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第二百五十二章 柯西估计(概率和统计)(1 / 1)

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1807年至1810年柯西在工学院学习,曾当过交通道路工程师。由于身体欠佳,接受了拉格朗日和拉普拉斯的劝告,放弃工程师而致力于纯数学的研究。柯西在数学上的最大贡献是在微积分中引进了极限概念,并以极限为基础建立了逻辑清晰的分析体系。这是微积分发展史上的精华,也是柯西对人类科学发展所做的巨大贡献。

有时看着这些密密麻麻的桥梁力学上的各种数据,柯西陷入沉思,在想这些数据意味着什么。

意味着不同的桥梁之间,这些数据是不同的。

但是差不多相同的桥梁,数据之间或许会有某种联系。

但数据过多,能不能处理成少些的有代表性的数据来体现这两个桥的联系?

或者找到关键数据来看看两个桥梁之间的不同。

这就需要一种把大量数据化简的能力,来识别不同桥梁,来识别桥梁出现的各种特征。

需要高维度性质的数据,向低维度数据转化。

在高维数据向低维数据转化时,使用最小二乘法的误差会有些大。

图形处理识别中,会用到降维算法。

柯西估计可以计算监督降维算法。

在样本生产过程中,由于训练是认为处理,一个不当操作的误差会导致生成大量不准确样本,而这些错误不可避免,所以识别率也会下降。

解决的方法是设计损失函数时,用柯西损失代替最小二乘法损失。

使用knn方法来找不同样本的特征时,由于距离小,不方便提取重要的区别信息。

所以要把距离改大些,才能更好的提取特征进行识别。

柯西估计写出了估计公式ζ(x)=log(1+(x/c)^2)。

喜欢数学心请大家收藏:数学心本站更新速度全网最快。

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