Consider the bivariate function f(x, y) = 10x + 5y - 2xy - 8x-2y+4, for x,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the bivariate function f(x, y) = 10x + 5y - 2xy - 8x-2y+4, for x, y = R. Figures 2 and 3 show two plots of the surface f(x, y) in three dimensions. (a) Compute the Hessian matrix of f(x, y) and prove that the function f(x, y) is convex. (b) Use the gradient descent method to find the minimum of f(x, y) and the values of xopt and Yopt corresponding to that minimum. Show the details of the iterations of the gradient descent. Indicate the initial values of x and y, and the learning rate value. Give xopt and Yopt with a precision of 10-. The K-means algorithm, also known as the Lloyd-Max algorithm in Information Theory, aims at assigning K centroids to a set of data. The centroids are points (or vectors) in Re, for a given dimension l. The set of data (cloud) has N points in Re. The centroids are also called means because each centroid is the mean of its neighbors. (c) Is the K-means doing supervised or unsupervised learning? Compare to a feedforward neural network. 200 150 z 100 50 0 200 150 z 100 50 0 Figure 2: Surface plot of f(x, y). 3 2 1 0 -2 3 x 2 1 -2 Figure 3: Another surface plot of f(x, y). App S Consider the bivariate function f(x, y) = 10x + 5y - 2xy - 8x-2y+4, for x, y = R. Figures 2 and 3 show two plots of the surface f(x, y) in three dimensions. (a) Compute the Hessian matrix of f(x, y) and prove that the function f(x, y) is convex. (b) Use the gradient descent method to find the minimum of f(x, y) and the values of xopt and Yopt corresponding to that minimum. Show the details of the iterations of the gradient descent. Indicate the initial values of x and y, and the learning rate value. Give xopt and Yopt with a precision of 10-. The K-means algorithm, also known as the Lloyd-Max algorithm in Information Theory, aims at assigning K centroids to a set of data. The centroids are points (or vectors) in Re, for a given dimension l. The set of data (cloud) has N points in Re. The centroids are also called means because each centroid is the mean of its neighbors. (c) Is the K-means doing supervised or unsupervised learning? Compare to a feedforward neural network. 200 150 z 100 50 0 200 150 z 100 50 0 Figure 2: Surface plot of f(x, y). 3 2 1 0 -2 3 x 2 1 -2 Figure 3: Another surface plot of f(x, y). App S
Expert Answer:
Related Book For
Quantitative Methods for Business
ISBN: 978-0324651751
11th Edition
Authors: David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey cam
Posted Date:
Students also viewed these programming questions
-
Q1. You have identified a market opportunity for home media players that would cater for older members of the population. Many older people have difficulty in understanding the operating principles...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Once down to about 15, the worlds only wild flock of whooping cranes now numbers a record 237 birds in its Texas Coastal Bend wintering ground (www.SunHerald.com). The average whooping crane egg...
-
Compare and contrast the tax treatment of interest from a Treasury bond and qualified dividends from corporate stock.
-
Where do worker compensation insurance costs get reported on the financial statements?
-
Positive accounts receivable confirmations are appropriate when: a. There is reason to believe that a substantial number of accounts may be in dispute. b. Control risk is low. c. Accounts receivable...
-
NewLife Hospital purchased a special X-ray machine. The machine, which cost $623,120, was expected to last ten years, with an estimated residual value of $63,120. After two years of operation (and...
-
How much power does Daniel produce if he transforms 2.4 kJ of chemical energy (in pizza that he ate that day) into kinetic energy and thermal energy in 12.5 s?
-
Officer Smith suspects that Laura committed a grizzly murder. If he had her DNA, he could test it against the DNA collected at the crime scene to see if it matched. Officer Smith followed Laura in...
-
Write a java program to display multiplication table of a given number?
-
A group of four young adults have been traveling from town to down committing various acts while they are together. They are good at what they do and have not been caught yet. Their luck is about to...
-
Your good friend Claire has finally had it with her husband Frank's shenanigans, and after years of fighting and disharmony, Claire decides to finally call it quits and file for a divorce. She has...
-
Police officers enjoy qualified immunity against civil suits. This is in an effort to decrease the number of frivolous lawsuits brought before a court and also to protect officers' discretion...
-
Write a java program to find out power of a given number ?
-
The following information relates to Gretan Ltd and Hutey Ltd. Both companies manufacture and sell calculators. Gretan Ltd Hutey Ltd Sales in units per year 20,000 20,000 Selling Price Rs500 Rs500...
-
In a large midwestern university, 30% of the students live in apartments. If 200 students are randomly selected, find the probability that the number of them living in apartments will be between 55...
-
Recall the Martin-Beck Company distribution system problem in Section 11.3. a. Modify the formulation shown in Section 11.3 to account for the policy restriction that one plant, but not two, must be...
-
Suppose that a decision maker faced with four decision alternatives and four states of nature develops the following profit payoff table: a. If the decision maker knows nothing about the...
-
Specialty Toys, Inc., sells a variety of new and innovative childrens toys and believes that the preholiday season is the best time to introduce a new toy. Many families use this time to look for new...
-
Derive the expression for the complex frequency response of an undamped torsional system.
-
A single-story building frame is subjected to a harmonic ground acceleration, as shown in Fig. 3.57. Find the steady-state motion of the floor (mass \(m\) ). Figure 3.57:- 22 -x(t) m (!) - A cos cot...
-
Find the horizontal displacement of the floor (mass \(m\) ) of the building frame shown in Fig. 3.57 when the ground acceleration is given by \(\ddot{x}_{g}=100 \sin \omega t \mathrm{~mm} /...
Study smarter with the SolutionInn App