Datasets:

lipaz
/

diamonds

Loaded the dataset (diamonds.csv)
Inspected its structure
Checked for missing values
Validated data types
Identified potential data issues such as:
- Zero or unrealistic values (especially in x, y, z)
- Extreme outliers in price and carat

0.3 Cleaning & Preprocessing Steps

We performed the following:

Removed or corrected invalid dimension values (e.g., x/y/z = 0)
Detected extreme outliers using boxplots
Standardized numeric distributions when needed
Encoded categorical variables
Created engineered features:
- volume = x * y * z
- price_per_carat = price / carat
- PCA components (pca1, pca2)
- Ratios (xy_ratio, yz_ratio, xz_ratio)

0.4 Core Analytical Questions

Throughout the project, we focused on several central questions:

1. Distribution & Quality of the Data

What do the numeric features look like?
Are there extreme outliers or incorrect values?

2. Relationship Between Size & Price

How strongly does carat determine price?
Do heavier diamonds increase in price linearly or exponentially?

3. Influence of Categorical Features

How do cut, color, and clarity affect pricing?
Are some categories overpriced or underpriced?

4. Multicollinearity & Feature Dependencies

Are x, y, z essentially duplicating carat?
What is the correlation structure?

5. Machine Learning Insights

Which features matter most for predict

Diamonds Dataset — Full EDA, Visualizations & Feature Analysis

This project explores the diamonds dataset using a full workflow:

Exploratory Data Analysis (EDA)
Outlier detection
Distribution analysis
Relationship analysis (carat–price, dimensions–price)
Correlation heatmaps
Clustering (PCA + KMeans)
Feature importance (Linear Regression + Random Forest)

All generated graphics are stored and displayed inside this repository.

1. Exploratory Data Analysis (EDA)

1.1 Boxplots — Outlier Detection

What we looked for

Detect extreme outliers in: carat, depth, table, x, y, z, price
Identify values that may distort models

What we found

Very strong outliers in price (long right tail)
Outliers in carat and the 3D dimensions x/y/z
depth & table are stable with minimal extreme values

1.2 Boxplots — Numeric Feature Comparison

What we looked for

Check consistency between numeric fields
Identify skewness and unusual patterns

What we found

Most numeric columns are right-skewed
carat, price, x/y/z show wide variance
Indicates the need for normalization before modeling

1.3 Distribution Plots — Numeric Features

What we looked for

Understand the shape of each numeric feature
Detect multimodality or measurement clusters

What we found

price = heavily right-skewed
carat = concentrated around 0.3–1.5
x/y/z = show clear clustered peaks → indicates standard diamond sizes in the market

1.4 Distribution (Histograms + KDE)

What we looked for

Compare distribution curves to understand typical ranges
Check for measurement errors

What we found

x/y/z show repeating peaks → indicates standard diamond cut proportions
price again shows extreme right-tail
No obvious errors except a few odd large values

2. Relationship Exploration

2.1 Carat vs Price — Colored by Cut

What we looked for

Understand how carat weight drives pricing
Check if cut quality influences pricing

What we found

Strong positive correlation: higher carat → higher price
High-cut diamonds (Ideal, Premium) form slightly higher price clusters
Clear size bands (0.5, 1.0, 1.5 carat) visible

2.2 Carat vs Price — Hexbin Density

What we looked for

Density concentration of the dataset
Identify the most common market prices

What we found

Dense cluster around 0.2–1.2 carat and $500–$6000
Very few large stones (3–5 carat)

2.3 ### Average Price by Cut, Color, and Clarity

![Overlay Density](

Key insights:

Cut: Premium diamonds have the highest average price, while Ideal tends to be lower.
Color: Colors I and J show higher average prices compared to others.
Clarity: SI2 appears with the highest average price, likely influenced by larger carat values within this group.

2.4 Diamonds Dimensions vs Price

What we looked for

Relationship between x, y, z dimensions and price

What we found

Strong increasing trend for all dimensions
x and y show the clearest linear relationship
Some unrealistic dimension values detected → outliers

3. Statistical Relationships

3.1 Correlation Matrix (Numeric)

What we looked for

Identify multicollinearity
See which features are most correlated with price

What we found

carat has the strongest correlation with price (0.92)
x, y, z strongly correlated with each other (>0.98)
depth & table weakly correlated

3.2 Heatmap — Key Numeric Features

What we found

Confirms carat is the #1 price driver
Dimensions act as proxies for carat
Confirms multicollinearity → PCA or feature reduction required

4. Advanced Visualizations

4.1 KMeans Clusters (PCA Visualization)

What we looked for

Whether diamonds naturally form clusters
If PCA can separate quality groups

What we found

The dataset forms clear clusters after PCA
Cluster 0 is dominant (majority of market)
Smaller clusters show unique structural patterns

4.2 Pairplot — Key Features

What we looked for

Examine all pairwise relationships visually

What we found

Strong linear relationships among x, y, z
Clear nonlinear trend for carat–price
Strong clustering by typical diamond sizes

5. Feature Importance

5.1 Linear Regression — Coefficients

What we looked for

Identify which features increase or decrease price

What we found

carat has the highest positive effect
Higher clarity grades reduce price impact (negative coefficients for lower clarity)
color J decreases price significantly

5.2 Random Forest — Top 20 Features

What we looked for

Nonlinear feature importance ranking
Impact of engineered features

What we found

price_per_carat = most powerful feature
volume & PCA components ranked very high
confirms importance of dimensional/size attributes
categorical dummy variables are much weaker

Regression Model Comparison

We evaluated three regression models:

Linear Regression (baseline)
Random Forest Regressor
Gradient Boosting Regressor

Results

Model	MAE	RMSE	R²
Linear Regression	0.0840	0.1248	0.9841
Random Forest	0.0042	0.0194	0.9996
Gradient Boosting	0.0250	0.0442	0.9980

Summary

Random Forest achieved the best performance: lowest errors and highest R².
Gradient Boosting also performed very well but was slightly weaker.
Linear Regression performed significantly worse, showing the price relationships are non-linear.

Conclusion

Random Forest is the best regression model and was selected as the final model for this part.

Part 7: Regression → Classification

Creating Price Classes (Quantile Binning)

To convert the continuous price variable into a classification target,
we split the data into three equal-sized groups (33% each) using quantiles.

Class 0 → bottom 33% (cheapest diamonds)
Class 1 → middle 33%
Class 2 → top 33% (most expensive diamonds)

This ensures balanced class sizes and prevents bias toward any group.

Class Balance Check

After creating the three price classes, we checked whether the classes were balanced.

Training Set:
Each class contains ~33% of the samples
Test Set:
Same distribution — ~33% per class

This confirms the split is balanced and suitable for training classification models.

8.1 Conceptual Questions

What is more important in our task — Precision or Recall?

In our diamond price classification task, precision is slightly more important.
We want to avoid labeling a low-value diamond as an expensive one (false positives).
This is especially relevant because misclassifying prices upward is more harmful than misclassifying downward.

What is more critical — False Positive or False Negative?

False Positives are more critical.
A False Positive here means:
The model predicts “expensive” when the diamond actually belongs to a cheaper class.

This type of error is more problematic in real-world scenarios (e.g., pricing, valuation, inventory management),
because it overestimates the diamond’s value and can lead to financial loss.

Part 8.3 — Classification Models Evaluation

After converting the regression problem into a 3-class classification task,
we trained and evaluated three models:

Logistic Regression
Random Forest
Gradient Boosting

What we evaluated

For each model we generated:

Classification Report (precision, recall, f1-score, support)
Confusion Matrix (to understand where the model makes mistakes)

Results Summary

All three models performed extremely well, with Gradient Boosting achieving the best scores:

Model	Accuracy	F1-macro
Logistic Regression	0.9866	0.9866
Random Forest	0.9926	0.9926
Gradient Boosting	0.9933	0.9933

Key Insights

All models classify the three price classes with very high precision and recall.
Gradient Boosting makes the fewest mistakes across classes.
Misclassifications mostly occur between adjacent price classes (e.g., class 1 ↔ class 2), which is expected because diamond prices are continuous.
No model suffers from class imbalance problems.

Confusion Matrices & Reports

Logistic Regression

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Random Forest

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Gradient Boosting

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Winner

Gradient Boosting is the best performing model
→ Highest Accuracy
→ Highest F1-macro
→ Most stable confusion matrix

This is the model selected for export and deployment.