L_(2,1)-norm robust regularized extreme learning machine for regression using CCCP method

As a way of training a single hidden layer feedforward network(SLFN),extreme learning machine(ELM)is rapidly becoming popular due to its efficiency.However,ELM tends to overfitting,which makes the model sensitive to noise and outliers.To solve this problem,L_(2,1)-norm is introduced to ELM and an L_(2,1)-norm robust regularized ELM(L_(2,1)-RRELM)was proposed.L_(2,1)-RRELM gives constant penalties to outliers to reduce their adverse effects by replacing least square loss function with a non-convex loss function.In light of the non-convex feature of L_(2,1)-RRELM,the concave-convex procedure(CCCP)is applied to solve its model.The convergence of L_(2,1)-RRELM is also given to show its robustness.In order to further verify the effectiveness of L_(2,1)-RRELM,it is compared with the three popular extreme learning algorithms based on the artificial dataset and University of California Irvine(UCI)datasets.And each algorithm in different noise environments is tested with two evaluation criterions root mean square error(RMSE)and fitness.The results of the simulation indicate that L_(2,1)-RRELM has smaller RMSE and greater fitness under different noise settings.Numerical analysis shows that L_(2,1)-RRELM has better generalization performance,stronger robustness,and higher anti-noise ability and fitness.

一种用于目标跟踪边界框回归的光滑IoU损失

边界框回归分支是深度目标跟踪器的关键模块,其性能直接影响跟踪器的精度.评价精度的指标之一是交并比(Intersection over union,IoU).基于IoU的损失函数取代了l_(n)-norm损失成为目前主流的边界框回归损失函数,然而IoU损失函数存在2个固有缺陷:1)当预测框与真值框不相交时IoU为常量0,无法梯度下降更新边界框的参数;2)在IoU取得最优值时其梯度不存在,边界框很难收敛到IoU最优处.揭示了在回归过程中IoU最优的边界框各参数之间蕴含的定量关系,指出在边界框中心处于特定位置时存在多种尺寸不同的边界框使IoU损失最优的情况,这增加了边界框尺寸回归的不确定性.从优化两个统计分布之间散度的视角看待边界框回归问题,提出了光滑IoU(Smooth-IoU,SIoU)损失,即构造了在全局上光滑(即连续可微)且极值唯一的损失函数,该损失函数自然蕴含边界框各参数之间特定的最优关系,其唯一取极值的边界框可使IoU达到最优.光滑性确保了在全局上梯度存在使得边界框更容易回归到极值处,而极值唯一确保了在全局上可梯度下降更新参数,从而避开了IoU损失的固有缺陷.提出的光滑损失可以很容易取代IoU损失集成到现有的深度目标跟踪器上训练边界框回归,在LaSOT、GOT-10k、TrackingNet、OTB2015和VOT2018测试基准上所取得的结果,验证了光滑IoU损失的易用性和有效性.