Project 3: Dissimilarities between data objects

Project 3: Dissimilarities between data objects

This project demonstrates how to measure similarities between data objects. These topics described are mostly in chapter 6 Statistical Machine Learning from ‘Practical Statistics for Data Scientists’. Cover in the project the following:

1. Find some data examples and show examples of calculating
   1. Euclidean distance
   2. L1 distance
2. Prove or disprove that Euclidean and L1 distance satisfy
   1. Positivity

d(x,y) >= 0 for all x and y,

d(x,y) == 0 only if x == y.

1. Symmetry

d(x,y) == d(y,x) for all x and y.

1. Triangle Inequality

d(x,z) <= d(x,y) + d(y,z) for all points x, y, and z

1. Explain why it is not possible or why it is possible to
   1. rearrange data so Euclidean distance gives the same meaning as Hamming distance
   2. show that measure d=1-cos(x,y) satisfies positivity, symmetry, and triangle Inequality
2. Draw conclusions about what is important when choosing the distance measure for the evaluation of dissimilarities between data objects.