Welcome to the Wiki page of the course '''Search Engines, WS 2009 / 2010'''. Lecturer: [[http://ad.informatik.uni-freiburg.de/staff/bast|Hannah Bast]]. Tutorials: [[http://ad.informatik.uni-freiburg.de/staff/celikik|Marjan Celikik]]. Course web page: [[http://ad.informatik.uni-freiburg.de/teaching/winter-term-2009-2010/suchmaschinen-vorlesung|click here]].

Here are PDFs of the slides of the lectures so far: [[attachment:SearchEnginesWS0910/lecture-1.pdf|Lecture 1]], [[attachment:SearchEnginesWS0910/lecture-2.pdf|Lecture 2]], [[attachment:SearchEnginesWS0910/lecture-3.pdf|Lecture 3]], [[attachment:SearchEnginesWS0910/lecture-4.pdf|Lecture 4]], [[attachment:SearchEnginesWS0910/lecture-5.pdf|Lecture 5]], [[attachment:SearchEnginesWS0910/lecture-6.pdf|Lecture 6]], [[attachment:SearchEnginesWS0910/lecture-7.pdf|Lecture 7]], [[attachment:SearchEnginesWS0910/lecture-8.pdf|Lecture 8]], [[attachment:SearchEnginesWS0910/lecture-9.pdf|Lecture 9]],
[[attachment:SearchEnginesWS0910/lecture-10.pdf|Lecture 10]].

Here are the recordings of the lectures so far (except Lecture 2, where we had problems with the microphone), LPD = Lecturnity recording: [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-1.lpd|Recording Lecture 1 (LPD)]], [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-3.lpd|Recording Lecture 3 (LPD)]], [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-4.lpd|Recording Lecture 4 (LPD)]], [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-5.lpd|Recording Lecture 5 (LPD without audio)]], [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-6.lpd|Recording Lecture 6 (LPD)]], [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-7.avi|Recording Lecture 7 (AVI)]], [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-8.avi|Recording Lecture 8 (AVI)]], [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-9.avi|Recording Lecture 9 (AVI)]], [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-10.avi|Recording Lecture 10 (AVI)]].

Here are PDFs of the exercise sheets so far: [[attachment:SearchEnginesWS0910/exercise-1.pdf|Exercise Sheet 1]], [[attachment:SearchEnginesWS0910/exercise-2.pdf|Exercise Sheet 2]], [[attachment:SearchEnginesWS0910/exercise-3.pdf|Exercise Sheet 3]], [[attachment:SearchEnginesWS0910/exercise-4.pdf|Exercise Sheet 4]], [[attachment:SearchEnginesWS0910/exercise-5.pdf|Exercise Sheet 5]], [[attachment:SearchEnginesWS0910/exercise-6.pdf|Exercise Sheet 6]], [[attachment:SearchEnginesWS0910/exercise-7.pdf|Exercise Sheet 7]], [[attachment:SearchEnginesWS0910/exercise-8.pdf|Exercise Sheet 8]], [[attachment:SearchEnginesWS0910/exercise-9.pdf|Exercise Sheet 9]], [[attachment:SearchEnginesWS0910/exercise-10.pdf|Exercise Sheet 10]].

Here are your solutions and comments on the previous exercise sheets: [[SearchEnginesWS0910/ExerciseSheet1|Solutions and Comments 1]], [[SearchEnginesWS0910/ExerciseSheet2|Solutions and Comments 2]], [[SearchEnginesWS0910/ExerciseSheet3|Solutions and Comments 3]], [[SearchEnginesWS0910/ExerciseSheet4|Solutions and Comments 4]], [[SearchEnginesWS0910/ExerciseSheet5|Solutions and Comments 5]], [[SearchEnginesWS0910/ExerciseSheet6|Solutions and Comments 6]], [[SearchEnginesWS0910/ExerciseSheet7|Solutions and Comments 7]], [[SearchEnginesWS0910/ExerciseSheet8|Solutions and Comments 8]], [[SearchEnginesWS0910/ExerciseSheet9|Solutions and Comments 9]].

The recordings of all lectures are now available, see above. Lecture 2 is missing because we had technical problems there. To play the Lecturnity recordings (.lpd files) you need the [[http://www.lecturnity.de/de/download/lecturnity-player|Lecturnity Player, which you can download here]]. I put the Camtasia recordings as .avi files, which you can play with any ordinary video player; I would recommend [[http://www.videolan.org/vlc|VLC]].

[[SearchEnginesWS0910/Rules|Here are the rules for the exercises as explained in Lecture 2]].

[[SearchEnginesWS0910/MidTermExam|Here is everything about the mid-term exam]].

[[SearchEnginesWS0910/ExerciseSheet10|Here you can upload your solutions for Exercise Sheet 10]]. The deadline is Thursday 21Jan10 at 4 pm.

== Questions and comments about Exercise Sheet 10 below this line (most recent on top) ==

Hi Mirko: no, I meant what I wrote. You can easily check that it makes sense from the matrix / vector dimensions: u_i is an m x 1 vector, s_i is an 1 x 1 scalar, v_i is an n x 1 vector and hence v_i' (the transpose of v_i) is a 1 x n vector. Hence wrt to matrix dimensions u_i * s_i * v_i' is m x 1 * 1 x 1 * 1 x n, which matches as it should and gives an m x n matrix. Ok? '''Hannah 19Jan10 23:32'''

About the last post: with A = sum{i=1, .... you mean ||A|| = sum{i=1, ..., so the frobenius-norm of A? and by v_i' you mean the row of i of V'? If so, i don't get ||A|| = sum{i=1,...,r} u_i * s_i * v_i'. Or am i totally wrong? I'm just confused. '''Mirko, 19.01, 22:18'''

Hi Björn + all: let the SVD of A be U * S * V' and let u_1,...,u_r be the r columns of U, and let v_1,...,v_r be the r columns of V (or, equivalently, the r rows of V'), where r is the rank of the matrix. Let s_1,...,s_r be the r diagnonal entries of S. Then convince yourself that you can write A = sum_{i=1,...,r} u_i * s_i * v_i'. With that, you easily get the SVD of A_k and also of A - A_k. Tell me if this helped you. '''Hannah 19Jan10 17:32'''

Hey, is it possible that for exercise 2 it's ||A||-||A_k|| instead of ||A-A_k||? We've just discussed this because we both were stuck and the later seems more obvious to us and provable with the hints provided. Of course, it is possible that we're mistaken somewhere. We managed to proove the lemmas from the hint but still fail to proove the statement from the exercise. Otherwise, we might need a hint to show that ||A-A_k|| = ||S-S_k|| while S_k is S with the values s_ij where i,j>k set to 0. '''Bjoern 19.1. 17:18'''

Ok, I added the marks to your individual pages now. If a mark does not correspond to the assignment scheme in my post below, please tell us. '''Hannah 19Jan10 1:56am'''

Hi Florian + all: yes, you are right, a matrix-vector multiplication is all that is needed to implement the power method. Concerning you mark for the first eight exercise sheets, you can easily compute it from the following point range -> mark assigment: 28 - 30 points = 1.0, 26 - 27 points = 1.3, 24-25 points = 1.7, 22 - 23 points = 2.0, 20 - 21 points = 2.3, 18 - 19 points = 2.7, 16 - 17 points = 3.0, 14 - 15 points = 3.3, 12 - 13 points = 3.7, 10 - 11 points = 4.0. Your total number of points (with the worst exercise sheet taken out of the counting) is already on your page, I will add the corresponding marks now. '''Hannah 19Jan10 1:45am'''

Am I right with the assumption that we do not even need a matrix-matrix multiplication for exercise 4 but just a matrix-vector multiplication? And another question, where can I find the mark for the first 8 exercise sheets? Thanks. '''Florian 18.Jan10 22:38'''

Oh yes you're right. I forgot to transpose V. Sorry my mistake. '''Jonas 18.Jan10 21:49'''

Hi Jonas, no I think it's correct, V is n x k and then the transpose of V is k x n, and that is what appears in the product of the SVD. '''Hannah 18Jan10 21:39'''

One Question: On slide 11 of lecture 10, shouldn't V be a kxn matrix instead of a nxk? '''Jonas 18.Jan10 20:39'''

Hi Jens + all: we applied this rule to your exercise sheets until the christmas break, that is, we simply took your worst sheet out of the counting. Given that there are only 4, at most 5, exercise sheets after the christmas break, the rule does not apply for those sheets. '''Hannah 18Jan10 18:19'''

I have a question about skipping an exercise sheet: At the beginning of the semester you said that we would be allowed to do this once. Does it still hold? '''Jens 18Jan10 18:07'''

Oh yes, sorry, I forgot, it's done now. '''Hannah 17Jan10 13:43'''

'''Matthias''' - Can you please upload the Slides for the Lec 10 as well?

Here is a major hint for Exercise 2. There are many ways to prove this, but one of the most natural is via these three steps, each of which is not too hard to prove. Note that, unlike in the lecture, in the hint below I use X' to denote the transpose of a matrix or vector X. This is a common notation in the numerics community (where as the pure algebra people prefer the T superscript). '''Hannah 14Jan10 23:37'''

{{{
(1) Prove that for an m x m matrix U with U' * U = I and for an arbitrary m x 1 vector x, the L2-norms of x and U*x are equal. The L2-norm of a vector x is defined as the square root of the sum of the squares of its components. It helps to observe that the square of the L2-norm of x can also be written as x' * x.

(2) Prove that for an m x m matrix U with U' * U = I and for an arbitrary m x n matrix A, the L2-norms of A and of U * A are equal. This is easy to prove using (1).

(3) Prove that if A has the singular value decomposition U * S * V', then the L2-norm of A is the same as the L2-norm of S.
}}}