###### Abstract  
In contrast to conventional localization methods, connectivity-based localization is a promising approach that leverages wireless links among network nodes. Here, the Euclidean distance matrix (EDM) plays a pivotal role in implementing the multidimensional scaling technique for the localization of wireless nodes based on pairwise distance measurements. This is based on the representation of complex datasets in lower-dimensional spaces, resulting from the mathematical property of an EDM being a low-rank matrix. However, EDM data are inevitably susceptible to contamination due to errors such as measurement imperfections, channel dynamics, and clock asynchronization. Motivated by the low-rank property of the EDM, we introduce a new pre-processor for connectivity-based localization, namely denoising-autoencoder-aided EDM reconstruction (DAE-EDMR). The proposed method is based on optimizing the neural network by inputting and outputting vectors of the eigenvalues of the noisy EDM and the original EDM, respectively. The optimized NN de-noises the contaminated EDM, leading to an exceptional performance in connectivity-based localization. Additionally, we introduce a relaxed version of DAE-EDMR, i.e., truncated DAE-EDMR (T-DAE-EDMR), which remains operational regardless of variations in the number of nodes between the training and test phases in NN operations. The proposed algorithms show a superior performance in both EDM denoising and localization accuracy. Moreover, the method of T-DAE-EDMR notably requires a minimal number of training datasets compared to that in conventional approaches such as deep learning algorithms. Overall, our proposed algorithms reduce the required training dataset's size by approximately one-tenth while achieving more than twice the effectiveness in EDM denoising, as demonstrated through our experiments. os 2025 15 2656 10  
the cost and considerably limit location-based applications. Consequently, conventional localization methods such as global positioning systems (GPSs) are not suitable, as their direct implementation in IoT networks involves prohibitive demands for sophisticated equipment and substantial energy consumption and cannot meet the required accuracy level, for instance, in industrial setups. These limitations have significantly restricted the practical scalability of IoT networks. To overcome these challenges, massive wireless connections in IoT networks are leveraged for the cooperative location estimation of IoT devices, which is called connectivity-based localization [2; 3; 4; 5; 6; 7; 8; 9]. This approach not only tackles the limitations of the conventional localization methods but also enhances the localization accuracy, resulting in more robust and energy-efficient localization within IoT networks. From an algorithmic standpoint, multidimensional scaling (MDS) is a widely employed collection of statistical methods which are extensively utilized to create mappings of items based on their distance, i.e., dissimilarity [10; 11; 12; 13; 14; 15]. MDS methods are able to represent complex datasets in spaces with lower dimensions; meanwhile, they maintain the dissimilarity relations among the items in the original datasets. Here, the Euclidean distance matrix (EDM) is the key information for implementing the MDS technique, which is constructed using pairwise distance measurements. The EDM serves as a useful description of the point sets and a solid foundation for localization algorithm design due to its effective description of the point sets. However, in real-world environments, EDM data are inevitably prone to contamination due to errors resulting from different sources, such as the measurement resolution, signal quality, network asynchronization, non line-of-sight (NLoS) conditions, and so on. In fact, the contamination in the EDM degrades the localization performance of the MDS, particularly in large-scale IoT networks.