I went with random initialization first and then talked through k-means++ as the better option.
Start by clarifying the problem and constraints, then outline the K-Means algorithm step-by-step, covering initialization, assignment, update, and convergence. Emphasize practical considerations like handling empty clusters and choosing k, and describe how you would test correctness with synthetic data and edge cases.
Pro tip: Mention that you would use K-Means++ for initialization to improve convergence and avoid poor local minima, and discuss how to handle empty clusters by reassigning them to the farthest points.
Ask about data size, dimensionality, expected runtime, and whether to implement K-Means++ or standard initialization. Confirm if any libraries are allowed for testing or if everything must be from scratch.
Describe centroid initialization (random or K-Means++), assignment of points to nearest centroid, update of centroids as mean of assigned points, and repeat until convergence (e.g., centroids unchanged or max iterations).
Explain how to compute distances efficiently (e.g., using vectorized operations), handle empty clusters (reassign to farthest point), and choose convergence criteria (e.g., tolerance on centroid movement).
Propose tests with synthetic data (e.g., well-separated blobs) to verify clustering, check edge cases (k=1, k=N, duplicate points), and validate convergence and stability across runs.
Discuss time complexity (O(N*K*D*iterations)), memory usage, and potential improvements like Mini-Batch K-Means for large datasets. Mention limitations (e.g., assumes spherical clusters).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by contrasting K-Means and GMM conceptually: K-Means performs hard assignment to spherical clusters, while GMM performs soft assignment with full covariance, modeling data as a mixture of Gaussians. Then, outline the EM algorithm steps (E-step: compute responsibilities; M-step: update parameters) and how to extend your K-Means code to implement GMM. Finally, discuss practical considerations like initialization, convergence, and trade-offs.
Pro tip: Emphasize that GMM is a probabilistic model that provides uncertainty estimates, which is crucial for downstream tasks like anomaly detection or recommendation systems. Also, mention that K-Means is a special case of GMM with equal spherical covariances and hard assignments.
Explain that K-Means assigns each point to exactly one cluster (hard assignment) and assumes clusters are spherical and equally sized, while GMM assigns probabilities to each cluster (soft assignment) and models clusters with full covariance matrices, allowing elliptical shapes and varying sizes.
Describe the Expectation-Maximization (EM) algorithm: in the E-step, compute the posterior probability (responsibility) of each Gaussian for each data point; in the M-step, update the means, covariances, and mixing coefficients using these responsibilities.
Outline how to modify K-Means code: replace hard assignments with responsibilities, add covariance matrices and mixing coefficients, and iterate E and M steps until convergence (e.g., log-likelihood change below threshold).
Discuss initialization (e.g., K-Means++ or random), convergence criteria, and potential issues like singular covariance matrices (regularization). Mention computational complexity and scalability.
Compare GMM and K-Means in terms of flexibility, computational cost, and interpretability. Highlight scenarios where GMM is preferred (e.g., overlapping clusters, density estimation) and where K-Means suffices (e.g., large-scale, spherical clusters).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.