df has 5 columns and 10 rows. After applying p = PCA(3) and p.fit(df), what is the shape of p.components_? Note: the rows of p.components_ are the principal components. (3, 5) (5, 3) (3, 10) (10, 3) explained_variance_ratio_ of a PCA model: array([0.4, 0.3, 0.2, 0.1]). How many components (at least) do we need to explain 80 percent (or more) of the variance of the original data? [1, 2, 3, 4] and starting centroids [0] and [5], what are the centroids after the first iteration of assigning points and updating centroids, using the iterative K-Means Clustering algorithm with Manhattan distance? [1.5, 3.5] [0, 5] [2, 4] [1, 3] PCA, which of the following approximately reconstructs the original dataframe df using the first three components? p = PCA() then W = p.fit_transform(df) and C = p.components_. W[:, :3] @ C[:3, :] + p.mean_ W[:, :3] @ C[:, :3] + p.mean_ W[:3, :] @ C[:3, :] + p.mean_ W[3:, :] @ C[:, :3] + p.mean_ LinearRegression KMeans SVC (support vector machine) PCA dw at [w1, w2, w3, w4] = [1, -1, 2, -2] is [-2, 2, -1, 1], if gradient descent w = w - alpha * dw is used, which variable will increase by the largest amount in the next iteration? w1 w2 w3 w4 max 2 w1 - w2 subject to w1 - w2 <= 1 and w1 + w2 >= 0 with w1, w2 >= 0 is written in the standard form max c * x subject A x <= b and x >= 0, what is the matrix A? Assume c = [2, -1] and b = [1, 0]. [[1, -1], [-1, -1]] [[1, -1], [1, 1]] [[-1, 1], [-1, -1]] [[-1, 1], [1, 1]] Last Updated: April 29, 2024 at 1:10 AM