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Mitigating label noise is a crucial problem in classification. Noise filtering is an effective method of dealing with label noise which does not need to estimate the noise rate or rely on any loss function. However, most filtering methods focus mainly on binary classification, leaving the more difficult counterpart problem of multiclass classification relatively unexplored. To remedy this deficit, we present a definition for label noise in a multiclass setting and propose a general framework for a novel label noise filtering learning method for multiclass classification. Two examples of noise filtering methods for multiclass classification, multiclass complete random forest (mCRF) and multiclass relative density, are derived from their binary counterparts using our proposed framework. In addition, to optimize the NI_threshold hyperparameter in mCRF, we propose two new optimization methods a new voting cross-validation method and an adaptive method that employs a 2-means clustering algorithm. Furthermore, we incorporate SMOTE into our label noise filtering learning framework to handle the ubiquitous problem of imbalanced data in multiclass classification. We report experiments on both synthetic data sets and UCI benchmarks to demonstrate our proposed methods are highly robust to label noise in comparison with state-of-the-art baselines. All code and data results are available at https//github.com/syxiaa/Multiclass-Label-Noise-Filtering-Learning.Truncated Newton (TN) methods have been a useful technique for large-scale optimization. Instead of obtaining the full Newton direction, a truncated method approximately solves the Newton equation with an inner conjugate gradient (CG) procedure (TNCG for the whole method). These methods have been employed to efficiently solve linear classification problems. However, even in this deeply studied field, various theoretical and numerical aspects were not completely explored. The first contribution of this work is to comprehensively study the global and local convergence when TNCG is applied to linear classification. Because of the lack of twice differentiability under some losses, many past works cannot be applied here. We prove various missing pieces of theory from scratch and clarify many proper references. The second contribution is to study the termination of the CG method. For the first time when TNCG is applied to linear classification, we show that the inner stopping condition strongly affects the convergence speed. We propose using a quadratic stopping criterion to achieve both robustness and efficiency. The third contribution is that of combining the study on inner stopping criteria with that of preconditioning. We discuss how convergence theory is affected by preconditioning and finally propose an effective preconditioned TNCG.Accurate identification and localization of the vertebrae in CT scans is a critical and standard pre-processing step for clinical spinal diagnosis and treatment. Existing methods are mainly based on the integration of multiple neural networks, and most of them use heatmaps to locate the vertebrae's centroid. However, the process of obtaining vertebrae's centroid coordinates using heatmaps is non-differentiable, so it is impossible to train the network to label the vertebrae directly. Therefore, for end-to-end differential training of vertebrae coordinates on CT scans, a robust and accurate automatic vertebral labeling algorithm is proposed in this study. First, a novel end-to-end integral regression localization and multi-label classification network is developed, which can capture multi-scale features and also utilize the residual module and skip connection to fuse the multi-level features. Second, to solve the problem that the process of finding coordinates is non-differentiable and the spatial structure of location being destroyed, an integral regression module is used in the localization network. It combines the advantages of heatmaps representation and direct regression coordinates to achieve end-to-end training and can be compatible with any key point detection methods of medical images based on heatmaps. Finally, multi-label classification of vertebrae is carried out to improve the identification rate, which uses bidirectional long short-term memory (Bi-LSTM) online to enhance the learning of long contextual information of vertebrae. The proposed method is evaluated on a challenging data set, and the results are significantly better than state-of-the-art methods (identification rate is 91.1% and the mean localization error is 2.2 mm). The method is evaluated on a new CT data set, and the results show that our method has good generalization.The further exploration of the neural mechanisms underlying the biological activities of the human brain depends on the development of large-scale spiking neural networks (SNNs) with different categories at different levels, as well as the corresponding computing platforms. Neuromorphic engineering provides approaches to high-performance biologically plausible computational paradigms inspired by neural systems. In this article, we present a biological-inspired cognitive supercomputing system (BiCoSS) that integrates multiple granules (GRs) of SNNs to realize a hybrid compatible neuromorphic platform. A scalable hierarchical heterogeneous multicore architecture is presented, and a synergistic routing scheme for hybrid neural information is proposed. The BiCoSS system can accommodate different levels of GRs and biological plausibility of SNN models in an efficient and scalable manner. Over four million neurons can be realized on BiCoSS with a power efficiency of 2.8k larger than the GPU platform, and the average latency of BiCoSS is 3.62 and 2.49 times higher than conventional architectures of digital neuromorphic systems. selleckchem For the verification, BiCoSS is used to replicate various biological cognitive activities, including motor learning, action selection, context-dependent learning, and movement disorders. Comprehensively considering the programmability, biological plausibility, learning capability, computational power, and scalability, BiCoSS is shown to outperform the alternative state-of-the-art works for large-scale SNN, while its real-time computational capability enables a wide range of potential applications.