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# Obesity Risk Factor Analysis in R

[GitHub](https://github.com/alvariitoSW/factores_riesgo_obesidad)

**Date:** December 2024
**Collaborators:** [Álvaro Martínez Gamo](https://alvariitosw.github.io/portfolio_personal/), David López Valdivia
**Technologies:** R

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# Obesity Level Classification and Analysis

## Project Overview

This project analyzes obesity levels using multiple statistical and machine learning techniques on a dataset containing demographic, dietary, and lifestyle information. The analysis implements dimensionality reduction, classification algorithms, and clustering methods to understand and predict obesity categories.

## Methodology

### 1. Data Visualization

Initial exploratory analysis of numerical variables:

- **Age**, **Height**, **Weight**: demographic characteristics
- **FCVC** (Frequency of vegetable consumption), **NCP** (Number of main meals), **CH2O** (Water consumption)
- **FAF** (Physical activity frequency), **TUE** (Time using technology)

Distribution histograms and pairwise correlation plots were generated to identify relationships between variables and obesity levels.

### 2. Principal Component Analysis (PCA)

PCA was applied to reduce dimensionality while preserving variance:

- Numerical variables were standardized
- Categorical variables (**Gender**, **family_history_with_overweight**, **FAVC**, **CAEC**, **SMOKE**, **SCC**, **CALC**, **MTRANS**) were treated as supplementary qualitative variables
- 8 principal components were extracted
- Scree plot visualized variance explained by each component
- Individual projections were colored by obesity level to identify separation patterns

![PCA with Group 1 including Obesity_Type_{2,3}, Group 2 including Overweight_Level_{1,2} and Obesity_Type_1, and Group 3 including Normal_Weight and Insufficient_Weight.](../../assets/projects/r-risk-analysis/pca.webp)

### 3. Linear Discriminant Analysis (LDA)

LDA was implemented for multiclass classification:

- Only numerical variables were retained for the model
- Data split: 70% training, 30% testing
- Projection onto discriminant functions (LD1 and LD2) visualized class separation
- Confusion matrix and accuracy metrics evaluated model performance

![LDA analysis with all labels separated by color.](../../assets/projects/r-risk-analysis/lda.webp)

### 4. Naive Bayes Classifier

A probabilistic approach assuming feature independence:

- Continuous variables with excessive precision were rounded to treat them as categorical
- Only **Age**, **Height**, and **Weight** remained as continuous variables (normalized)
- All other variables converted to factors
- Model trained on 70% of data, tested on remaining 30%
- Accuracy calculated from confusion matrix

### 5. K-Means Clustering

Unsupervised learning to discover natural groupings:

- All categorical variables encoded numerically
- Optimal cluster number determined using:
    - **Elbow method**: identifies diminishing returns in within-cluster sum of squares
    - **Silhouette method**: measures cluster cohesion and separation
- K-Means applied for k=2 and k=3 clusters
- Results visualized via PCA projection and pairwise variable plots
- Clusters compared against actual obesity levels to assess alignment

## Risk Factors Analysis (from PDF)

The analysis identifies key obesity risk factors across multiple dimensions:

**Dietary Factors:**

- High calorie food consumption (FAVC)
- Low vegetable intake (FCVC)
- Eating patterns (CAEC, NCP)
- Water consumption (CH2O)

**Behavioral Factors:**

- Physical activity frequency (FAF)
- Technology usage time (TUE)
- Smoking habits (SMOKE)
- Calorie monitoring (SCC)

**Genetic/Demographic:**

- Family history of overweight
- Age, gender, height, weight

These factors collectively contribute to obesity classification across seven levels: Insufficient Weight, Normal Weight, Overweight Level I-II, and Obesity Type I-III.

## Results Summary

- **PCA**: Effectively reduced dimensionality while maintaining class distinctions
- **LDA**: Provided strong classification accuracy with clear discriminant functions
- **Naive Bayes**: Achieved competitive performance despite independence assumption
- **Clustering**: Revealed natural groupings partially aligned with obesity categories