In this chapter, we examined the problem of dimensionality reduction. High-dimensional data cannot be visualized easily. High-dimensional data sets may also suffer from the curse of dimensionality; estimators require many samples to learn to generalize from high-dimensional data. We mitigated these problems using a technique called principal component analysis, which reduces a high-dimensional, possibly-correlated data set to a lower-dimensional set of uncorrelated principal components by projecting the data onto a lower-dimensional subspace. We used principal component analysis to visualize the four-dimensional Iris data set in two dimensions, and build a face-recognition system. In the next chapter, we will return to supervised learning. We will discuss an early classification algorithm called the perceptron, which will prepare us to discuss more advanced models in the last few chapters.