April 2019
Intermediate to advanced
172 pages
4h 39m
Chinese
Content preview from 精通特征工程
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82
第 6 章
数据降维：使用
PCA
挤压数据
通过自动数据收集和特征生成技术，可以快速获取大量特征，但不是所有特征都是有用
的。第
3
章和第
4
章讨论了基于频率的过滤技术和特征缩放技术，它们可以作为消除无用
特征的手段。下面仔细研究一下使用
主成分分析
（
principal component analysis
，
PCA
）来
降低特征维度这个问题。
从本章开始，我们要研究基于模型的特征工程技术。在此之前介绍的大部分技术可以在不
考虑数据的情况下进行定义。例如，基于频率的过滤可以表述为“除去所有小于
n
的计
数”，不用考虑数据本身的更多性质，就可以实现这种技术。
与之不同的是，基于模型的技术需要来自于数据的信息。例如，
PCA
要根据数据的主轴
进行定义。在前面的章节中，数据、特征和模型之间总是有一个明确的界限，但从本章开
始，它们之间的区别会变得越来越模糊。这也正是当前特征学习研究的热点所在。
6.1
直观理解
数据降维就是在保留重要信息的同时消除那些“无信息量的信息”。“无信息量”有多种定
义方法，
PCA
关注的是线性相关性。在附录
A.2
节中，我们将数据矩阵的列空间描述为所
有特征向量的生成空间。如果列空间的秩小于特征总数，那么多数特征就是几个关键特征
的线性组合。线性相关的特征是对空间和计算能力的浪费，因为它们包含的信息可以从更
少的几个特征中推导出来。为了避免这种情况，
PCA
试图将数据挤压到一个维度大大小于
原空间的线性子空间，从而消除这些“臃肿”。
我们在图中画出特征空间中的数据点集合。每个圆点表示一个数据点，整个数据点集合形 ...
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I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.