Indicate whether each of the following changes to a set of data will affect the Euclidean distances between points, and a clustering algorithm such as hclust. If there is any effect, indicate under what circumstances it will be largest. (a). Rescale the variables, multiplying each one by a different constant. (b). Multiply each variable by the same constant. (c). Rotating the data by multiplying it by an orthonormal matrix (hint: PCA loadings are one orthogonal matrix. If you want, you can use PCA to answer this question.) (d). Projecting the data onto the first 5 principal components. Note: You should answer this question using mathematical arguments

Indicate whether each of the following changes to a set of data will affect the Euclidean distances between points, and a clustering algorithm such as hclust. If there is any effect, indicate under what circumstances it will be largest. (a). Rescale the variables, multiplying each one by a different constant. (b). Multiply each variable by the same constant. (c). Rotating the data by multiplying it by an orthonormal matrix (hint: PCA loadings are one orthogonal matrix. If you want, you can use PCA to answer this question.) (d). Projecting the data onto the first 5 principal components. Note: You should answer this question using mathematical arguments

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 2CEXP

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