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Second-Order Structure Optimization of Fully Complex-Valued Neural Networks 全复值神经网络的二阶结构优化
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-19 DOI: 10.1109/TETCI.2024.3360308
Zhidong Wang;He Huang
This paper focuses on proposing a second-order complex-valued incremental learning (CVIL) algorithm for the structure optimization of fully complex-valued neural networks (FCVNNs). The main purpose of this study is to integrate the structure optimization and parameter learning of FCVNNs into a unified framework such that good generalization is guaranteed. A hybrid training strategy is firstly developed for FCVNNs with fixed structure. By introducing complex-valued sparse matrices and generalized augmented hidden output matrix, nonlinear parameters between the hidden and input neurons are trained by complex-valued Levenberg-Marquardt (CLM) algorithm and linear parameters between the output and hidden neurons are obtained by complex-valued least squares (CLS) algorithm. Starting with an initial FCVNN, hidden neurons are added one by one once the training falls in the plateau. It is theoretically shown that the objective function is monotonously decreasing after adding hidden neuron and successive learning is immediately continuous with the latest training results. Repetition training is avoided and thus training efficiency is achieved. The experimental results on the channel modulation identification and real-valued pattern classification tasks are provided to demonstrate that the developed algorithm is superior to some existing ones for the training of FCVNNs.
本文主要针对全复值神经网络(FCVNN)的结构优化提出了一种二阶复值增量学习(CVIL)算法。本研究的主要目的是将 FCVNNs 的结构优化和参数学习整合到一个统一的框架中,从而保证良好的泛化效果。首先,针对固定结构的 FCVNNs 开发了一种混合训练策略。通过引入复值稀疏矩阵和广义增强隐藏输出矩阵,利用复值莱文伯格-马夸特(CLM)算法训练隐藏神经元和输入神经元之间的非线性参数,利用复值最小二乘法(CLS)算法获得输出神经元和隐藏神经元之间的线性参数。从初始 FCVNN 开始,一旦训练达到高原,就逐个添加隐藏神经元。理论证明,添加隐藏神经元后,目标函数单调递减,且连续学习与最新训练结果立即连续。避免了重复训练,从而提高了训练效率。在信道调制识别和实值模式分类任务上的实验结果表明,所开发的算法在 FCVNN 的训练上优于现有的一些算法。
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引用次数: 0
Fast Video-Based Point Cloud Compression Based on Early Termination and Transformer Model 基于提前终止和变压器模型的快速视频点云压缩
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-16 DOI: 10.1109/TETCI.2024.3360290
Yihan Wang;Yongfang Wang;Tengyao Cui;Zhijun Fang
Video-based Point Cloud Compression (V-PCC) was proposed by the Moving Picture Experts Group (MPEG) to standardize Point Cloud Compression (PCC). The main idea of V-PCC is to project the Dynamic Point Cloud (DPC) into auxiliary information, occupancy, geometry, and attribute videos for encoding utilizing High Efficiency Video Coding (HEVC), Versatile Video Coding (VVC), etc. Compared with the previous PCC algorithms, V-PCC has achieved a significant improvement in compression efficiency. However, it is accompanied by substantial computational complexity. To solve this problem, this paper proposes a fast V-PCC method to decrease the coding complexity. Taking into account the coding characteristic of V-PCC, the geometry and attribute maps are first classified into occupied and unoccupied blocks. Moreover, we analyze Coding Unit (CU) splitting for geometry and attribute map. Finally, we propose fast V-PCC algorithms based on early termination algorithm and transformer model, in which the early termination method is proposed for low complexity blocks in the geometry and attribute map, and the transformer model-based fast method is designed to predict the optimal CU splitting modes for the occupied block of the attribute map. The proposed algorithms are implemented with typical DPC sequences on the Test Model Category 2 (TMC2). The experimental results imply that the average time of the proposed method can significantly reduce 56.39% and 55.10% in the geometry and attribute map, respectively, with negligible Bjontegaard-Delta bitrate (BD-rate) compared with the anchor method.
基于视频的点云压缩(V-PCC)是由移动图像专家组(MPEG)为规范点云压缩(PCC)而提出的。V-PCC 的主要思想是将动态点云(DPC)投射到辅助信息、占位、几何和属性视频中,利用高效视频编码(HEVC)、多功能视频编码(VVC)等进行编码。与之前的 PCC 算法相比,V-PCC 在压缩效率方面有了显著提高。然而,它也伴随着巨大的计算复杂性。为解决这一问题,本文提出了一种快速 V-PCC 方法,以降低编码复杂度。考虑到 V-PCC 的编码特性,首先将几何图形和属性图划分为占用块和未占用块。此外,我们还分析了几何图形和属性图的编码单元(CU)分割。最后,我们提出了基于早期终止算法和变压器模型的快速 V-PCC 算法,其中针对几何图形和属性图中的低复杂度块提出了早期终止方法,并设计了基于变压器模型的快速方法来预测属性图中已占用块的最佳 CU 分割模式。在测试模型类别 2(TMC2)上使用典型的 DPC 序列实现了所提出的算法。实验结果表明,与锚定方法相比,所提方法在几何图形和属性图上的平均时间可分别显著减少 56.39% 和 55.10%,而比特率(BD-rate)则可忽略不计。
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引用次数: 0
Joint Spectrum and Power Allocation in Wireless Network: A Two-Stage Multi-Agent Reinforcement Learning Method 无线网络中的联合频谱和功率分配:两阶段多代理强化学习法
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-16 DOI: 10.1109/TETCI.2024.3360305
Pengcheng Dai;He Wang;Huazhou Hou;Xusheng Qian;Wenwu Yu
This paper investigates the application of multi-agent reinforcement learning (MARL) algorithm to solve the joint spectrum and power allocation problem (JSPAP) in wireless network. The objective of JSPAP is to optimize the subband selection and transmit power levels for links, with the aim of maximizing the sum-rate utility function. To address the JSPAP with discrete subband selection and continuous power allocation, most existing algorithms rely on a centralized optimizer and the instantaneous global channel state information, which can be challenging to implement in large wireless networks with time-varying subbands. To conquer such limitation, a two-stage MARL algorithm is proposed, which comprises a top layer network for selecting subbands across all links and a bottom layer network for determining the transmit power levels for all transmitters. By utilizing the value decomposition technique in the top layer network, the links can cooperatively select transmission subbands, effectively resolving non-stationarity issues in wireless network. Additionally, in the bottom layer network of the proposed two-stage MARL algorithm, each transmitter selects the transmit power level based solely on the local information, thereby effectively reducing computational burden. Empirical experiments demonstrate the effectiveness of the proposed two-stage MARL algorithm by comparison with the state-of-the-art RL algorithms and fractional programming algorithms.
本文研究了如何应用多代理强化学习(MARL)算法来解决无线网络中的联合频谱和功率分配问题(JSPAP)。JSPAP 的目标是优化链路的子带选择和发射功率水平,以实现总速率效用函数的最大化。为了解决具有离散子带选择和连续功率分配的 JSPAP 问题,大多数现有算法都依赖于集中优化器和瞬时全局信道状态信息,这在具有时变子带的大型无线网络中实施起来具有挑战性。为了克服这种限制,我们提出了一种两阶段 MARL 算法,它由一个用于在所有链路上选择子带的顶层网络和一个用于确定所有发射机发射功率水平的底层网络组成。通过在顶层网络中使用值分解技术,各链路可以协同选择传输子带,从而有效解决无线网络中的非稳态问题。此外,在所提出的两阶段 MARL 算法的底层网络中,每个发射机仅根据本地信息选择发射功率级别,从而有效减轻了计算负担。通过与最先进的 RL 算法和分数编程算法进行比较,实证实验证明了所提出的两阶段 MARL 算法的有效性。
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引用次数: 0
Autopilot Controller of Fixed-Wing Planes Based on Curriculum Reinforcement Learning Scheduled by Adaptive Learning Curve 基于自适应学习曲线调度的课程强化学习的固定翼飞机自动驾驶控制器
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-16 DOI: 10.1109/TETCI.2024.3360322
Lun Li;Xuebo Zhang;Chenxu Qian;Runhua Wang;Minghui Zhao
In this paper, we present a novel curriculum reinforcement learning method that can automatically generate a high-performance autopilot controller for a 6-degree-of-freedom (6-DOF) aircraft with an unknown dynamic model, which is difficult to be handled using traditional control methods. In this method, a sigmoid-like learning curve is elegantly introduced to generate goals (the desired heading, altitude, and velocity) from easy to hard for autopilot. The shape of the learning curve can be intelligently adjusted to adapt to the training process of Proximal Policy Optimization (PPO). In addition, the conflict between multiple goals in autopilot training is solved by designing an adaptive reward function. Furthermore, the control inputs can avoid large oscillations by filtering the outputs from PPO with a first-order filter to ensure the smoothness. A series of simulation results show that the proposed method can not only observably improve the success rate and stability of training but also has superior performance in settling time and robustness compared with the traditional PID control and a state-of-the-art (SOTA) method. In the end, the applications of the controller, including the navigation task, pursuit-evasion, and dogfighting, are demonstrated to prove its feasibility to multiple tasks.
本文提出了一种新颖的课程强化学习方法,可为具有未知动态模型的 6 自由度(6-DOF)飞机自动生成高性能自动驾驶控制器,而传统的控制方法很难处理这一问题。在这种方法中,优雅地引入了一条类似于西格玛的学习曲线,为自动驾驶仪生成由易到难的目标(所需航向、高度和速度)。学习曲线的形状可以智能调整,以适应近端策略优化(PPO)的训练过程。此外,通过设计自适应奖励函数,解决了自动驾驶训练中多个目标之间的冲突。此外,通过对 PPO 的输出进行一阶滤波以确保平滑性,从而避免了控制输入的大幅振荡。一系列仿真结果表明,与传统的 PID 控制和最先进的(SOTA)方法相比,所提出的方法不仅能明显提高训练的成功率和稳定性,而且在平稳时间和鲁棒性方面也有更出色的表现。最后,还演示了该控制器的应用,包括导航任务、追击-规避和斗犬,以证明其在多种任务中的可行性。
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引用次数: 0
RobustEdge: Low Power Adversarial Detection for Cloud-Edge Systems RobustEdge:面向云边缘系统的低功耗对抗检测
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-16 DOI: 10.1109/TETCI.2024.3360316
Abhishek Moitra;Abhiroop Bhattacharjee;Youngeun Kim;Priyadarshini Panda
In practical cloud-edge scenarios, where a resource constrained edge performs data acquisition and a cloud system (having sufficient resources) performs inference tasks with a deep neural network (DNN), adversarial robustness is critical for reliability and ubiquitous deployment. Adversarial detection is a prime adversarial defense technique used in prior literature. However, in prior detection works, the detector is attached to the classifier model and both detector and classifier work in tandem to perform adversarial detection that requires a high computational overhead which is not available at the lowpower edge. Therefore, prior works can only perform adversarial detection at the cloud and not at the edge. This means that in case of adversarial attacks, the unfavourable adversarial samples must be communicated to the cloud which leads to energy wastage at the edge device. Therefore, a low-power edge-friendly adversarial detection method is required to improve the energy efficiency of the edge and robustness of the cloud-based classifier. To this end, RobustEdge proposes Quantization-enabled Energy Separation (QES) training with “early detection and exit” to perform edge-based low cost adversarial detection. The QEStrained detector implemented at the edge blocks adversarial data transmission to the classifier model, thereby improving adversarial robustness and energy-efficiency of the Cloud-Edge system. Through extensive experiments on CIFAR10, CIFAR100 and TinyImagenet, we find that 16-bit and 12-bit quantized detectors achieve a high AUC score $>$ 0.9 while improving the energy-efficiency of the cloud-edge system by $>166times$ compared to prior cloud-based adversarial detection approaches.
在实际的云边缘场景中,资源受限的边缘执行数据采集,而云系统(拥有充足的资源)使用深度神经网络(DNN)执行推理任务,对抗鲁棒性对于可靠性和泛在部署至关重要。对抗检测是之前文献中使用的一种主要对抗防御技术。然而,在之前的检测工作中,检测器是附加在分类器模型上的,检测器和分类器协同工作,以执行对抗检测,这需要很高的计算开销,而低功耗边缘不具备这种能力。因此,先前的工作只能在云端而非边缘执行对抗检测。这意味着在发生对抗性攻击时,必须将不利的对抗性样本传送到云端,从而导致边缘设备的能源浪费。因此,需要一种低功耗的边缘友好对抗检测方法来提高边缘的能效和基于云的分类器的鲁棒性。为此,RobustEdge 提出了 "早期检测和退出 "的量化能量分离(Quantization-enabled Energy Separation,QES)训练,以执行基于边缘的低成本对抗检测。在边缘实施的 QES 训练检测器会阻止向分类器模型传输对抗数据,从而提高云边缘系统的对抗鲁棒性和能效。通过在 CIFAR10、CIFAR100 和 TinyImagenet 上的大量实验,我们发现 16 位和 12 位量化检测器实现了较高的 AUC 得分 $>$0.9,同时与之前的基于云的对抗检测方法相比,云边系统的能效提高了 $>166/times$。
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引用次数: 0
RSTNet: Recurrent Spatial-Temporal Networks for Estimating Depth and Ego-Motion RSTNet:用于估计深度和自我运动的递归时空网络
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-15 DOI: 10.1109/TETCI.2024.3360329
Tuo Feng;Dongbing Gu
Depth map and ego-motion estimations from monocular consecutive images are challenging to unsupervised learning Visual Odometry (VO) approaches. This paper proposes a novel VO architecture: Recurrent Spatial-Temporal Network (RSTNet), which can estimate the depth map and ego-motion from monocular consecutive images. The main contributions in this paper include a novel RST-encoder layer and its corresponding RST-decoder layer, which can preserve and recover spatial and temporal features from inputs. Our RSTNet extracts appearance features from input images, and extracts structure and temporal features from intermediate results for ego-motion estimation. Our RSTNet also includes a pre-trained network to detect dynamic objects from the difference between full and rigid optical flows. A novel auto-mask scheme is designed in the loss function to deal with some challenging scenes. Our evaluation results on the KITTI odometry benchmark show our RSTNet outperforms some of the existing unsupervised learning approaches.
从单目连续图像中估计深度图和自我运动对于无监督学习的视觉位置测量(VO)方法来说是一项挑战。本文提出了一种新型 VO 架构:Recurrent Spatial-Temporal Network (RSTNet),它可以从单眼连续图像中估计深度图和自我运动。本文的主要贡献包括一个新颖的 RST 编码器层和相应的 RST 解码器层,它们可以从输入中保留和恢复空间和时间特征。我们的 RSTNet 从输入图像中提取外观特征,并从中间结果中提取结构和时间特征,用于自我运动估计。我们的 RSTNet 还包括一个预先训练好的网络,用于从完整光流和刚性光流之间的差异中检测动态物体。在损失函数中设计了一种新颖的自动掩码方案,以应对一些具有挑战性的场景。我们在 KITTI 测速基准上的评估结果表明,我们的 RSTNet 优于现有的一些无监督学习方法。
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引用次数: 0
A Multi-Population Based Evolutionary Algorithm for Many-Objective Recommendations 基于多群体的多目标推荐进化算法
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-13 DOI: 10.1109/TETCI.2024.3359093
Lei Zhang;Huabin Zhang;Zihao Chen;Sibo Liu;Haipeng Yang;Hongke Zhao
Multi-objective evolutionary algorithms (MOEAs) have been proved to be competitive in recommender systems. As the application scenarios of recommender systems become increasingly complex, the number of objectives to be considered in the recommender systems increases. However, most existing multi-objective recommendation algorithms lead to increased environmental selection pressure as the number of objectives increases. To tackle the issue, in this paper, we propose a multi-population based evolutionary algorithm named MP-MORS for many-objective recommendations, where two subpopulations and one major population are used to evolve and interact to find high-quality solutions. Specifically, the objectives are firstly divided into those evaluated on individual users (defined as IndObjectives) and those evaluated on all users (defined as as AllObjectives). Then two subpopulations are suggested to optimize the two types of objectives respectively, with which the potential good solutions can be easily found. In addition, the major population considers the balance of all objectives and refines these potential good solutions. Finally, a set of high-quality solutions can be obtained by the proposed adaptive population interaction strategy. Experiments on the datasets Movielens and Douban show that the proposed MP-MORS outperforms the state-of-the-art algorithms for many-objective recommendations.
多目标进化算法(MOEAs)已被证明在推荐系统中具有竞争力。随着推荐系统的应用场景变得越来越复杂,推荐系统中需要考虑的目标数量也随之增加。然而,大多数现有的多目标推荐算法都会随着目标数量的增加而导致环境选择压力增大。为了解决这个问题,本文提出了一种基于多种群的进化算法,名为 MP-MORS,用于多目标推荐,其中使用两个子种群和一个主种群进行进化和交互,以找到高质量的解决方案。具体来说,首先将目标分为对单个用户进行评估的目标(定义为 IndObjectives)和对所有用户进行评估的目标(定义为 AllObjectives)。然后建议两个子群分别对这两类目标进行优化,这样就能很容易地找到潜在的好解决方案。此外,主群还会考虑所有目标的平衡,并完善这些潜在的优秀解决方案。最后,通过所提出的自适应种群交互策略,可以获得一组高质量的解决方案。在 Movielens 和豆瓣数据集上的实验表明,所提出的 MP-MORS 优于最先进的多目标推荐算法。
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引用次数: 0
Game of Drones: Intelligent Online Decision Making of Multi-UAV Confrontation 无人机游戏:多无人机对抗的智能在线决策
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-13 DOI: 10.1109/TETCI.2024.3360282
Da Liu;Qun Zong;Xiuyun Zhang;Ruilong Zhang;Liqian Dou;Bailing Tian
Due to the characteristics of the small size and low cost of unmanned aerial vehicles (UAVs), Multi-UAV confrontation will play an important role in future wars. The Multi-UAV confrontation game in the air combat environment is investigated in this paper. To truly deduce the confrontation scene, a physics engine is established based on the Multi-UAV Confrontation Scenario (MCS) framework, enabling the real-time interaction between the agent and environment while making the learned strategies more realistic. To form an effective confrontation strategy, the Graph Attention Multi-agent Soft Actor Critic Reinforcement Learning with Target Predicting Network (GA-MASAC-TP Net) is firstly proposed for Multi-UAV confrontation game. The merits lie in that the Multi-UAV trajectory prediction, considering interactions among targets, is incorporated innovatively into the Multi-agent reinforcement learning (MARL), enabling Multi-UAVs to make decisions more accurately based on situation prediction. Specifically, the Soft Actor Critic (SAC) algorithm is extended to the Multi-agent domain and embed with the graph attention neural network into the Actor, Critic network, so the UAV could aggregate the information of the spatial neighbor teammates based on the attention mechanism for better collaboration. The comparative experiment and ablation study demonstrate the effectiveness of the proposed algorithm and the state-of-art performance in the MCS.
由于无人机体积小、成本低的特点,多无人机对抗将在未来战争中扮演重要角色。本文研究了空战环境下的多无人机对抗博弈。为了真实推演对抗场景,本文建立了基于多无人机对抗场景(MCS)框架的物理引擎,实现了代理与环境的实时交互,同时使学习到的策略更加逼真。为了形成有效的对抗策略,首先提出了针对多无人机对抗博弈的图注意多代理软代理批评强化学习与目标预测网络(GA-MASAC-TP Net)。其优点在于创新性地将考虑目标间相互作用的多无人机轨迹预测纳入多代理强化学习(MARL),使多无人机能够根据情况预测做出更准确的决策。具体而言,将软行动者批判(Soft Actor Critic,SAC)算法扩展到多机器人领域,并将图注意神经网络嵌入到行动者、批判网络中,使无人机可以基于注意机制聚合空间相邻队友的信息,以实现更好的协作。对比实验和消融研究证明了所提算法的有效性,以及在 MCS 中的先进性能。
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引用次数: 0
IM-LIF: Improved Neuronal Dynamics With Attention Mechanism for Direct Training Deep Spiking Neural Network IM-LIF:利用注意力机制改进神经元动力学,直接训练深度尖峰神经网络
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-13 DOI: 10.1109/TETCI.2024.3359539
Shuang Lian;Jiangrong Shen;Ziming Wang;Huajin Tang
Spiking neural networks (SNNs) are increasingly applied to deep architectures. Recent works are developed to apply spatio-temporal backpropagation to directly train deep SNNs. But the binary and non-differentiable properties of spike activities force directly trained SNNs to suffer from serious gradient vanishing. In this paper, we first analyze the cause of the gradient vanishing problem and identify that the gradients mostly backpropagate along the synaptic currents. Based on that, we modify the synaptic current equation of leaky-integrate-fire neuron model and propose the improved LIF (IM-LIF) neuron model on the basis of the temporal-wise attention mechanism. We utilize the temporal-wise attention mechanism to selectively establish the connection between the current and historical response values, which can empirically enable the neuronal states to update resilient to the gradient vanishing problem. Furthermore, to capture the neuronal dynamics embedded in the output incorporating the IM-LIF model, we present a new temporal loss function to constrain the output of the network close to the target distribution. The proposed new temporal loss function could not only act as a regularizer to eliminate output outliers, but also assign the network loss credit to the voltage at a specific time point. Then we modify the ResNet and VGG architecture based on the IM-LIF model to build deep SNNs. We evaluate our work on image datasets and neuromorphic datasets. Experimental results and analysis show that our method can help build deep SNNs with competitive performance in both accuracy and latency, including 95.66% on CIFAR-10, 77.42% on CIFAR-100, 55.37% on Tiny-ImageNet, 97.33% on DVS-Gesture, and 80.50% on CIFAR-DVS with very few timesteps.
尖峰神经网络(SNN)越来越多地应用于深度架构。最近的研究成果开发出了应用时空反向传播来直接训练深度 SNN 的方法。但是,由于尖峰活动的二元性和非差异性,直接训练的 SNNs 会出现严重的梯度消失。本文首先分析了梯度消失问题的原因,发现梯度主要是沿着突触电流反向传播的。在此基础上,我们修改了泄漏-整合-发射神经元模型的突触电流方程,并在时序注意机制的基础上提出了改进的 LIF(IM-LIF)神经元模型。我们利用时向注意机制选择性地建立当前响应值与历史响应值之间的联系,从而通过经验使神经元状态的更新能够抵御梯度消失问题。此外,为了捕捉包含在 IM-LIF 模型输出中的神经元动态,我们提出了一种新的时间损失函数,以限制网络输出接近目标分布。提出的新时间损失函数不仅可以作为消除输出异常值的正则化器,还可以将网络损失信用分配给特定时间点的电压。然后,我们基于 IM-LIF 模型修改了 ResNet 和 VGG 架构,以构建深度 SNN。我们在图像数据集和神经形态数据集上评估了我们的工作。实验结果和分析表明,我们的方法有助于构建深度 SNN,在准确率和延迟方面都具有竞争力,包括在 CIFAR-10 上达到 95.66%,在 CIFAR-100 上达到 77.42%,在 Tiny-ImageNet 上达到 55.37%,在 DVS-Gesture 上达到 97.33%,在 CIFAR-DVS 上达到 80.50%,而且只需很少的时间步。
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引用次数: 0
Large-Scale Structured Output Classification via Multiple Structured Support Vector Machine by Splitting 通过拆分多重结构化支持向量机进行大规模结构化输出分类
IF 5.3 3区 计算机科学 Q1 Mathematics Pub Date : 2024-02-13 DOI: 10.1109/TETCI.2024.3360339
Chun-Na Li;Yi Li;Yuan-Hai Shao
Structured support vector machine (SSVM) is an effective method on coping with problems involving complex outputs such as multiple dependent output variables and structured output spaces. However, its training process is very time consuming for large-scale data with complex structure and many classes. In this paper, to improve the efficiency of SSVM, we propose a multiple structured support vector machine (MSSVM) for structured output classification via the idea of splitting large into small. By constructing novel classification loss for each class, MSSVM solves a series of smaller optimization problems rather than one large-size optimization problem in SSVM. Therefore, MSSVM greatly reduces the training speed of SSVM. In addition, the structured output label information and discriminative information are embedded in the introduced losses in a simple but effective way. Experiments on multiclass classification, ordinal regression and hierarchical classification datasets demonstrate the efficiency and effectiveness of the proposed MSSVM.
结构化支持向量机(SSVM)是处理复杂输出问题(如多因变量输出和结构化输出空间)的有效方法。然而,对于结构复杂、类别众多的大规模数据,其训练过程非常耗时。在本文中,为了提高 SSVM 的效率,我们通过化大为小的思想,提出了一种用于结构化输出分类的多结构支持向量机(MSSVM)。通过为每个类别构建新的分类损失,MSSVM 解决了一系列较小的优化问题,而不是 SSVM 中的一个大型优化问题。因此,MSSVM 大大降低了 SSVM 的训练速度。此外,结构化输出标签信息和判别信息被简单而有效地嵌入到引入的损失中。在多类分类、序数回归和分层分类数据集上的实验证明了所提出的 MSSVM 的效率和有效性。
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