Publications by Amber Ferger
DATA 605 - Assignment 4, Problem Set 1
Problem Set 1 In this problem, we’ll verify using R that SVD and Eigenvalues are related as worked out in the weekly module. Given a 3 x 2 matrix A: \[A = \left[\begin{array}{cc} 1 & 2 & 3 \\ -1 & 0 & 4 \end{array}\right]\] write code in R to compute \(X = AA^T\) and \(Y = A^TA\). Then, compute the eigenvalues and eigenvectors of X and Y...
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DATA 605 - Assignment 4, Problem Set 2
Problem Set 2 Using the procedure outlined in section 1 of the weekly handout, write a function to compute the inverse of a well-conditioned full-rank square matrix using co-factors. In order to compute the co-factors, you may use built-in commands to compute the determinant. Your function should have the following signature: \[B = myinverse(A)\...
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DATA 605 - Week 4 Discussion
Chapter LT, Section LT, Question C31 (pg.340) Question For the linear transformation S compute the preimages. \[S: C^3 \rightarrow C^3, \; \; \; \; S\left(\Biggl[\begin{array}{cc} a \\ b \\ c \end{array}\Biggr]\right) = \left[\begin{array}{cc} a-2b-c \\ 3a-b+2c \\ a+b+2c \end{array}\right]\] \[S^{-1}\left(\Biggl[\begin{array}{cc} -2 ...
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DATA 605 - Assignment 3, Problem Set 2
Problem Set 2 Compute the eigenvalues and eigenvectors of the matrix A. You’ll need to show your work. You’ll need to write out the characteristic polynomial and show your solution. \[ A = \left[\begin{array}{cc} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6 \end{array}\right] \] Characteristic Equation: \[P_{A}(x) = det(A-xI_{3})\] \[=\left|\...
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DATA 605 - Assignment 3, Problem Set 1
Problem Set 1 Problem 1 What is the rank of matrix A? \[ A = \left[\begin{array}{cc} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \end{array}\right] \] The rank of the matrix is 4 because there are 4 pivots: \[ R_2 = R_1+R_2 \left[\begin{array}{cc} 1 & 2 & 3 & 4 \\ 0 & 2 & 4 & 7 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & ...
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DATA 605 - Assignment 2, Problem Set 2
Problem Set 2 Matrix factorization is a very important problem. There are supercomputers built just to do matrix factorizations. Every second you are on an airplane, matrices are being factorized. Radars that track flights use a technique called Kalman filtering. At the heart of Kalman Filtering is a Matrix Factorization operation. Kalman Filters...
780 sym R (1312 sym/3 pcs)
DATA 605: Week 1 Homework
Problem Set 1 You can think of vectors representing many dimensions of related information. For instance, Netflix might store all the ratings a user gives to movies in a vector. This is clearly a vector of very large dimensions (in the millions) and very sparse as the user might have rated only a few movies. Similarly, Amazon might store the ite...
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DATA 605 - Week 1 Discussion
Chapter SLE, Section SSLE - Question C30 (pg.14) C30† Find all solutions to the linear system: x + y = 5 2x − y = 3 To solve this system of equations, we will first multiply equation 1 by -2 and add to equation 2: x + y = 5 - 3y = -7 Now we can divide equation 2 by -3 to solve for y: x + y = 5 y = 7/3 Lastly, we will plug our value for y i...
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DATA 607: Final Presentation
Where should I go next?: An exploration of travel ratings vs costAmber Ferger12/11/2019 Agenda Problem General Approach Results Challenges Research Question Does cost affect traveler ratings on TripAdvisor? European Cost Index: Compares the daily cost of traveling to a variety of European cities TripAdvisor: Provides user-ranked profiles of ...
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DATA 607: Final Project
The Project Research Question: Does cost affect traveler ratings on TripAdvisor? For the past few years, I have been very interested in exploring the world and traveling as much as I can. For my final project, I thought it would be interesting to take a look at a bunch of different European cities to see what effect cost has on travel ratings. I...
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