Project 02: Discretization & Encoding¶

Chapter 4 — Data Quality and Preprocessing

What This Project Does¶

This project demonstrates how to convert continuous and ordinal data into discrete numeric representations:

Equal-Width Binning — divide the value range into N bins of equal width
Equal-Depth Binning — divide sorted values into N bins with equal count
One-Hot Encoding — convert nominal categories into binary columns
Natural Number Encoding — map ordinal categories to 0, 1, 2, ...
Gray Code Encoding — adjacent categories differ by exactly 1 bit
Thermometer Code Encoding — n-th category has n ones from the left

The demo explicitly solves Exercise Q1, Q2, and Q3 from the Chapter 4 exercise sheet and prints Expected vs. Computed comparisons.

Concepts Covered¶

Technique	Use Case	Section in Notes
Equal-width bins	Continuous → ordinal; uniform boundaries	4.1
Equal-depth bins	Continuous → ordinal; balanced bin counts	4.2
One-hot encoding	Nominal → numeric for ML algorithms	5.1
Natural numbers	Ordinal → simple integer codes	5.2
Gray code	Ordinal → minimize bit-flip errors	5.2
Thermometer code	Ordinal → strict cumulative encoding	5.2

Files¶

File	Language	Description
`discretization_encoding.py`	Python 3	Full implementation, pure stdlib
`discretization_encoding.R`	R	Same operations using base R

Usage¶

Python¶

python discretization_encoding.py

R¶

Rscript discretization_encoding.R

Exercise Q&A Solved in This Project¶

Q1: Discretize [31,38,42,29,46,23,83,43,51,55,27,35] into 4 bins¶

Equal-Width: W = (83-23)/4 = 15 - Bin 0: [23, 37] -> values: 23, 27, 29, 31, 35 - Bin 1: [38, 52] -> values: 38, 42, 43, 46, 51 - Bin 2: [53, 67] -> values: 55 - Bin 3: [68, 83] -> values: 83

Equal-Depth: 3 values per bin (12 values / 4 bins) - Bin 0: {23, 27, 29} - Bin 1: {31, 35, 38} - Bin 2: {42, 43, 46} - Bin 3: {51, 55, 83}

Q2: One-Hot Encoding for Food column¶

Categories: American, Chinese, Italian, Other

Row	Food	American	Chinese	Italian
0	Chinese	0	1	0
1	Italian	0	0	1
2	American	1	0	0
3	Chinese	0	1	0
4	Italian	0	0	1

Q3: Gray Code for Distance values¶

Distance	Integer	Gray Code
very_close	0	000
close	1	001
far	2	011
very_far	3	010
too_far	4	110

Excel How-To¶

Equal-Width Binning with IF / VLOOKUP¶

Suppose your data is in column A (A2:A13), you want 4 equal-width bins.

Step 1: Compute bin width in a helper cell:

E1: =( MAX($A$2:$A$13) - MIN($A$2:$A$13) ) / 4

Step 2: Define bin boundaries in a lookup table (e.g., columns G:H):

G1: Lower    H1: Bin_Label
G2: =MIN($A$2:$A$13)          H2: 0
G3: =G2+$E$1                  H3: 1
G4: =G3+$E$1                  H4: 2
G5: =G4+$E$1                  H5: 3

Step 3: Assign each value a bin using VLOOKUP (approximate match):

B2: =VLOOKUP(A2, $G$2:$H$5, 2, TRUE)

Copy down to B13.

VLOOKUP with TRUE (approximate match) finds the largest boundary <= the value, which exactly maps to the equal-width bin definition.

One-Hot Encoding with IF formulas¶

Suppose Food values are in column A (A2:A6). Categories are American, Chinese, Italian, Other.

Column B (American):

B2: =IF(A2="American", 1, 0)

Column C (Chinese):

C2: =IF(A2="Chinese", 1, 0)

Column D (Italian):

D2: =IF(A2="Italian", 1, 0)

Column E (Other):

E2: =IF(A2="Other", 1, 0)

Copy each formula down the column.

Tip: You can also use a single formula with COUNTIF for dynamic categories:

B2: =IF($A2=B$1, 1, 0)

where row 1 contains the category names (American, Chinese, Italian, Other). This lets you fill the entire grid by copying one formula in all directions.