Internet of Things (IoT) connects the physical world and the cyber world to offer intelligent services by data mining for big data. Each big data sample typically involves a large number of attributes, posing a remarkable challenge on the high-order possibilistic c-means algorithm (HOPCM). Specially, HOPCM requires high-performance servers with a large-scale memory and a powerful computing unit, to cluster big samples, limiting its applicability in IoT systems with low-end devices such as portable computing units and embedded devises which have only limited memory space and computing power. In this paper, we propose two high-order possibilistic c-means algorithms based on the canonical polyadic decomposition (CP-HOPCM) and the tensor-train network (TT-HOPCM) for clustering big data. In detail, we use the canonical polyadic decomposition and the tensor-train network to compress the attributes of each big data sample. To evaluate the performance of our algorithms, we conduct the experiments on two representative big data datasets, i.e., NUS-WIDE-14 and SNAE2, by comparison with the conventional high-order possibilistic c-means algorithm in terms of attributes reduction, execution time, memory usage and clustering accuracy. Results imply that CP-HOPCM and TT-HOPCM are potential for big data clustering in IoT systems with low-end devices since they can achieve a high compression rate for heterogeneous samples to save the memory space significantly without a significant clustering accuracy drop.