主成分分析（PCA）是现代数据分析的一个支柱，它是一个被广泛使用但很少被理解的黑匣子。

Principal component analysis (PCA) is amainstay of modern data analysis - a black box that is widely used but poorlyunderstood.

本文的目的是要消除黑匣子背后隐藏的魔力。

The goal of this paper is to dispel themagic behind this black box.

本教程着重于为主成分分析的工作原理和原因建立起一个坚实的直观认识；此外，还通过从简单的直观认识中派生出具体的数学知识。

This tutorial focuses on building a solidintuition for how and why principal component analysis works; furthermore, itcrystallizes this knowledge by deriving from simple intuitions, the mathematicsbehind PCA .

本教程既不回避非正式地解释说明，也不回避真实的数学问题。

This tutorial does not shy away fromexplaining the ideas informally, nor does it shy away from the mathematics.

本文希望通过解决这两个方面的问题，使得各类读者能够更好地了解PCA，并明白何时、如何以及为什么应用该技术。

The hope is that by addressing bothaspects, readers of all levels will be able to gain a better understanding ofPCA as well as the when, the how and the why of applying this technique.

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