Logistic regression is often used to solve linear binary classification problems such as machine vision,speech recognition,and handwriting recognition.However,it usually fails to solve certain nonlinear multi-classifi...Logistic regression is often used to solve linear binary classification problems such as machine vision,speech recognition,and handwriting recognition.However,it usually fails to solve certain nonlinear multi-classification problem,such as problem with non-equilibrium samples.Many scholars have proposed some methods,such as neural network,least square support vector machine,AdaBoost meta-algorithm,etc.These methods essentially belong to machine learning categories.In this work,based on the probability theory and statistical principle,we propose an improved logistic regression algorithm based on kernel density estimation for solving nonlinear multi-classification.We have compared our approach with other methods using non-equilibrium samples,the results show that our approach guarantees sample integrity and achieves superior classification.展开更多
A toric origami manifold,introduced by Cannas da Silva,Guillemin and Pires,is a generalization of a toric symplectic manifold.For a toric symplectic manifold,its equivariant Chern classes can be described in terms of ...A toric origami manifold,introduced by Cannas da Silva,Guillemin and Pires,is a generalization of a toric symplectic manifold.For a toric symplectic manifold,its equivariant Chern classes can be described in terms of the corresponding Delzant polytope and the stabilization of its tangent bundle splits as a direct sum of complex line bundles.But in general a toric origami manifold is not simply connected,so the algebraic topology of a toric origami manifold is more difficult than a toric symplectic manifold.In this paper they give an explicit formula of the equivariant Chern classes of an oriented toric origami manifold in terms of the corresponding origami template.Furthermore,they prove the stabilization of the tangent bundle of an oriented toric origami manifold also splits as a direct sum of complex line bundles.展开更多
Relation contexts have been proved to be useful for many challenging vision tasks.In the field of3D object detection,previous methods have been taking the advantage of context encoding,graph embedding,or explicit rela...Relation contexts have been proved to be useful for many challenging vision tasks.In the field of3D object detection,previous methods have been taking the advantage of context encoding,graph embedding,or explicit relation reasoning to extract relation contexts.However,there exist inevitably redundant relation contexts due to noisy or low-quality proposals.In fact,invalid relation contexts usually indicate underlying scene misunderstanding and ambiguity,which may,on the contrary,reduce the performance in complex scenes.Inspired by recent attention mechanism like Transformer,we propose a novel 3D attention-based relation module(ARM3D).It encompasses objectaware relation reasoning to extract pair-wise relation contexts among qualified proposals and an attention module to distribute attention weights towards different relation contexts.In this way,ARM3D can take full advantage of the useful relation contexts and filter those less relevant or even confusing contexts,which mitigates the ambiguity in detection.We have evaluated the effectiveness of ARM3D by plugging it into several state-of-the-art 3D object detectors and showing more accurate and robust detection results.Extensive experiments show the capability and generalization of ARM3D on 3D object detection.Our source code is available at https://github.com/lanlan96/ARM3D.展开更多
基金The authors would like to thank all anonymous reviewers for their suggestions and feedback.This work was supported by National Natural Science Foundation of China(Grant No.61379103).
文摘Logistic regression is often used to solve linear binary classification problems such as machine vision,speech recognition,and handwriting recognition.However,it usually fails to solve certain nonlinear multi-classification problem,such as problem with non-equilibrium samples.Many scholars have proposed some methods,such as neural network,least square support vector machine,AdaBoost meta-algorithm,etc.These methods essentially belong to machine learning categories.In this work,based on the probability theory and statistical principle,we propose an improved logistic regression algorithm based on kernel density estimation for solving nonlinear multi-classification.We have compared our approach with other methods using non-equilibrium samples,the results show that our approach guarantees sample integrity and achieves superior classification.
基金supported by the National Natural Science Foundation of China(Nos.11801186,11901218)。
文摘A toric origami manifold,introduced by Cannas da Silva,Guillemin and Pires,is a generalization of a toric symplectic manifold.For a toric symplectic manifold,its equivariant Chern classes can be described in terms of the corresponding Delzant polytope and the stabilization of its tangent bundle splits as a direct sum of complex line bundles.But in general a toric origami manifold is not simply connected,so the algebraic topology of a toric origami manifold is more difficult than a toric symplectic manifold.In this paper they give an explicit formula of the equivariant Chern classes of an oriented toric origami manifold in terms of the corresponding origami template.Furthermore,they prove the stabilization of the tangent bundle of an oriented toric origami manifold also splits as a direct sum of complex line bundles.
基金National Nature Science Foundation of China(62132021,62102435,62002375,62002376)National Key R&D Program of China(2018AAA0102200)NUDT Research Grants(ZK19-30)。
文摘Relation contexts have been proved to be useful for many challenging vision tasks.In the field of3D object detection,previous methods have been taking the advantage of context encoding,graph embedding,or explicit relation reasoning to extract relation contexts.However,there exist inevitably redundant relation contexts due to noisy or low-quality proposals.In fact,invalid relation contexts usually indicate underlying scene misunderstanding and ambiguity,which may,on the contrary,reduce the performance in complex scenes.Inspired by recent attention mechanism like Transformer,we propose a novel 3D attention-based relation module(ARM3D).It encompasses objectaware relation reasoning to extract pair-wise relation contexts among qualified proposals and an attention module to distribute attention weights towards different relation contexts.In this way,ARM3D can take full advantage of the useful relation contexts and filter those less relevant or even confusing contexts,which mitigates the ambiguity in detection.We have evaluated the effectiveness of ARM3D by plugging it into several state-of-the-art 3D object detectors and showing more accurate and robust detection results.Extensive experiments show the capability and generalization of ARM3D on 3D object detection.Our source code is available at https://github.com/lanlan96/ARM3D.
