Abstract. There are two scalings for the convergence analysis of tau-leaping methods in the literature. This paper attempts to resolve this debate in the paper. We point out the shortcomings of both scalings. We systematically develop the weak Ito-Taylor expansion based on the infinitesimal generator of the chemical kinetic system and generalize the rooted tree theory for ODEs and SDEs driven by Brownian motion to rooted directed graph theory for the jump processes. We formulate the local truncation error analysis based on the large volume scaling. We find that even in this framework the midpoint tau-leaping does not improve the weak local order for the covariance compared with the explicit tau-leaping. We propose a procedure to explain the numerical order behavior by abandoning the dependence on the volume constant V from the leading error term. The numerical examples validate our arguments. We also give a general global weak convergence analysis for the explicit tau-leaping type methods in the large volume scaling.

The positioning error of ball screw feed systems is mainly caused by thermal elongation of the screw shaft in machine tools. In this article, an adaptive on-line compensation method of positioning error for the ball screw shaft is established. In order to explore the thermal–solid mechanism of ball screw feed drive systems, the experiments were carried out. An exponential fitting equation is presented to obtain the temperature relationship between the temperature sensitive point and its center of each heat source based on the finite element method of the feed drive system. Consequently, based on time and position exponential distribution functions, a variable separation model of heat transfer is established. Furthermore, based on the heat transfer model of multiple varying and moving heat sources, an adaptive on-line analytical compensation model of positioning error is presented. Finally, the effect of the adaptive on-line analytical compensation model of positioning error is verified through the experiments. And, this model has self-adaptive ability and robustness. Therefore, this adaptive on-line analytical compensation model based on the heat transfer theory can be applied in real-time compensation of positioning error.

Gesture is a natural form of human communication, and it is of great significance in human–computer interaction. In the dynamic gesture recognition method based on deep learning, the key is to obtain comprehensive gesture feature information. Aiming at the problem of inadequate extraction of spatiotemporal features or loss of feature information in current dynamic gesture recognition, a new gesture recognition architecture is proposed, which combines feature fusion network with variant convolutional long short‐term memory (ConvLSTM). The architecture extracts spatiotemporal feature information from local, global and deep aspects, and combines feature fusion to alleviate the loss of feature information. Firstly, local spatiotemporal feature information is extracted from video sequence by 3D residual network based on channel feature fusion. Then the authors use the variant ConvLSTM to learn the global spatiotemporal information of dynamic gesture, and introduce the attention mechanism to change the gate structure of ConvLSTM. Finally, a multi‐feature fusion depthwise separable network is used to learn higher‐level features including depth feature information. The proposed approach obtains very competitive performance on the Jester dataset with the classification accuracies of 95.59%, achieving state‐of‐the‐art performance with 99.65% accuracy on the SKIG (Sheffifield Kinect Gesture) dataset.

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A novel semi-supervised learning method is proposed to better utilize labeled and unlabeled samples to improve classification performance. However, there is exists the limitation that Laplace regularization in a semi-supervised extreme learning machine (SSELM) tends to lead to poor generalization ability and it ignores the role of labeled information. To solve the above problems, a Joint Regularized Semi-Supervised Extreme Learning Machine (JRSSELM) is proposed, which uses Hessian regularization instead of Laplace regularization and adds supervised information regularization. In order to solve the problem of slow convergence speed and the easy to fall into local optimum of marine predator algorithm (MPA), a multi-strategy marine predator algorithm (MSMPA) is proposed, which first uses a chaotic opposition learning strategy to generate high-quality initial population, then uses adaptive inertia weights and adaptive step control factor to improve the exploration, utilization, and convergence speed, and then uses neighborhood dimensional learning strategy to maintain population diversity. The parameters in JRSSELM are then optimized using MSMPA. The MSMPA-JRSSELM is applied to logging oil formation identification. The experimental results show that MSMPA shows obvious superiority and strong competitiveness in terms of convergence accuracy and convergence speed. Also, the classification performance of MSMPA-JRSSELM is better than other classification methods, and the practical application is remarkable.

Hyperspectral Images (HSIs) contain enriched information due to the presence of various bands, which have gained attention for the past few decades. However, explosive growth in HSIs’ scale and dimensions causes “Curse of dimensionality” and “Hughes phenomenon”. Dimensionality reduction has become an important means to overcome the “Curse of dimensionality”. In hyperspectral images, labeled samples are more difficult to collect because they require many labor and material resources. Semi-supervised dimensionality reduction is very important in mining high-dimensional data due to the lack of costly-labeled samples. The promotion of the supervised dimensionality reduction method to the semi-supervised method is mostly done by graph, which is a powerful tool for characterizing data relationships and manifold exploration. To take advantage of the spatial information of data, we put forward a novel graph construction method for semi-supervised learning, called SLIC Superpixel-based l 2 , 1 -norm Robust Principal Component Analysis (SURPCA2,1), which integrates superpixel segmentation method Simple Linear Iterative Clustering (SLIC) into Low-rank Decomposition. First, the SLIC algorithm is adopted to obtain the spatial homogeneous regions of HSI. Then, the l 2 , 1 -norm RPCA is exploited in each superpixel area, which captures the global information of homogeneous regions and preserves spectral subspace segmentation of HSIs very well. Therefore, we have explored the spatial and spectral information of hyperspectral image simultaneously by combining superpixel segmentation with RPCA. Finally, a semi-supervised dimensionality reduction framework based on SURPCA2,1 graph is used for feature extraction task. Extensive experiments on multiple HSIs showed that the proposed spectral-spatial SURPCA2,1 is always comparable to other compared graphs with few labeled samples.