代写书稿:PCA的发明历史

代写书稿:PCA的发明历史

PCA的发明是在1901年由卡尔皮尔森的努力。它是力学中主轴定理的一个类比。然而,在20世纪30年代后期,哈罗德·霍特林(Harold Hoteling)对此进行了独立的发展。人们常常将PCA归因于Hotelling(1933),但不能认为它是绝对正确的。这些方程建立在二次曲面和形式的主轴上,有许多不同的形式,在分析学的经典几何中是众所周知的(Bro & Smilde, 2014)。在高尔顿(1889),主成分分析似乎有了一些温和的开端,其中主轴与相关椭球体之间首次有了联系。皮尔逊(1901)发明的技术有一个完整的讨论,这些技术已经完全应用于MacDonell(1902)。
Burt (1949) (Bowen & Guo, 2011)在研究中考虑了PCA在适当属性下分析数据的历史。PCA最重要的优点是它可以很容易地沟通和执行。在仪器验证中,它可以被明确地归为一种有效的方法。此外,即使存在某些假设如多元正态分布(Abdi & Williams, 2010)违反,也总有获得稳定估计的空间。然而,PCA也有一些缺点或缺点。一个重要的问题在于对样本的依赖,即部分结果对样本的依赖。再往前看,因素的解决方案往往反映项目的每一个困难,而不是提供任何具体的基础结构。

代写书稿:PCA的发明历史

The invention of PCA took place in the year 1901 by the efforts of Karl Pearson. It was presented as an analogue for the theorem of principal axis in mechanics. However, later on during the 1930s, there was an independent development of the same by Harold Hoteling. There is often attribution of PCA to Hotelling (1933) but cannot be considered absolutely correct. The equations were established in the principal axes of quadratic surfaces and forms, in a number of different forms, and were well-known across the classical geometry of analytics (Bro & Smilde, 2014). There seem to be some modest beginnings of PCA in Galton (1889), in which for the first time there was connection of principal axes with the correlation ellipsoid. There is a complete discussion on the techniques invented by Pearson (1901), and these techniques had been fully applied to MacDonell (1902).
The prior history of PCA in the analysis of data, under appropriate attributes, has been considered in the research by Burt (1949) (Bowen & Guo, 2011). The most significant pros of PCA is that it can be communicated and conducted easily. It can be clearly classified as a valid method in the validation of instrument. In addition, there is always scope of obtaining stable estimates even if there is violation of certain assumptions such as multivariate normal distribution (Abdi & Williams, 2010). However, there are certain disadvantages or cons of PCA as well. One significant issue lies in the dependence on sample, with partial dependence of the findings over the sample. Further ahead, a solution of factor tend to be reflecting each and every difficulty of the items instead of providing any specific underlying construct.