## 1 Introduction  
Space debris, consisting of non-functional man-made objects in orbit or those re-entering the atmosphere, including fragments and components [1], has become the principal source of space pollution. With the growing number of space activities, the accumulation of space debris is becoming an ever-increasing problem. According to the latest data on the Space Track website, there are over 19,000 cataloged fragments larger than >10 cm in size orbiting the Earth. This debris poses a severe threat to spacecraft in near-Earth space, and its uncontrolled re-entry into the atmosphere can also threaten the safety of life and property on the ground. Detecting and identifying space debris is critical for ensuring the safety and sustainability of space resource development and utilization [2, 3]. Optical methods, in particular, offer the advantages of high recognition and \"what you see is what you get\", making them an important means of debris monitoring [4, 5]. In recent years, imaging resolutions have dramatically improved, and the inclusion of spectral information has further enhanced identification accuracy. Nevertheless, there are still challenges such as homospectral dissimilarity and classification difficulties. The results of several studies on space target polarization observation experiments, as well as simulation analyses, have demonstrated the significant advantages of polarization detection methodsin enhancing detection capabilities [6], reducing atmospheric effects [7], and retrieving target materials [8]. Recent studies suggest that using optical methods to detect and identify space debris is becoming increasingly important and is expected to be a critical approach in the future [9]. In this context, how to use the extra polarization information to further enhance the ability to classify and identify pieces has become an additional area of intense study interest. The prerequisite of classification is clustering, and research on this is particularly urgent. Clustering is a technology that groups samples with similar characteristic attributes into the same category for classification. Unlike other methods that rely on external parameters, clustering analyzes the characteristics of existing data to directly cluster data [10; 11]. The Fuzzy C-means clustering algorithm (FCM), an unsupervised clustering technique proposed by [PERSON] [12; 13], is an algorithm that assigns each data point to a cluster based on its degree of membership [14], which overcomes the limitations of binary clustering, and it has become a representative algorithm for clustering targets with a clear number of cluster cores [15]. Its iterative implementation, low storage cost, and high execution efficiency have been widely used in image segmentation processing [16; 17], and it can be combined with other algorithms to extract image feature information for fusion classification processing [18; 19; 20; 21]. FCM has found widespread applications in medical brain tissue [22], tumor tissue [23], and cytology images [24]. These applications essentially convert respective images into data information, and cluster the data using FCM [25; 26]. FCM is used in reference [27] to further cluster the border pictures, while reference [28] applies the FCM algorithm to classify water color information and optimizes the value of the fuzzy index m to enhance classification accuracy by mitigating the sharp boundaries that can be generated by traditional clustering methods. The fuzzy membership of border points necessitates flexible criteria for determining membership in the method used for spatial debris grouping based on polarization information. [PERSON] and his team were the first to propose a method that combines generative topographic maps (GTM) and FCM [29; 30]; [PERSON] and his team proposed a novel method called Conditional Fuzzy C-Means, which has been extended to neural network classifiers [31; 32; 33].