SMOTE Comparative Analysis

A side-by-side comparison of a custom SMOTE implementation against the smotefamily R library, with statistical similarity metrics and visualisations.

---

What is SMOTE?

SMOTE (Synthetic Minority Over-sampling Technique) addresses class imbalance by generating synthetic samples for the minority class. For each minority observation, it interpolates between the point and one of its k nearest neighbours:

synthetic = x_i + λ · (x_nn − x_i),   λ ~ Uniform(0, 1)

---

Project Structure

.
├── smote_main.R        # Entry point — run this file only
├── smote_function.R    # Custom SMOTE implementation
├── smote_data.R        # Data preparation & synthetic sample generation
├── smote_plots.R       # All plot definitions
└── smote_compose.R     # patchwork layout & render

Module dependency chain

smote_main.R
  └── smote_function.R   (defines smote_custom())
  └── smote_data.R       (depends on smote_function.R)
  └── smote_plots.R      (depends on smote_data.R)
  └── smote_compose.R    (depends on smote_plots.R)

---

Usage

All files must be in the same directory. Open smote_main.R and run it:

source("smote_main.R")

The script auto-installs any missing packages, runs all modules in order, and renders the final plot in the RStudio viewer.

---

Dependencies

Package	Role
smotefamily	Library SMOTE baseline
ggplot2	All plots
patchwork	Multi-panel layout
dplyr	Data wrangling
tidyr	Reshaping for density plot
png / grid	Fixed-dimension rendering in RStudio

Install all at once:

install.packages(c("smotefamily", "ggplot2", "patchwork", "dplyr", "tidyr", "png"))

---

Dataset

Iris (datasets::iris) — setosa species used as the minority class (50 observations, 4 numeric features).

Parameter	Value
Over-sampling rate	400% (4×)
Nearest neighbours k	3
Random seed	42

---

Output

The final plot (smote_comparison.png) contains 5 panels arranged in two rows.

Row 1 — Scatter plots (Petal Length × Petal Width)

Panel	Description
Custom SMOTE	Synthetic points only. Annotation box shows n, mean ± SD for Petal Length and Petal Width.
Overlay	Both implementations overlaid with original points in black. High overlap between red (▲) and blue (■) indicates consistent behaviour.
smotefamily Library	Synthetic points only. Same annotation as Custom SMOTE panel for direct comparison.

Row 2 — Distributional analysis

Panel	Description
Similarity Metrics	Per-feature heatmap with two descriptive metrics (see below). Green = similar, red = divergent.
Feature-wise Density	Kernel density curves for all 4 features across Original, Custom, and Library sets.

Similarity metrics

Metric	Formula	Interpretation
Mean diff	abs(mean(custom) − mean(library))	Distance between central tendencies. Near 0 = both methods centre synthetic points in the same region.
SD diff	abs(sd(custom) − sd(library))	Distance between spreads. Near 0 = both methods produce similar variability.

How to read the results

A well-implemented custom SMOTE should show:

• Scatter plots with similar point density and range to the library output
• Overlay panel with high overlap between custom and library points
• Density curves that closely track each other and the original distribution
• Mean diff and SD diff values close to 0 across all features

Large deviations in any of these indicate a discrepancy in interpolation logic, neighbour selection, or random sampling behaviour.

---

Example Output

---

References

• Chawla, N. V., et al. (2002). SMOTE: Synthetic Minority Over-sampling Technique. Journal of Artificial Intelligence Research, 16, 321–357.
• Siriseriwan, W. (2019). smotefamily: A Family of SMOTE Based Over-Sampling Techniques. R package version 1.3.1.
• Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2), 179–188.