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Machine Learning Lab
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How is SVD related to PCA when applied to a mean-centered data matrix X (n x d)?
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How does EM for GMMs fundamentally differ from K-Means?
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Given an m x n matrix A, the Singular Value Decomposition is A = U * Sigma * V-transpose. Which correctly describes U, Sigma, and V-transpose?
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For a dataset with C = 4 classes and d = 50 features, what is the maximum number of discriminant directions LDA can produce?
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Before applying PCA to a dataset containing features with very different scales (e.g., age 0-100 and income 0-500000), what preprocessing step is essential?
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Bagging primarily reduces which component of prediction error, and why?
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After one iteration of K-Means (K=2), the following 2D points are assigned to Cluster 1: (1,1), (3,3), (5,1). What is the x-coordinate of the new centroid for Cluster 1?
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A lab dataset has 10,000 samples, 200 features, and 5 labeled classes. You want to visualize the data in 2D before classification. Which approach is most appropriate?
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A dataset has 3 features. After PCA, the eigenvalues of the covariance matrix are: lambda_1 = 8, lambda_2 = 4, lambda_3 = 2. What percentage of variance is explained by the first two principal components (rounded to the nearest whole number)?
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A 2D dataset has two clusters: one circular and one elongated (high variance in x, low variance in y). K-Means performs poorly. Why would EM/GMM with full covariances handle this better?
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