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4250Explained Variance Ratio 5A PCA model has component variances 4 and 1. After whitening, what variance should the second whitened component have?机器学习简单数值题未尝试面试订阅4251Rank-1 PCA Reconstruction 1A centered two-feature dataset has covariance matrix [[1.8, 2.4], [2.4, 8.2]]. What is the second principal-component direction and its variance?机器学习中等数值题未尝试面试订阅4256PCA Whitening Coordinates 1A centered point has PC scores (2, -1) on orthonormal loadings v1=(1,0) and v2=(0,1). If the original mean is (5,7), what reconstructed point do the first two PCs produce?机器学习中等数值题未尝试面试订阅4257PCA Whitening Coordinates 2A PCA model has eigenvalues 5, 2, and 1. If you keep the first two PCs, what fraction of variance is discarded?机器学习中等数值题未尝试面试订阅4258PCA Whitening Coordinates 3A whitened PCA transform scales raw PC scores by dividing by the square roots of eigenvalues 9 and 4. If the raw scores are (6,4), what are the whitened scores?机器学习中等数值题未尝试面试订阅4259PCA Whitening Coordinates 4A centered point is x=(5,0), and the first PC loading is v=(0.6,0.8). What point do you get by projecting x onto PC1 alone?机器学习中等数值题未尝试面试订阅4261Why Standardization Can Change PCA DramaticallyWhy is standardizing features often important before PCA when the raw variables use very different units?机器学习中等essay未尝试面试订阅4262Why Whitening Can Amplify NoiseWhy can aggressive whitening make downstream models numerically noisier?机器学习中等essay未尝试面试订阅4263Why PCA Helps Before Some ModelsWhy does flipping the sign of a principal-component loading vector not change the PCA solution in substance?机器学习中等essay未尝试面试订阅4264When PCA Can HurtWhen can PCA actually hurt a predictive pipeline?机器学习中等essay未尝试面试订阅4265A Fast Sanity Check for PCA QuestionsWhy might the first principal component be poor for predicting a label even though it explains the most variance?机器学习中等essay未尝试面试订阅4266k-Means Assignment Step 1A point in clustering has average within-cluster distance a=2 and smallest average distance to another cluster b=5. What is its silhouette score?机器学习简单数值题未尝试面试订阅4267k-Means Assignment Step 2A 1D cluster currently contains points [1,2,7]. What centroid does k-means assign to that cluster in the update step?机器学习简单数值题未尝试面试订阅4268k-Means Assignment Step 3A 2D cluster contains points (0,0), (2,4), and (4,2). What centroid does k-means assign to that cluster?机器学习简单数值题未尝试面试订阅4269k-Means Assignment Step 4A 2-component GMM has priors 0.6 and 0.4. At point x, the component likelihoods are 0.1 and 0.3. What posterior responsibility does component 2 get?机器学习简单数值题未尝试面试订阅4270k-Means Assignment Step 5A DBSCAN run uses minPts=5, counting the point itself. A point has 5 neighbors within eps. Is it a core point?机器学习简单数值题未尝试面试订阅4271k-Means Centroid Update 1In 1D, clusters A= 0,2 and B= 5,9 . What is their average-linkage distance?机器学习简单数值题未尝试面试订阅4272k-Means Centroid Update 2A 1D k-means step has current centroids 0 and 10, and the assigned points are 1,2 to the first cluster and 9 to the second. What are the updated centroids?机器学习简单数值题未尝试面试订阅4273k-Means Centroid Update 3A cluster contains points [1,2,4]. What is its within-cluster SSE around the cluster mean?机器学习简单数值题未尝试面试订阅4274k-Means Centroid Update 4Under Ward linkage, what merge cost increase do two singleton clusters at positions 1 and 4 have in 1D?机器学习简单数值题未尝试面试订阅