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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]]. | 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]]. |
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Here are .lpd files of the recordings of the lectures so far (except Lecture 2, where we had problems with the microphone): [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-1.lpd|Lecture 1]] [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-3.lpd|Lecture 3]] [[http://vulcano.informatik.uni-freiburg.de/lecturnity/lecture-4.lpd|Lecture 4]]. | 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)]]. |
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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]]. | 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]]. |
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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]] | 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]]. |
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= Exercise Sheet 3 = The recordings of all lectures are now available, see above. Lecture 2 is missing because we had technical problems there. To play the recordings (it's .lpd files) you need the Lecturnity Player. [[http://www.lecturnity.de/de/download/lecturnity-player|You can download the player for free here]]. |
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]]. |
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[[SearchEnginesWS0910/ExerciseSheet4|Here you can upload your solutions for Exercise Sheet 4]]. | [[SearchEnginesWS0910/MidTermExam|Here is everything about the mid-term exam]]. |
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== Questions or comments below this line, most recent on top please == I accidentally loaded the ZIP file instead of the PDF(My eyes are heavy...). But i couldn't overwrite the pdf file on the wiki now. So I loaded it in my_name_ex1.pdf. I hope this won't occur any problems. '''Jonas 16Nov09 11.41pm''' |
[[SearchEnginesWS0910/ExerciseSheet10|Here you can upload your solutions for Exercise Sheet 10]]. The deadline is Thursday 21Jan10 at 4 pm. |
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---- /!\ '''Edit conflict - other version:''' ---- I accidentally loaded the ZIP file instead of the PDF(My eyes are heavy...). But i couldn't overwrite the pdf file on the wiki now. So I loaded it in my_name_ex1.pdf. I hope this won't occur any problems. '''Jonas 16Nov09 11.41pm'' |
== Questions and comments about Exercise Sheet 10 below this line (most recent on top) == |
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---- /!\ '''Edit conflict - your version:''' ---- | Thanks for the additional hint for exercise 2, I think I finally managed to get a solution with it. Then I have another question to exercise 4: is it enough if the program outputs the eigenvector or should it also give the corresponding maximal eigenvalue? '''Florian 20Jan10 18:25''' |
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---- /!\ '''End of edit conflict''' ---- | 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''' |
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To Florian: This was very well explained in the lecture (it is still there on the slides). It means the speed-up achieved by reading and decompressing your compressed list compared to when the list is read in uncompressed format. As your inverted list is randomly generated, you might have different speed-ups for different inverted lists. In order to have any speed-up, of course, your compression scheme should really work and reduce the size of the inverted list + should not be too inefficient. One extreme example for inefficient code would be using strings instead of bit-shifting for your coding. '''Marjan 8:38pm''' | 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''' |
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What is meant with the best speedup for Exercise 4 which we should add on the solution page? The best speedup for just reading the data from disk or the best speedup for reading and decompressing the list? '''Florian 16Nov09 8:12pm''' | 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''' |
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To Dragos: Gap encoding + Elias code is not trivial at all and you can use it. Gap encoding + Byte code is also fine. '''Marjan 16Nov09 2:15pm''' | 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''' |
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Is it ok to use Elias code for the compressing from Exercise 4(2)? Or it's too 'trivial'?:)'''Dragos 16Nov09 14.14''' | 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''' |
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To Florian + all: A single number doesn't really make sense, does it? For the discussion part of the exercise, think in terms of probability distributions, as we did in the lecture (when discussing which probability distribution a certain encoding is optimal for). For the example, give a sequence of numbers. '''Hannah 15Nov09 9:41pm''' | 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''' |
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To Johannes + all: Yes, good idea. I will anyway at some point in the next weeks hand out a sheet where you have the opportunity to give feedback on the lectures and the exercises. But yes, why not give me that feedback on the current exercise sheet already now. Let me refine your proposal a bit. It would be useful for me if you would provide ''two'' grades: one for the hardness (pick one of: too hard for me, challenging but feasible, not very hard) and one for the amount of work (pick one of: too much for me, a lot but feasible, not more than for other lectures). It would also be helpful if you would not just give a grade but put your opinion into words. It's no problem if you are critical but please stay polite. I will take your comments seriously, don't worry. '''Hannah 15Nov09 9:33am''' | 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''' |
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In Exercise we should "give an example of data for which k = x is the best choice". What is meant by "an example of data" here? A single number or a set of numbers or anything else? '''Florian 15Nov09 8:52pm''' | Oh yes you're right. I forgot to transpose V. Sorry my mistake. '''Jonas 18.Jan10 21:49''' |
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I'd like to suggest that everyone grades the exercise sheet from 1 (for "way to easy") to 10 ("way to hard"). This might provide the professor with the feedback she asks for in the lecture. How about that idea? '''Johannes 2009-11-15T20:40L''' | 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''' |
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To Florian + all: yes, sorry, I forgot to mention this in the lecture. Marjan already explained how to clear the disk cache. Let me add to this an explanation what the disk cache actually is. Whenever you read a (part of a) file from disk, the operating system of your computed will use whatever memory is currently unused to store that (part of the) file there. When you read it again and the (part of the) file hasn't changed and the memory used to store it has not been used otherwise in the meantime, than that data is read right from memory, which is much faster than reading it from disk. Usually that effect is desirable, because it speeds up things, but when you do experiments, it is undesirable, because it leads to unrealistically good running times, especially when carrying out an experiment many times in a row. '''Hannah 15Nov09 8:10pm''' | One Question: On slide 11 of lecture 10, shouldn't V be a kxn matrix instead of a nxk? '''Jonas 18.Jan10 20:39''' |
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To Florian: Indeed, we were running out of time and there was no room for this in the lecture. I can suggest to you few ways how to clear the disk cache: before carrying out your final experiment, read a large amount of data (let's say close to the amount of RAM you have) from disk - this will ensure that your data (the inverted list) is cleared from the disk cache and replaced by something else (thus an actual reading from disk get's timed, and not reading from RAM). Another way is to restart your computer before doing the timing. '''Marjan 15Nov09 7:27pm''' | 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''' |
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In exercise 4 it says: "Important note: Whenver you measure running times for reading data from disk, you have to clear the disk cache before, as discussed in the lecture". I think that this was not discussed in the lecture? What do we have to do here? '''Florian 15Nov09 7:15pm''' | 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''' |
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@Bit shifting: The syntax for that is actually the same, irrespectively of whether you use Java, C++, perl, python, or whatever. The >> operator shifts to the right, the << operator shifts to the left, the & operator ands the bits of the two operands and the | operator ors the bits of the two operands. Very simple. You will also find zillions of example programs on the web by typing something like ''java bit shifting'' into Google or whatever your favorite search engine is. '''Hannah 15Nov09 1:16''' | Oh yes, sorry, I forgot, it's done now. '''Hannah 17Jan10 13:43''' |
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Hi Marius + all: For Exercise 4, an inverted list of size m with doc ids from the range [1..n] is simply a sorted list of m numbers from the range [1..n]. I leave it to you, whether your lists potentially contain duplicates (as in 3, 5, 5, 8, 12, ...) or whether you generate them in a way that they don't contain duplicates (as in 3, 5, 8, 17, ...). It doesn't really matter for the exercise whether your list has duplicated or not. In any case, consider simple flat lists like in the two examples I gave (and like all the examples I gave in this and past lectures), not lists of lists or anything. '''Hannah 15Nov09 1:12am''' | '''Matthias''' - Can you please upload the Slides for the Lec 10 as well? |
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@Mirko: Sure, but an inverted list is a list of words where the Doc-IDs are attached to each words in which the words occur. So for Example: If word no. 5 occurs in Doc1, Doc2 and Doc3 and word no. 2 occurs in Doc5, the list would look like: 5 -> Doc1, Doc2, Doc3; 2 -> Doc5. Or am I mistaken? My question then is, how long should these attached lists be in average case? I mean, one could imagine that we got 1mil. documents over 3 words, so these lists could get very large... | 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''' |
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EDIT: Oh ok. Now, I see your point. It's not an index, it's a list. Okay. So, what is an inverted list with Doc-IDs, then? | {{{ (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. |
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EDIT EDIT: And to your question, Mirko, take a look at http://snippets.dzone.com/posts/show/93. Especially at Comment no. 2. Maybe this helps... I think, Java supports StreamWriters/Readers that are able to write/read bytes. '''Marius 11/14/2009 08:46pm''' | (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). |
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EDIT EDIT EDIT: Sorry, me again. Well, I bothered Wikipedia which redirects from http://en.wikipedia.org/wiki/Inverted_list to Inverted Index. So it seems to me, this is being used as a synonym. Actually, I think I'm confused enough, now. I'll better wait for any responses... ;-) '''Marius 11/14/2009 9:08 pm''' @ Marius: i think we are supposed to generate one inverted __list__ of size m, with doc ids from 1..n (therefore n>=m, because no duplicates?). Now a question from my side: ex.4, programming the compression in __java__, is there any __good__ tutorial about how to handle the bit-stuff? (otherwise, i think, it would cost me too much time..) '''Mirko 14Nov09, 19:18''' Hi, do you have any suggestions what the best numbers for m and n in exercise 4 should look like? Or are we supposed to mess around a bit with ints and longs? And: How long should the list of documents in the inverted index be? '''Marius 14Nov09 6:40pm''' And just to clarify what a single-cycle permutation is. Here is an example for an array of size 5 with a permutation that is a single cycle: 5 4 1 3 2. Why single cycle? Well, A[1] = 5, A[5] = 2, A[2] = 4, A[4] = 3, A[3] = 1. (My indices in this example are 1,...,5 and not 0,...,4.) Here is an example of a permutation with three cycles: 2 1 4 3 5. The first cycle is A[1] = 2, A[2] =1. The second cycle is A[3] = 4, A[4] = 3. The third cycle is A[5] = 5. '''Hannah 12Nov09 8:04pm''' Hi Daniel + all, I don't quite understand your question and your example (if your array is 1 5 3 4 2, why is A[1] = 3?). In case you refer to the requirement of the exercise that the permutation consists only of a single cycle. That is because your code should go over each element exactly once (it should, of course, stop after n iterations, where n is the size of the array). If your permutation has more than one cycle, it is hard to achieve that. Also note that for both (1) and (2), the sum of the array values should be sum_i=1,...,n i = n * (n+1) / 2. '''Hannah 12Nov09 7:54pm''' Hi, I just looked at the new exercise sheet 4, in exercise 1 we should generate a permutation and sum the resulting array up, am I wrong or doesn't iterating method two iterate throw the whole array in every situation. for ex.: n= 5 permutation: 1 5 3 4 2, then A[1] = 3, A[A[1]]= A[3] = 1, A[1] = 3 ... '''Daniel 12Nov09 19:44pm''' |
(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. }}} |
Welcome to the Wiki page of the course Search Engines, WS 2009 / 2010. Lecturer: Hannah Bast. Tutorials: Marjan Celikik. Course web page: click here.
Here are PDFs of the slides of the lectures so far: Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8, Lecture 9, Lecture 10.
Here are the recordings of the lectures so far (except Lecture 2, where we had problems with the microphone), LPD = Lecturnity recording: Recording Lecture 1 (LPD), Recording Lecture 3 (LPD), Recording Lecture 4 (LPD), Recording Lecture 5 (LPD without audio), Recording Lecture 6 (LPD), Recording Lecture 7 (AVI), Recording Lecture 8 (AVI), Recording Lecture 9 (AVI), Recording Lecture 10 (AVI).
Here are PDFs of the exercise sheets so far: Exercise Sheet 1, Exercise Sheet 2, Exercise Sheet 3, Exercise Sheet 4, Exercise Sheet 5, Exercise Sheet 6, Exercise Sheet 7, Exercise Sheet 8, Exercise Sheet 9, Exercise Sheet 10.
Here are your solutions and comments on the previous exercise sheets: Solutions and Comments 1, Solutions and Comments 2, Solutions and Comments 3, Solutions and Comments 4, Solutions and Comments 5, Solutions and Comments 6, Solutions and Comments 7, Solutions and Comments 8, 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 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 VLC.
Here are the rules for the exercises as explained in Lecture 2.
Here is everything about the mid-term exam.
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)
Thanks for the additional hint for exercise 2, I think I finally managed to get a solution with it. Then I have another question to exercise 4: is it enough if the program outputs the eigenvector or should it also give the corresponding maximal eigenvalue? Florian 20Jan10 18:25
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.