Handwritten mathematical expression recognition aims to automatically generate LaTeX sequences from given images. Currently, attention-based encoder-decoder models are widely used in this task. They typically generate target sequences in a left-to-right (L2R) manner, leaving the right-to-left (R2L) contexts unexploited. In this paper, we propose an Attention aggregation based Bi-directional Mutual learning Network (ABM) which consists of one shared encoder and two parallel inverse decoders (L2R and R2L). The two decoders are enhanced via mutual distillation, which involves one-to-one knowledge transfer at each training step, making full use of the complementary information from two inverse directions. Moreover, in order to deal with mathematical symbols in diverse scales, an Attention Aggregation Module (AAM) is proposed to effectively integrate multi-scale coverage attentions. Notably, in the inference phase, given that the model already learns knowledge from two inverse directions, we only use the L2R branch for inference, keeping the original parameter size and inference speed. Extensive experiments demonstrate that our proposed approach achieves the recognition accuracy of 56.85 % on CROHME 2014, 52.92 % on CROHME 2016, and 53.96 % on CROHME 2019 without data augmentation and model ensembling, substantially outperforming the state-of-the-art methods. The source code is available in https://github.com/XH-B/ABM.

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support vector machine (SVM) has been shown to exhibit superior predictive power compared to traditional approaches in many studies, such as mechanical equipment monitoring and diagnosis. However, SVM training is very costly in terms of time and memory consumption due to the enormous amounts of training data and the quadratic programming problem. In order to improve SVM training speed and accuracy, we propose a modified incremental support vector machine (MISVM) for regression problems in this paper. The main concepts are that using the distance from the margin vectors which violate the Karush-Kuhn-Tucker (KKT) condition to the final decision hyperplane to evaluate the importance of each margin vectors, and the margin vectors whose distance is below the specified value are preserved, the others are eliminated. Then the original SVs and the remaining margin vectors are used to train a new SVM. The proposed MISVM can not only eliminate the unimportant samples such as noise samples, but also preserved the important samples. The effectiveness of the proposed MISVMs is demonstrated with two UCI data sets. These experiments also show that the proposed MISVM is competitive with previously published methods.

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Sensitive and accurate fault features from the vibration signals of planetary gearboxes are essential for fault diagnosis, in which extreme learning machine (ELM) techniques have been widely adopted. To increase the sensitivity of extracted features fed in ELM, a novel feature extraction method is put forward, which takes advantage of the transient dynamics and the reconstructed high-dimensional data from the original vibration signal. First, based on fast kurtosis analysis, the range of transient dynamics of a vibration signal is located. Next, with the extracted kurtosis information, with variational mode decomposition, a series of intrinsic mode functions are decomposed; the ones that fall into the obtained ranges are selected as transient features, corresponding to maximum kurtosis value. Fed by the transient features, a hierarchical ELM model is well-trained for fault classification. Furthermore, a denoising auto-encoder is used to optimize input weight and threshold of implicit learning node of ELM, satisfying orthogonal condition to realize the layering of its hidden layers. Finally, a numerical case and an experiment are conducted to verify the performance of the proposed method. In comparison with its counterparts, the proposed method has a better classification accuracy in the aiding of transient features.