1. True or False "True' ' implies the statement is always true, and statements are made in the context of this class. Provide a one sentence explanation for your answer. (a) K-means clustering always finds the global optimum of the objective function. (b) The correlation between the first principal component (PC) score and the second is higher than the correlation between the second principal component (PC) score and the third. (c) The number of clusters K must be specified in advance when using K-Means (d) The maximum number of principal components is always equal to the number of the original features. (e) Increasing the number of clusters (K) always reduces the within-cluster sum of squares (WCSS). (f) The principal components are linear combinations of the original features. 2 You are given a dataset X R104 that has been standardized before applying PCA. Below are the loading vectors (each column corresponds to a principal component) and the principal component scores for the first 5 observations