Implement K-Means and compare with GMM
K-Means Clustering Implementation and GMM Comparison
Implement K-Means clustering from scratch for a given dataset X of shape (n_samples, n_features) and a specified number of clusters k.
Your implementation must adhere to the following steps and considerations:
- Centroid Initialization: Initialize
kcentroids. - Assignment Step: Assign each data point to its nearest centroid.
- Update Step: Recompute centroids as the mean of all points assigned to them.
- Iteration and Convergence: Repeat the assignment and update steps until either convergence is achieved or a maximum number of iterations is reached.
- Edge Case Handling: Address edge cases, specifically how to handle empty clusters.
- Convergence Criteria: Include a robust test for convergence. Acceptable criteria include, but are not limited to, unchanged point assignments, centroid movement falling below a specified tolerance, or a non-increasing within-cluster loss (e.g., sum of squared distances).
Follow-up Questions
After completing the coding task, be prepared to discuss the following:
- Explain the fundamental differences between Gaussian Mixture Modeling (GMM) and K-Means clustering.
- Describe how you would train a Gaussian Mixture Model using the Expectation-Maximization (EM) algorithm.
- Identify specific scenarios or data characteristics where you would prefer to use GMM over K-Means.
AI interview prep
Core dilemma
Balancing the algorithmic correctness and numerical stability of a fundamental clustering algorithm with a deep theoretical understanding of its probabilistic counterpart (GMM) and the EM algorithm, all while considering practical application scenarios and their respective trade-offs.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Implement K-Means and compare with GMM
K-Means Clustering Implementation and GMM Comparison
Implement K-Means clustering from scratch for a given dataset X of shape (n_samples, n_features) and a specified number of clusters k.
Your implementation must adhere to the following steps and considerations:
- Centroid Initialization: Initialize
kcentroids. - Assignment Step: Assign each data point to its nearest centroid.
- Update Step: Recompute centroids as the mean of all points assigned to them.
- Iteration and Convergence: Repeat the assignment and update steps until either convergence is achieved or a maximum number of iterations is reached.
- Edge Case Handling: Address edge cases, specifically how to handle empty clusters.
- Convergence Criteria: Include a robust test for convergence. Acceptable criteria include, but are not limited to, unchanged point assignments, centroid movement falling below a specified tolerance, or a non-increasing within-cluster loss (e.g., sum of squared distances).
Follow-up Questions
After completing the coding task, be prepared to discuss the following:
- Explain the fundamental differences between Gaussian Mixture Modeling (GMM) and K-Means clustering.
- Describe how you would train a Gaussian Mixture Model using the Expectation-Maximization (EM) algorithm.
- Identify specific scenarios or data characteristics where you would prefer to use GMM over K-Means.