lipaz/diamonds

Project Walkthrough Video Click here to watch the video

0. Project Overview & Initial Workflow

0.1 Project Goal

The main objective of this project was to analyze the diamonds dataset and understand:

• —What drives the price of a diamond,
• —How physical attributes (carat, x/y/z dimensions) behave,
• —How categorical qualities (cut, color, clarity) influence pricing,
• —And which features are the most important for predictive modeling.

This includes EDA, feature engineering, dimensionality reduction, clustering, and model interpretation.

0.2 Initial Setup & Data Loading

Before analysis, we:

1. 1.Loaded the dataset (diamonds.csv)
2. 2.Inspected its structure
3. 3.Checked for missing values
4. 4.Validated data types
5. 5.Identified potential data issues such as:
6. 6.Zero or unrealistic values (especially in x, y, z)
7. 7.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 (xyratio, yzratio, 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

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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

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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

[image]

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)

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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

[image]

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

[image]

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

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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)

[image]

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

[image]

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)

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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

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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

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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

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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

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:

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.