Jianshu Zhang, Chengxuan Qian, Haosen Sun, Haoran Lu, Dingcheng Wang, Letian Xue, Han Liu. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

As a fundamental mathematical problem in the field of machine learning, the linear separability test still lacks a theoretically complete and computationally efficient method. This paper proposes and proves a sufficient and necessary condition for linear separability test based on a sphere model. The advantage of this test method is two-fold: (1) it provides not only a qualitative test of linear separability but also a quantitative analysis of the separability of linear separable instances; (2) it has low time cost and is more efficient than existing test methods. The proposed method is validated through a large number of experiments on benchmark datasets and artificial datasets, demonstrating both its correctness and efficiency.

In this study, by using the quaternion algebra, multiple‐parameter fractional quaternion Fourier transform (MPFrQFT) is proposed to generalise the conventional multiple‐parameter fractional Fourier transform (MPFrFT) to quaternion signal processing in a holistic manner. First, the new transform MPFrQFT and its inverse transform are defined. An efficient discrete implementation method of MPFrQFT is then proposed, in which the relationship between MPFrQFT and MPFrFT of four components is utilised for a quaternion signal. Finally, a new colour image encryption algorithm based on the proposed MPFrQFT and the double random phase encoding technique is proposed to evaluate the performance of the proposed MPFrQFT. Experimental results demonstrate that: (i) the computational time of the proposed implementation method is almost a half of the direct method's time; (ii) the proposed MPFrQFT‐based encryption algorithm has an overall better performance than eight compared algorithms in security test and robustness test: it is more secure than the compared frequency‐based algorithms due to the larger key space and the more sensitive key ‘transform orders’; it is also more robust than the compared spatial‐domain algorithms.

Fuzzy c‐means (FCMs) with spatial constraints have been considered as an effective algorithm for image segmentation. The well‐known Gaussian mixture model (GMM) has also been regarded as a useful tool in several image segmentation applications. In this study, the authors propose a new algorithm to incorporate the merits of these two approaches and reveal some intrinsic relationships between them. In the authors model, the new objective function pays more attention on spatial constraints and adopts Gaussian distribution as the distance function. Thus, their model can degrade to the standard GMM as a special case. Our algorithm is fully free of the empirically pre‐defined parameters that are used in traditional FCM methods to balance between robustness to noise and effectiveness of preserving the image sharpness and details. Furthermore, in their algorithm, the prior probability of an image pixel is influenced by the fuzzy memberships of pixels in its immediate neighbourhood to incorporate the local spatial information and intensity information. Finally, they utilise the mean template instead of the traditional hidden Markov random field (HMRF) model for estimation of prior probability. The mean template is considered as a spatial constraint for collecting more image spatial information. Compared with HMRF, their method is simple, easy and fast to implement. The performance of their proposed algorithm, compared with state‐of‐the‐art technologies including extensions of possibilistic fuzzy c‐means (PFCM), GMM, FCM, HMRF and their hybrid models, demonstrates its improved robustness and effectiveness.

Wireless sensor networks are deployed in areas we are interested in to help users to retrieve raw data. Due to the limited power, it is desired that data retrieving routing protocols are energy efficient, and energy consumption can be balanced among all nodes so that lifetime of WSNs can be prolonged. In this paper, we propose a centralized clustering geographic energy aware routing (GEAR-CC) for wireless sensor networks. It has the dominance of both hierarchical routing and geographic energy aware routing. As a centralized algorithm, it takes full advantage of base station's sufficient power to conduct every transmission in the wireless sensor network. In GEAR-CC, the base station can easily formulate the optimal transmitting schemes for all sensor nodes based on the global information of topology and energy. The optimization is achieved by making trade-off between energy cost and node's residual power. Simulation results show that GEAR-CC can dramatically balance residual energy of each node to avoid hot-spot phenomenon, and the time the first cluster dies in network using GEAR-CC is about 1.57 times of clustering direct transmission routing and 1.32 times of cluster-head-to-cluster-head (CH-to-CH) routing.