Question: (10 marks) A normalized data set is stored in X -0.922 -1.618 X= 1.862 0.575 2.003 0.004 0.837 0.676 The SVD of X is X

(10 marks) A normalized data set is stored in X -0.922 -1.618 X= 1.862 0.575 2.003 0.004 0.837 0.676 The SVD of X is X = UEV' with -0.659 10.498 0.565 -0.021 0.425 0.089 0. 438 0.786 -0.608 -0.585 -0.168 0.498 ,I= diag (2 407, 2.217,0.225, 0.1001. -0.124 0.624 -0.679 0.366 Carry out dimension reduction with respect to the singular value threshold of = 0.3: find the image of x1.Given that E = diag ( 12. 407, 2.217, 0.225 , 0.100), we keep the first three singular values ( 12. 407, 2.217, 0.225) Since, They are greater than 0.3. Let's denote the reduced Singular value Matrix as Eyed and the Corresponding reduced matrices Ured and VredEred = diag ( 12.407, 2.217, 0.225) 0. 438 Ured - 0- 608 - 0.595 - 0.168 - O. 65 0.496 0 .565 - 0.021 Vred = O. 4 25 0.099 0.786 0.0 - 0. 124P 0. 624 - 0.679 0.366 The reduced matrix X, is obtained by Multiplying Ured by Ered and then multiplying by Vred X1 = Ured. Ered Vred calculate the product: XI 0.438 -0.608 -0. 595 . diag ( 12.407, 2. 217, 0.225). 0.168 0. 65 0.496 0.565 D. 425 0.099 0-786 0 .124 0.624 - 0. 679 - 0.021 0. 0 0. 366 Performing the matrix Multiplication will gives us the Image of X

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

A normalized data set is stored in the matrix X: 1.766 -0.922 0.862 0.555 0.204 2.003 0.937 0.166 The SVD of X is X = UVT with 0.659 0.496 0.565 -0.021 0.425 0.099 0.438 0.786 0.608 0.595 -0.168...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Suppose that R(A, B, C) is a relational schema with functional dependencies F = {A, B C, C B}. (i) Is this schema in 3NF? Explain. [2 marks] (ii) Is this schema in BCNF? Explain. [2 marks] (b)...

lup ] (d) Show how a generating (or "mother") wavelet (x) can spawn a family of "daughter" wavelets jk(x) by simple shifting and scaling operations, and explain the advantages of representing...

State what is meant by a directed graph and a strongly connected component. Illustrate your description by giving an example of such a graph with 8 vertices and 12 edges that has three strongly...

FORMATIVE ASSESSMENT 2 [100 MARKS] Read the project scenario below and answer ALL the questions that follow. SCENARIO Consider the scenario that you are a biology teacher that has always found the...

Question 2 A factory makes products using parts that are identified by letters A to L. Each product is made of at least 3 different parts, and is identified by a product code made up of letters...

Data Analyses & Report Submission Prepare your written report by taking into account the following points: Set out all your calculations for different parts of Tasks 1 and 2 below Present your...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

Fred and Sally own a profitable business that deals in windsurfing equipment. They are the only UK agents to import Dryline sails from Germany, and in addition to this they sell a variety of boards...

In Example7. 5, explain how the 0.9773 and the 0.0228 were obtained and what they are used for.

Dotcom, Inc. went public in 2 0 0 1 . The offer price was $ 6 0 . Furthermore, the first quoted price amounted to $ 6 3 . 5 . Overall, 8 3 3 , 0 0 0 shares were sold, of which 9 3 , 0 0 0 were sold...

On 1 March 2007 DB Limited issued R560 000 15% debentures at R98. The debentures were to be redeemed at par in four equal annual payments starting 28 February 2010. Required: Journalise the above...