues, some researchers have proposed the ILR-RPCA-back CLR statistical model. This model involves transforming the raw geochemical data through an isometric logarithm (ILR) transformation and subsequently applying robust principal component analysis (RPCA) for data processing. The scores and loads obtained from RPCA are then transformed into the centered logratio (CLR) space using the U-matrix [14]. While this method has been applied in the analysis of geochemical data related to magma-hydrothermal ore deposits [14; 15], challenges in interpretation and other aspects persist (please refer to Section 4 for more details). Moreover, the combination elements extracted during the analysis of the above method, particularly in small-scale geochemical data, are predominantly associated with environmental (background) elements rather than ore-forming elements. In the Gangdese metallogenic belt, the porphyry copper deposits exhibit a distinct combination of mineralization elements. Utilizing spatial overlay analysis pertaining to deposit genesis is more advantageous for identifying porphyry copper deposits. In the eastern section of the Gangdese metallogenic belt, which is known as the largest district for dense porphyry copper deposits, numerous large and super large deposits like Qulong, Tinggong, Chongjiang, Jiama, and Bairong have been discovered. However, in the western section of the belt, the number of discovered deposits remains relatively limited. Due to the limitations of traditional methods in identifying complex anomalies and low-delay anomalies, it becomes necessary to employ advanced theories and techniques to guide prospecting efforts for porphyry copper deposits in the western section of the Gangdese metallogenic belt.