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Reading 18: Dimensionality Reduction

Reading 18: Dimensionality Reduction#

For the class on Monday, April 8th

Reading assignments#

  1. Read the following sections of [ICVG20] (note that many subsections are skipped):

    • Chap. 7 “Dimensionality and Its Reduction”

      • Sec. 7.1 “The Curse of Dimensionality”

      • Sec. 7.2 “The Data Sets Used in This Chapter”

      • Sec. 7.3 “Principal Component Analysis”

        • Sec. 7.3.2 “The Application of PCA”

        • (You can skip all other subsections under 7.3)

      • (Skip Sec. 7.4)

      • Sec. 7.5 “Manifold Learning”

        • Sec. 7.5.1 “Locally Linear Embedding” (first paragraph only; rest is optional)

        • (You can skip all other subsections under 7.5)

Questions#

Hint

Submit your answer on Canvas. Due at noon, Monday, April 8th.

  1. List anything from your reading that confuses you. Explain why they confuse you. You are strongly encouraged to think about what questions you have about the reading, but if you really have no questions at all, please briefly summarize what you have learned from this reading assignment.

  2. The PCA is a way to transform the input features.

    • What is the constraint on the transformation? (Can it be any possible transformation, or of only a certain kind?)

    • What does the transformation aim to achieve? (After the transformation, what does the first principal component correspond to?)

Discussion Preview#

Note

We will discuss the following in class. They are included here so that you have a chance to think about them before class. You need not submit your answers as part of this assignment.

  1. Dimensionality reduction is sometimes called “embedding,” especially in modern ML. If we think of PCA as a standard technique of dimensionality reduction, then we can think of embedding as a more general and flexible way to achieve a similar goal. We will discuss the concept of “embedding” and its examples.

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