Publications by PK O’Flaherty
DATA605 WK4 Homework
Assignment With seventeen provided jpg data files, build and visualize eigenimagery that accounts for 80% of the variability. References For a roadmap and codehow we relied heavily on Doctor Larry’s rpubs.com/R-Minator/eigenshoes. Preamble In this project we are encoding images of 17 distinct shoes into a matrix of data. The first eigenvector i...
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DATA605 WK1 Homework
Assignment One of the most useful applications for linear algebra in data science is image manipulation. We often need to compress, expand, warp, skew, etc. images. To do so, we left multiply a transformation matrix by each of the point vectors. For this assignment, build the first letters for both your first and last name using point plots in R. T...
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DATA605 WK2 Homework
Problem Set 1 Part 1 Show that \(A^TA \neq AA^T\) in general. (Proof and demonstration.) Proof Here we take a generalized 2x2 matrices with elements (a,b,c,d) and show how changing the order of multiplication with it’s transpose provides different results unless (a,b,c,d) meet specific criteria. Transposition Here we transpose A. \[ A= \le...
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DATA605 WK3 Homework
Library In this assignment we’ll use functions from the Matrix package in R to verify our work. library('Matrix') Problem Set 1 Part 1 What is the rank of the matrix A? \[ A= \left[ {\begin{array}{cccc} 1 & 2 & 3 & 4 \\ -1 & 0 & 1 & 3 \\ 0 & 1 & -2 & 1 \\ 5 & 4 & -2 & -3 \\ \end{array} } \right] \] Solved by Hand ...
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DATA605 Final Project Part 2
Read Data Our data is publicly available as the Ames Housing Data but we’ve collected it from the Kaggle competition House Prices Advanced Regression Techniques to use in part 3 of the final project. Here we’re downloading it from our Github account. The target value is SalePrice, there are 78 predictors and one ID column, with 1460 rows in ou...
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DATA605 Final Project Part 3
Final Project 2b - Kaggle Join the Kaggle competition House Prices Advanced Regression Techniques and build some type of multiple regression model and submit your model to the competition board. Provide your complete model summary and results with analysis. Report your Kaggle.com user name and score. Provide a screen snapshot of your score with you...
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DATA605 Final Project Part 1
Generate X, Y & Z X~Gamma Generate a random variable \(X\) that has 10,000 random Gamma pdf values, with \(n\) greater than 3 and \(\lambda\) between 2 and 10. I interpret this question differently. The Gamma distribution is the amount of time before a fixed number of random events occur. \(n\) would be the number of random Gamma pdf values genera...
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DATA605 WK14 Homework
Instructions Work out the Taylor Series expansions for the following popular functions. For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. \(f(x)=\frac{1}{(1-x)}\) Solution 1 Start with the formula: \(\displaystyle\sum_{n=0}^\infty\frac{f^{(n)}(c)}{n!}(x-c)^n\) Obtain ...
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DATA605 WK13 Homework
Problem 1 Use integration by substitution to solve the integral below. \(\int 4e^{-7x}dx\) Solving 1 First we have to put the integral into a form like: \(c\int e^uu'dx\) Which for our case would be: \(\frac{-4}{7}\int e^{-7x}(-7)dx\) Once we substitute u and du it’s simpler to solve: \(\frac{-4}{7}\int e^udu\) which evaluates to: \(\frac{-4}{7}...
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DATA605 WK12 Homework
Assignment instructions Follow a series of instructions on WHO data from 2008, provided with the assignment. Load Data I uploaded the assignment data to GitHub. The following variables and descriptions were provided with the assignment instructions: Country: name of the country LifeExp: average life expectancy for the country in years InfantSurviv...
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