In the original belief function (BF) theory, a precise-valued belief structure has been widely used to represent uncertain information. However, this mentioned belief structure is difficult to effectively measure the specific hesitant situation, especially when decision makers have a set of possible values for the belief assignments of focal elements. In order to model the hesitant nature of the behavior of people to make a decision under uncertainty, we propose a hesitant fuzzy belief structure (HFBS) that is based on the BF theory and the recent hesitant fuzzy set theory. We also present the novel rule of combination of HFBS that is used and evaluated in a wearable human activity recognition (HAR) system coupled with an extreme learning machine. The evaluation of this new HFBS approach is done from two benchmark datasets. We clearly show its effectiveness and its superiority compared to various methods used classically for the wearable HAR.

Due to the corruptions or noises that existed in real-world data sets, the affinity graphs constructed by the classical spectral clustering-based subspace clustering algorithms may not be able to reveal the intrinsic subspace structures of data sets faithfully. In this article, we reconsidered the data reconstruction problem in spectral clustering-based algorithms and proposed the idea of “relation reconstruction.” We pointed out that a data sample could be represented by the neighborhood relation computed between its neighbors and itself. The neighborhood relation could indicate the true membership of its corresponding original data sample to the subspaces of a data set. We also claimed that a data sample’s neighborhood relation could be reconstructed by the neighborhood relations of other data samples; then, we suggested a much different way to define affinity graphs consequently. Based on these propositions, a sparse relation representation (SRR) method was proposed for solving subspace clustering problems. Moreover, by introducing the local structure information of original data sets into SRR, an extension of SRR, namely structured sparse relation representation (SSRR) was presented. We gave an optimization algorithm for solving SRR and SSRR problems and analyzed its computation burden and convergence. Finally, plentiful experiments conducted on different types of databases showed the superiorities of SRR and SSRR.

In recent years, wearable sensor-based human activity recognition (HAR) is becoming more and more attractive, especially in health monitoring and sports management. However, in order to obtain high-quality HAR, it is often necessary to get sufficient labeled activity data, which is very difficult, time-consuming, and costly in a natural environment. To tackle this problem, multisource domain adaptation (DA) is a promising method that aims to learn enough multisource prior knowledge from labeled activity data, and then transfer this learned knowledge to the target unlabeled dataset. Thus, this article presents a novel multisource weighted DA with evidential reasoning (w-MSDAER) for HAR, which can effectively utilize complementary knowledge between multiple sources. Specifically, we first use the strategy of distribution alignment to learn local domain-invariant classifiers based on multisource domains. And then the reliabilities of these derived classifiers are comprehensively evaluated according to the belief function based technique for order preference by similarity to ideal solution (BF-TOPSIS). Finally, the discounting fusion method is used to fuse the local classification results. Comprehensive experiments are conducted on two open-source datasets, and the results show that the proposed w-MSDAER significantly outperforms other state-of-art methods.

Classical radial basis function network (RBFN) is widely used to process the non‐linear separable data sets with the introduction of activation functions. However, the setting of parameters for activation functions is random and the distribution of patterns is not taken into account. To process this issue, some scholars introduce the kernel clustering into the RBFN so that the clustering results are related to the parameters about activation functions. On the base of the original kernel clustering, this study further discusses the influence of kernel clustering on an RBFN when the setting of kernel clustering is changing. The changing involves different kernel‐clustering ways [bubble sort (BS) and escape nearest outlier (ENO)], multiple kernel‐clustering criteria (static and dynamic) etc. Experimental results validate that with the consideration of distribution of patterns and the changes of setting of kernel clustering, the performance of an RBFN is improved and is more feasible for corresponding data sets. Moreover, though BS always costs more time than ENO, it still brings more feasible clustering results. Furthermore, dynamic criterion always cost much more time than static one, but kernel number derived from dynamic criterion is fewer than the one from static.