AutoSave O OFF m A .CG ... CSE575-HW02 - Saved to my Mac Q Home Insert Draw Design Layout References Mailings Review View Acrobat ? Tell me Share Editing Comments Calibri (Bo... v 13 |A A Aav Ap AaBbCcDdEe AaBbCcDdEe AaBbCcDc AaBbCcDdE AaBb( AaBbCcDdEE|AaBbCcDdEe AaBbCcDdEe IA paste I Uvab x x A DAY Normal No Spacing Heading 1 Heading 2 Title Subtitle Subtle Emph Emphasis Styles Dictate Editor Create and Share Request Pan Adobe PDF Signatures 4) [10 points] If we run K-means on the above dataset to find six clusters (i.e., K = 6). What is the optimal cluster assignment for each data point? (5 points)? What is the corresponding value of the loss function J for the optimal clustering assignment (5 points)? 3 Unconstrained Optimization [20 points] We want to minimize a function f(x)=x7+5x2 in a two-dimensional Euclidean space where x =[x,, x2]. Answer the following questions. 1) [5 points] What is the gradient at point x = [5, 1]? 2) [5 points] What is the steepest descent direction at point x? 3) [5 points] Suppose we want to perform the backtrack line search at point x along direction -Vf(x), using a =0.4 and B=0.9. What is the computed step-size? 4) [5 points] Suppose we want to perform the exact line search at point x along direction -Vf(x), what is the computed step-size? Page 3 of 4 670 words English (United States) Focus E 199%