How to measure similarities between data objects

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Reference no: EM133765618

Project: 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:

Find some data examples and show examples of calculating
Euclidean distance
L1 distance
Prove or disprove that Euclidean and L1 distance satisfy
Positivity
d(x,y) >= 0 for all x and y,

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

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

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.

Reference no: EM133765618

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