Project 01: Distance Measures¶

Overview¶

This project implements and demonstrates all distance measures covered in Chapter 5 of the Data Analytics course. Understanding distance (or similarity) is foundational to all clustering algorithms — they all depend on some notion of how "far apart" two objects are.

Concepts Covered¶

Single-Attribute Distances¶

Quantitative distance: |a - b| — for continuous numeric attributes like age or income
Ordinal distance: |pos_a - pos_b| / (n-1) — for ranked attributes like education level
Nominal distance: 0 if equal, 1 if different — for categorical attributes like color or country

Multi-Attribute Distances (Minkowski Family)¶

Minkowski distance (general): (sum |x_k - y_k|^r)(1/r)
Manhattan distance (r=1): Sum of absolute differences — useful for grid-like spaces
Euclidean distance (r=2): Straight-line distance — most common in practice
Chebyshev distance (r=inf): Maximum of absolute differences

String/Sequence Distances¶

Hamming distance: Number of positions that differ (equal-length strings/binary)
Edit (Levenshtein) distance: Minimum insert/delete/substitute operations to convert one string to another

Files¶

File	Description
`distance_measures.py`	All distance functions with demos
`project_README.md`	This file

How to Run¶

python distance_measures.py

No external libraries required. Uses Python standard library only.

Expected Output¶

The script will print:

Single-attribute distances for the Friends dataset (Andrew vs Carolina)
Minkowski distances for r = 1, 2, 3, and infinity
Hamming distance examples from the lecture
Edit distance example: "Johnny" vs "Jonston"
Full distance matrix for the 6-person Friends dataset

Friends Dataset Used¶

Person    Age   Education
Andrew    55    1
Bernhard  43    2
Carolina  37    5
Dennis    82    3
Eve       23    3.2
Fred      46    5

Key Formulas¶

Quantitative:  d(a,b) = |a - b|
Ordinal:       d(a,b) = |pos_a - pos_b| / (n - 1)
Nominal:       d(a,b) = 0 if a==b, else 1
Minkowski:     d(x,y) = (sum_k |x_k - y_k|^r)^(1/r)
Hamming:       d(s1,s2) = count of positions where s1[i] != s2[i]
Edit:          d(s1,s2) = min cost of insert + delete + substitute operations

Learning Goals¶

After completing this project you should be able to: - Explain the difference between quantitative, ordinal, and nominal distance - Compute Manhattan and Euclidean distance by hand for small examples - Understand why Hamming requires equal-length strings but edit distance does not - Compute a distance matrix for a small dataset