0:00:13 | okay |
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0:00:14 | this is gonna be |

0:00:15 | a short presentation |

0:00:16 | i problems |

0:00:18 | and the title of the talk is the general framework for a a choice D based indexing and retrieval with |

0:00:24 | a order data |

0:00:26 | it this is done with my |

0:00:27 | i a student should lee and formers to |

0:00:30 | and channel shown she who is now it to nokia research |

0:00:37 | and the |

0:00:38 | the goal is to do retrieval |

0:00:41 | and indexing indexing and retrieval |

0:00:44 | based on motion trajectory data |

0:00:46 | this is an an all problem people first begin to look at this |

0:00:50 | issue in the late nineties |

0:00:53 | and |

0:00:54 | a done a quite a bit of work |

0:00:56 | a most of the work centres round |

0:00:58 | yeah |

0:01:00 | doing it and using different modalities to reduce the dimensionality |

0:01:03 | we introduced in two thousand and three a method of doing it using pca |

0:01:08 | but then we wanted to extend it to working with |

0:01:11 | yeah have multiple trajectory simultaneously |

0:01:14 | and so we had to work in tensor space |

0:01:17 | and so we try to do something like pca intense or space |

0:01:20 | and we to the number of different techniques |

0:01:23 | a yeah |

0:01:24 | for |

0:01:24 | for tensor decomposition |

0:01:26 | based on |

0:01:27 | yeah |

0:01:28 | using higher order S D |

0:01:31 | and paris type model and another technique which we develop their cells |

0:01:35 | and the word various off |

0:01:37 | what we don't gonna focus on to they use the issue of how to deal |

0:01:41 | this |

0:01:41 | problem when you're dealing with tensor |

0:01:44 | but now of the query dimensionality does not mention |

0:01:47 | does not match the tense a dimensionality |

0:01:50 | meaning |

0:01:51 | you may have a different number of objects |

0:01:53 | a um |

0:01:54 | different like |

0:01:56 | or |

0:01:57 | in particular the case that we have here is different number of camp |

0:02:01 | so we actually are dealing with a different number of objects and different number of cameras |

0:02:05 | and the query we for example may have a single camera |

0:02:08 | and the database has multiple camera |

0:02:11 | and so the question is how can you do this the without having to we compute |

0:02:15 | a separate indexing for each scenario |

0:02:19 | and some than the talk a a a a little bit about |

0:02:21 | the invariance properties of the H of as U D |

0:02:25 | and how to apply to the indexing retrieval problem and present some experimental result |

0:02:31 | and so the basic scenario of using a a high order svd for indexing and retrieval |

0:02:37 | consist of |

0:02:38 | looking at multiple motion trajectory |

0:02:41 | and of from |

0:02:42 | yeah of multiple targets simultaneously |

0:02:45 | and then |

0:02:46 | i |

0:02:47 | having a compact representation in the form of a tensor as |

0:02:51 | and finally reducing the dimensionality and in this particular case but going to focus on a order is but |

0:02:58 | a more more properly people refer to it as tucker decomposition that would be a more accurate |

0:03:04 | in know processing that term |

0:03:06 | a choice of D of becoming brain |

0:03:08 | even though it's not use the terminology |

0:03:11 | uh they |

0:03:13 | origin of this is the following so if you look at a single |

0:03:17 | trajectory we can model it to say to L usually X and Y coordinates |

0:03:22 | of the trajectory over time |

0:03:24 | if we have two trajectories |

0:03:26 | we model it as a matrix |

0:03:28 | if |

0:03:28 | and we look at then i at the space of all of these |

0:03:31 | pair of trajectories |

0:03:33 | we get a tensor |

0:03:34 | a three dimensional array |

0:03:37 | and this is from what a single camera |

0:03:39 | if we now want to extend that for looking at multiple cameras in particular and this case two cameras |

0:03:45 | we have to three dimensional or rate or a four dimensional array |

0:03:49 | and so it forms a higher-order tensor |

0:03:52 | and you can continue this using multi modality you could like this |

0:03:55 | same trick for doing indexing and retrieval |

0:03:58 | yeah |

0:03:58 | for having different modalities |

0:04:01 | you can go higher dimension and higher dimension |

0:04:04 | no the reason we wanna work with a choice is with is because of the following theorem and what i |

0:04:09 | done the here is i've actually just the |

0:04:11 | loosely paraphrase |

0:04:13 | the the and words |

0:04:14 | that precise mathematical description of the theory |

0:04:17 | a paper |

0:04:18 | and about uh um |

0:04:19 | a page and a half of the paper |

0:04:21 | devoted to the proof of the theorem |

0:04:23 | but basically with the cr says is something which is quite into it |

0:04:27 | a we are all familiar with the for a transform |

0:04:31 | and if you have a multi the dimension of for a transform any now wanna take yeah the three dimensional |

0:04:36 | for transform that thing |

0:04:37 | and you now to take that two dimensional fourier transform only |

0:04:40 | it's sufficient to just simply look at the corresponding to the mentioned |

0:04:44 | they will have |

0:04:45 | the the you can just take the inverse with respect to the third one and will have the right |

0:04:49 | two dimensional fourier transform |

0:04:51 | and the reason for that is because of the orthogonality property |

0:04:54 | of the four yeah base |

0:04:56 | and the same thing is true a here |

0:04:58 | that is if i take a age of is he D and i decompose at it's decomposed into a tensor |

0:05:04 | and |

0:05:05 | in |

0:05:06 | unitary matrices |

0:05:07 | and so because of the a or orthogonality with the unitary property of those matrix |

0:05:12 | if find out think the scene it's sub tensor |

0:05:16 | so to get portion of the original tensor |

0:05:18 | and |

0:05:20 | i you can apply to a H of P D |

0:05:22 | i will get the same corresponding unitary matrices |

0:05:26 | for the dimensions of a in which i chosen for the subtensor tensor |

0:05:29 | and i do not need to calculate them again from scratch |

0:05:32 | which means of the corresponding indexing of the sub tensor |

0:05:35 | would be identical |

0:05:36 | a a of the same mold |

0:05:39 | or the same unit are a major |

0:05:41 | so if you want to precise mathematical description of what i just said and what's written here |

0:05:46 | it's in the paper and a proof of it is in the paper |

0:05:48 | and i should say one more thing this is uh a a result that was first |

0:05:52 | oh for three the mention tensor |

0:05:55 | yeah three order tensor |

0:05:57 | by that change how how as part of is a P D as at university of london |

0:06:02 | and what have done in this paper is |

0:06:03 | extended to our bit-rate dimension |

0:06:06 | the result |

0:06:06 | it |

0:06:07 | always true no matter what dimension |

0:06:10 | but it is a critically important thing for us because if we were to work with a different type of |

0:06:14 | decomposition |

0:06:15 | like paris |

0:06:16 | or parallel factor analysis |

0:06:18 | or can a call or any of the other one |

0:06:21 | a property fail |

0:06:23 | and we would be unable to do anything that we're doing in this paper |

0:06:26 | because you would have |

0:06:27 | to we compute everything from scratch for each such that |

0:06:32 | and so that that we have this property we can proceed along the lines of the original work that we |

0:06:38 | did for tensor decomposition |

0:06:39 | X this time we do it a lot a sub tensor is only |

0:06:43 | so the indexing part |

0:06:45 | and proceeds along the very same lines we have a H of ways P the we compute for the tensor |

0:06:50 | in this case the four dimensional tensor |

0:06:53 | and |

0:06:54 | a with take the mode |

0:06:56 | of the query |

0:06:58 | and do it |

0:06:59 | similar decomposition but this time we do it only along |

0:07:03 | the M |

0:07:04 | a modes if we choose |

0:07:06 | and then yeah are we |

0:07:09 | slice |

0:07:10 | and a T have |

0:07:11 | in index set tensor as |

0:07:14 | and with the number of index tensor is is computed |

0:07:16 | a the following |

0:07:18 | for |

0:07:21 | and for the retrieval procedure we simply |

0:07:24 | and a compare the query index |

0:07:27 | and yeah |

0:07:28 | to the to the query tensor that we that we have obtained before |

0:07:32 | and then a just simply do a frobenius norm between the two |

0:07:36 | so the algorithm to be compute |

0:07:38 | is essentially the same |

0:07:40 | as we presented a uh several years back |

0:07:43 | on |

0:07:43 | tensor |

0:07:44 | base |

0:07:45 | a a comparison for indexing and retrieval of motion trajectory |

0:07:49 | the main difference between this work and uh uh and our previous |

0:07:53 | is in our previous work it was generic didn't care what |

0:07:56 | tensor decomposition channel |

0:07:59 | and it applied it on the same |

0:08:01 | a dimensionality of then sir for the query |

0:08:03 | and for the data |

0:08:04 | and that's a |

0:08:05 | a strong assumption |

0:08:07 | yeah because we we have no control over the query size |

0:08:10 | and this is especially true when you're dealing with multiple cameras |

0:08:13 | and multiple camera tensor |

0:08:15 | a queries |

0:08:16 | because |

0:08:17 | not all cameras have access to the same trajectory simultaneously |

0:08:21 | and so of the main difference here is that we are only looking at the substance or |

0:08:25 | for which they gave available |

0:08:27 | and then |

0:08:28 | comparing compare and then |

0:08:29 | obtaining the corresponding a uh |

0:08:32 | query representation from our original in |

0:08:36 | which is index over all possible modality |

0:08:40 | and so here the uh experimental results for work |

0:08:44 | and uh these are collection of |

0:08:47 | tensor is of a from the caviar datasets from in |

0:08:52 | and |

0:08:53 | these are from two cameras sets |

0:08:56 | and this is the uh precision-recall recall curve |

0:08:58 | corresponding and this is for complete queries |

0:09:02 | and |

0:09:03 | the |

0:09:06 | resulting yeah uh these that the in matrix sizes |

0:09:10 | and here are are are the indexing time and retrieval time |

0:09:13 | and i should say that the uh |

0:09:16 | indexing time is |

0:09:17 | for a choice of be D are traditionally very good |

0:09:20 | and where they suffer is a which remote time |

0:09:22 | we do not |

0:09:23 | remedy this |

0:09:24 | and yeah |

0:09:25 | we |

0:09:27 | the of five well perform the retrieval times here |

0:09:30 | and what we have to say is that we have to pay this price |

0:09:33 | if we want to have the flexibility |

0:09:35 | of dealing with different yeah size subtensor as |

0:09:38 | in the query and a database |

0:09:43 | and |

0:09:43 | here we do the same thing but for partial queries |

0:09:48 | so they query and the data size are not same size |

0:09:52 | and these are the corresponding precision recall curve |

0:10:03 | so |

0:10:04 | short |

0:10:05 | our our am am main |

0:10:07 | messages |

0:10:08 | a shows with D or type decomposition |

0:10:11 | because of its sort the orthogonality |

0:10:13 | is particularly useful in applications where |

0:10:16 | you |

0:10:17 | do not know in advance |

0:10:19 | what are the dimensionality is and you need to make |

0:10:21 | a mix and match it during query time |

0:10:24 | and so we have applied this general principle in our case to motion trajectories |

0:10:28 | but it can be applied to any higher order data |

0:10:31 | an analysis with the retrieval or not |

0:10:34 | and show that it actually yeah |

0:10:36 | the |

0:10:37 | very well |

0:10:40 | thank you very much |