Assignment #5
1. Consider the following simple IR situation. We have five keywords and six documents. The term-document matrix is given by the following matrix F.
D1 D2 D3 D4 D5 D6
K1 1 0 1 0 0 0
K2 0 1 0 0 0 0
K3 1 1 0 0 0 0
K4 1 0 0 1 1 0
K5 0 0 0 1 0 1
(i) Obtain the singular value decomposition of F.
(ii) Reconstruct F ignoring the smaller of the two singular values.
(iii) Show the representation of the documents and the keywords in the 2-D space after SVD application.
(iv) Using the cosine similarity measure in the LSI space, calculate the document similarity matrix.
2.
This exercise is based on Section 9.4 of Recommender System chapter. In this section, the issue of sparse entries in the user-item matrix is discussed with the SVD approach. Carefully read the chapter and do Exercise 9.4.1 given on page 316. Provide details of calculations of each step of your work.
3.
Compute the PageRank vector of the following graph. Assume p = 0.2.
CSI 5810 Assignment #5 1.Consider the following simple IR situation. We have five keywords and six documents. The term-document matrix is given by the following matrix F. D1 D2 D3D4D5D6 K1101000 K2 010000 K3110000 K4100110 K5000101 (i) Obtain the singular value decomposition of F. (ii) Reconstruct F ignoring the smaller of the two singular values. (iii) Show the representation of the documents and the keywords in the 2-D space after SVD application. (iv) Using the cosine similarity measure in the LSI space, calculate the document similarity matrix. 2. This exercise is based on Section 9.4 of Recommender System chapter. In this section, the issue of sparse entries in the user-item matrix is discussed with the SVD approach. Carefully read the chapter and do Exercise 9.4.1 given on page 316. Provide details of calculations of each step of your work. 3. Compute the PageRank vector of the following graph. Assume p = 0.2. Consider the following simple IR situation. We have tive keywords and six documents. The term-document matrix is given by the following matrix F. DI Dz D3 D4 D5 D6 KI 1 0 1 0 0 0 K2 0 1 0 0 0 0 K3 1 1 0 0 0 0 K& 1 0 0 1 1 0 Ks 0 0 0 1 0 1 (i) Obtain the singular value decomposition of F. ) Reconstruct F ignoring the smaller of the two singular values. (iii) Show the representation of the documents and the keywords in the 2-D space after SVD application. (iv) Using the cosine similarity measure in the LSI space, calculate the document similarity matrix.