A normed space is said to have ball-covering property if its unit sphere can be contained in the union of countably many open balls off the origin. This paper shows that for every ε>0 every Banach space with a w*-...A normed space is said to have ball-covering property if its unit sphere can be contained in the union of countably many open balls off the origin. This paper shows that for every ε>0 every Banach space with a w*-separable dual has a 1+ε-equivalent norm with the ball covering property.展开更多
By a ball-covering B of a Banach space X, we mean that B is a collection of open （or closed） balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided ...By a ball-covering B of a Banach space X, we mean that B is a collection of open （or closed） balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that universal finite representability and B-convexity of X can be characterized by properties of ball-coverings of its finite dimensional subspaces.展开更多
经典分类模型总是假定测试样本属于训练类之一,然而在网络安全、身份识别、医学诊断等非合作模式识别中往往存在许多非训练类例外模式,这时由于分类器缺乏拒识能力,只能给出错误判决。为此,本文构造了一种基于区分性投影结合最小L1球覆...经典分类模型总是假定测试样本属于训练类之一,然而在网络安全、身份识别、医学诊断等非合作模式识别中往往存在许多非训练类例外模式,这时由于分类器缺乏拒识能力,只能给出错误判决。为此,本文构造了一种基于区分性投影结合最小L1球覆盖的可拒识双层近邻分类器。该方法针对一类分类器忽略类别间区分性描述的不足,定义一种能够表征各训练类模式细节信息的差分矢量,形成新的差分特征。在差分特征空间进行L1范数最大化主成分分析(Ll-normmaximization principal component analysis,PCA-L1)构建新的区分性投影方法即差分矢量PCA-L1特征提取。然后,在投影空间对各类别分别建立最小L1球覆盖决策边界,这样对于输入的测试模式,便可做出拒识或者接受处理的判决。最后,针对接受的输入模式,再通过最近邻测试得到识别结果。在UCI数据库、MNIST手写体数据库和CMU AMP人脸表情数据库上的实验结果表明本文方法对训练类测试样本具有较高正确识别率的同时,同时能够对非训练类测试样本进行有效地拒识,在实际模式识别领域具有一定的应用价值。展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10471114,10771175)
文摘A normed space is said to have ball-covering property if its unit sphere can be contained in the union of countably many open balls off the origin. This paper shows that for every ε>0 every Banach space with a w*-separable dual has a 1+ε-equivalent norm with the ball covering property.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10771175, 10801111 and 11101340)the Natural Science Foundation of Fujian Province (Grant No. 2010J05012) the Fundamental Research Funds for the Central Universities (Grant Nos. 2010121001 and 2011121039)
文摘By a ball-covering B of a Banach space X, we mean that B is a collection of open （or closed） balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that universal finite representability and B-convexity of X can be characterized by properties of ball-coverings of its finite dimensional subspaces.
文摘经典分类模型总是假定测试样本属于训练类之一,然而在网络安全、身份识别、医学诊断等非合作模式识别中往往存在许多非训练类例外模式,这时由于分类器缺乏拒识能力,只能给出错误判决。为此,本文构造了一种基于区分性投影结合最小L1球覆盖的可拒识双层近邻分类器。该方法针对一类分类器忽略类别间区分性描述的不足,定义一种能够表征各训练类模式细节信息的差分矢量,形成新的差分特征。在差分特征空间进行L1范数最大化主成分分析(Ll-normmaximization principal component analysis,PCA-L1)构建新的区分性投影方法即差分矢量PCA-L1特征提取。然后,在投影空间对各类别分别建立最小L1球覆盖决策边界,这样对于输入的测试模式,便可做出拒识或者接受处理的判决。最后,针对接受的输入模式,再通过最近邻测试得到识别结果。在UCI数据库、MNIST手写体数据库和CMU AMP人脸表情数据库上的实验结果表明本文方法对训练类测试样本具有较高正确识别率的同时,同时能够对非训练类测试样本进行有效地拒识,在实际模式识别领域具有一定的应用价值。
