Dimensionality Reduction - Stanford University
Chapter 11 Dimensionality Reduction There are many sources of data that can be viewed as a large matrix. We saw in Chapter 5 how the Web can be represented as a transition matrix. In Chapter 9, the utility matrix was a point of focus. And in Chapter 10 we examined matrices that represent social networks. In many of these matrix
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Chapter 9 Recommendation Systems There is an extensive class of Web applications that involve predicting user responses to options. Such a facility is called a recommendation system. We shall begin this chapter with a survey of the most important examples of these systems. However, to bring the problem into focus, two good examples of
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Chapter 11 Key Vocabulary 178 Lesson 11-1 180 Lesson 11-2 181 Lesson 11-3 182 Lesson 11-4 184 Lesson 11-5 185 Lesson 11-6 187 Lesson 11-7 189 Lesson 11-8 190 Lesson 11-9 191 Chapter 11 Review 192 Chapter 11 Big Idea Questions 196 Chapter 12 Key Vocabulary 198 Lesson 12-1 200 Lesson 12-2 201 Lesson 12-3 203 Lesson 12-4 204 Lesson 12-5 205 Lesson ...
1 →R 2 isaringhomomorphism00AY , 00AZ (8) ϕ: R 1 →R 2 is of ﬁnite presentation, or R 2 is a ﬁnitely presented R 1-algebra,seeDeﬁnition6.1, 00B0 (9) ϕ: R 1 →R 2 isofﬁnitetype,orR 2 isaﬁnitetypeR 1-algebra,seeDeﬁnition 6.1, 00B1 (10) ϕ: R 1 →R 2 isﬁnite,orR 2 isaﬁniteR 1-algebra, (11) Risa(integral)domain00B2 , (12 ...
11 +a 22 +···+ann=sum of λ’s. 5 Projectionshave λ=1and0. Reﬂections have 1and−1. Rotations haveeiθ and e−iθ: complex! This chapter enters a new part of linear algebra. The ﬁrst par t was about Ax = b: balance and equilibrium and steady state. …
algebra. These are the key equations of least squares: The partial derivatives of kAx bk2 are zero when ATAbx DATb: The solution is C D5 and D D3. Therefore b D5 3t is the best line—it comes closest to the three points. At t D0, 1, 2 this line goes through p D5, 2, 1. It could not go through b D6, 0, 0. The errors are 1, 2, 1. This is the ...