Distributed Semi-Supervised Multi-Dimensional Uncertain Data Classification over Networks

Distributed multi-dimensional classification, where multiple nodes over a network induce a multi-dimensional classifier based on their own local data and a little information exchanged from neighbors, has received extensive attention in the academic community recently. Nevertheless, we observe that the classical distributed multi-dimensional classification formulation requires all training data to have definite feature attributes and complete labels. However, in real-world scenarios, due to measurement errors in distributed networks, the collected data samples consist of attributes with uncertainty. Additionally, a substantial proportion of multi-dimensional data faces challenges in label acquisition. Therefore, the key to achieving satisfactory performance in such a case is designing an effective method to model the input uncertainty and exploit weakly supervised information from the training data. Considering this, in this paper, we design a novel misclassification loss function that extracts effective information from uncertain data by treating it as the integral of misclassification loss over the potential data distribution. Additionally, we propose a new explicit feature mapping for constructing a nonlinear discriminant function. Based on this, we further put forward a novel manifold regularization term to recover multi-dimensional labels and simplify the original objective function to enable it to be optimized. By leveraging the gradient descent method, we optimize the simplified decentralized cost function and obtain the global optimal solution. We evaluate the performance of the proposed distributed semi-supervised multi-dimensional uncertain data classification algorithm, namely the dSMUDC algorithm, on several real datasets. The results of our experiments indicate that, in terms of all metrics, our proposed algorithm outperforms existing approaches to a significant extent.