Distributed Partial Label Multi-Dimensional Classification via Label Space Decomposition

Multi-dimensional classification (MDC), in which the training data are concurrently associated with numerous label variables across many dimensions, has garnered significant interest recently. Most of the current MDC methods are based on the framework of supervised learning, which induces a predictive model from a large amount of precisely labeled data. So, they are challenged to obtain satisfactory learning results in the situation where the training data are not annotated with precise labels but assigned with ambiguous labels. Besides, the current MDC algorithms only consider the scenario of centralized learning, where all training data are handled at a single node for the purpose of classifier induction. However, in some real applications, the training data are not consolidated at a single fusion center, but rather are dispersedly distributed among multiple nodes. In this study, we focus on the problem of decentralized classification involving partial multi-dimensional data that have partially accessible candidate labels, and develop a distributed method called dPL-MDC for learning with these partial labels. In this algorithm, we conduct one-vs.-one decomposition on the originally heterogeneous multi-dimensional output space, such that the problem of partial MDC can be transformed into the issue of distributed partial multi-label learning. Then, by using several shared anchor data to characterize the global distribution of label variables, we propose a novel distributed approach to learn the label confidence of the training data. Under the supervision of recovered credible labels, the classifier can be induced by exploiting the high-order label dependencies from a common low-dimensional subspace. Experiments performed on various datasets indicate that our proposed method is capable of achieving learning performance in distributed partial MDC.