Homework 5

For any exercise where you’re writing code, insert a code chunk and make sure to label the chunk. Use a short and informative label. For any exercise where you’re creating a plot, make sure to label all axes, legends, etc. and give it an informative title. For any exercise where you’re including a description and/or interpretation, use full sentences. Make a commit at least after finishing each exercise, or better yet, more frequently. Push your work regularly to GitHub, and make sure all checks pass.

For this Homework, find the types of clustering, their pros and cons, and implementation here.

Clustering Techniques on Energy Data

Welcome to this analytical exploration using unsupervised machine learning, specifically clustering algorithms, on a dataset related to energy production and consumption. This assignment, leveraging the #TidyTuesday owid-energy.csv dataset, aims to uncover hidden structures within the energy sector data.


Implement various clustering methods to reveal patterns in energy production, consumption, and their environmental impacts. Optimize clustering parameters and analyze the clusters to extract actionable insights.


Part 1: Data Preparation

Task 1: Data Preprocessing

  • Import and initially explore the dataset.
  • Clean the data by handling missing values and duplicates.
  • Standardize data types for analysis.
  • Conduct a preliminary analysis to understand the features related to energy metrics.

Task 2: Exploratory Data Analysis (EDA)

  • Visualize potential clusters within the energy data.
  • Select features for clustering based on energy consumption types, production sources, and environmental impacts.


  • Use visualization libraries to explore distributions and relationships. Consider creating scatter plots or pair plots to identify potential clusters.
  • Perform correlation analysis to aid in feature selection, focusing on variables that represent different aspects of energy data.

Part 2: Clustering Methods Implementation and Analysis

Task 1: Feature Selection and Data Preparation

  • Select relevant features for clustering
  • Standard scale the data as appropriate

Task 2: K-Means Clustering

  • Use the Calinski-Harabasz method to determine the optimal number of clusters (more robust than Elbow Method).
  • Implement the K-Means algorithm and visualize the resulting clusters.
  • Interpret the clusters focusing on energy production and consumption patterns.

Task 3: Hierarchical Clustering

  • Perform hierarchical clustering and create a dendrogram to visualize the cluster hierarchy.
  • Compare the clusters obtained with K-Means and interpret their relevance to energy data.

Task 4: DBSCAN

  • Implement the DBSCAN algorithm to identify dense clusters within the energy data.
  • Analyze the sensitivity of DBSCAN parameters and their impact on cluster formation.
  • Interpret the clusters, especially focusing on outliers and anomalies in energy patterns.


  • DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a clustering algorithm that groups points that are closely packed together, marking as outliers the points that lie alone in low-density regions. It works well when the clusters are of a similar density.

  • Before we proceed with DBSCAN, we need to decide on two parameters:

    • eps: The maximum distance between two samples for one to be considered as in the neighborhood of the other.
    • min_samples: The number of samples in a neighborhood for a point to be considered as a core point.
  • A common approach to determine eps is to look at the average distance to the nearest n points for each point, plotting the sorted results. Let’s use this method to estimate a suitable eps value for our dataset. We can then perform DBSCAN clustering with the estimated eps and a reasonable min_samples value.

Part 3: Model-based Clustering

Task 1: Fit a Gaussian Mixture Model to the scaled energy data.

  • Determine the optimal number of Gaussian components using model selection criteria such as the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC).
  • Assign each data point to the most probable cluster given by the model.

Task 2: Cluster Characterization

  • Analyze the means and covariances of each Gaussian component to understand the defining features of each cluster.
  • Characterize clusters by examining the distribution of key features within each cluster, such as energy source types, per capita consumption, and carbon intensity metrics.

Task 3: Outlier Detection and Analysis

  • Use the GMM probability density estimates to identify outliers, which are points with low probabilities of belonging to any cluster.
  • Discuss the potential implications of the outliers in the context of energy data, considering aspects such as unusual energy usage patterns or atypical energy source mixes.

Task 4: Cluster Validation

  • Validate the clusters by assessing their silhouette scores or comparing the clusters to known labels or external datasets if available.
  • Evaluate the clusters’ stability by comparing the results of GMM with those from K-Means or hierarchical clustering.

Task 5: Reporting and Visualization

  • Prepare a comprehensive report that summarizes the findings, including visualizations of the clusters, characteristics of each cluster, and any identified outliers.
  • Create visual aids, such as ellipses representing the Gaussian components in two dimensions, to help interpret and communicate the clustering results.

Deliverables: - A comprehensive Jupyter Notebook containing all code, visualizations, and analyses. - A detailed report summarizing the exploratory data analysis, clustering techniques used, and insights derived from the clusters.

Submission Guidelines: - Submit your Jupyter Notebook and report via GitHub, ensuring that your repository is well-organized and your commit messages are informative.

Grading Rubric: Your submission will be evaluated based on the completeness and correctness of the analysis, the quality of visualizations, the thoroughness of the documentation, and adherence to submission guidelines.

Best of luck! May your analysis shed light on significant patterns within the energy sector.