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4247Explained Variance Ratio 2PCA produces eigenvalues 12, 3, and 1. What is the smallest number of principal components needed to explain at least 90% of the variance?机器学习简单数值题未尝试面试订阅4248Explained Variance Ratio 3A centered point is x=(3,1), and the first principal-component loading is v=(2,1)/sqrt(5). What is the PC1 score of x?机器学习简单数值题未尝试面试订阅4249Explained Variance Ratio 4A rank-1 PCA approximation keeps only score 4 on loading vector v=(1,2)/sqrt(5). What reconstructed centered point does it produce?机器学习简单数值题未尝试面试订阅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4275k-Means Centroid Update 5Clusters A= 1,4 and B= 6,8 are compared under complete linkage in 1D. What distance is used?机器学习简单数值题未尝试面试订阅4276Within-Cluster Sum of Squares 1A DBSCAN point has 4 neighbors within eps when minPts=5, so it is not core. If eps is increased and the neighborhood count becomes 6, what status change occurs?机器学习中等数值题未尝试面试订阅4277Within-Cluster Sum of Squares 2A 1D cluster has members [0,2,4], so its centroid is 2. If an outlier 10 is added to the cluster, by how much does the centroid shift?机器学习中等数值题未尝试面试订阅4278Within-Cluster Sum of Squares 3A point has silhouette inputs a=3 and b=5. If b falls to 4 while a stays fixed, how much does the silhouette score decrease?机器学习中等数值题未尝试面试订阅4279Within-Cluster Sum of Squares 4In a 2-component GMM with equal priors, component 1 has likelihood 0.2 at x while component 2 has likelihood 0.1, so responsibility 1 is 2/3. If component 2's likelihood rises to 0.2, what does responsibility 1 become?机器学习中等数值题未尝试面试订阅4280Within-Cluster Sum of Squares 5The Euclidean distance between (0,0) and (3,40) is computed on raw features. If the second feature is standardized by dividing it by 10 while the first is unchanged, what new distance do you get?机器学习中等数值题未尝试面试订阅4291Weight Decay Shrinkage 1A hidden unit has pre-dropout activation 3.2. You apply inverted dropout with keep probability 0.8. If the unit is kept on this training pass, what value is forwarded after dropout?机器学习简单数值题未尝试面试订阅4292Weight Decay Shrinkage 2A 4-class classifier uses label smoothing with epsilon = 0.2, distributing epsilon uniformly across all 4 classes including the true class. If class 3 is the correct label, what smoothed target vector do you train on?机器学习简单数值题未尝试面试订阅