0:00:13 okay this is gonna be a short presentation i problems and the title of the talk is the general framework for a a choice D based indexing and retrieval with a order data it this is done with my i a student should lee and formers to and channel shown she who is now it to nokia research and the the goal is to do retrieval and indexing indexing and retrieval based on motion trajectory data this is an an all problem people first begin to look at this issue in the late nineties and a done a quite a bit of work a most of the work centres round yeah doing it and using different modalities to reduce the dimensionality we introduced in two thousand and three a method of doing it using pca but then we wanted to extend it to working with yeah have multiple trajectory simultaneously and so we had to work in tensor space and so we try to do something like pca intense or space and we to the number of different techniques a yeah for for tensor decomposition based on yeah using higher order S D and paris type model and another technique which we develop their cells and the word various off what we don't gonna focus on to they use the issue of how to deal this problem when you're dealing with tensor but now of the query dimensionality does not mention does not match the tense a dimensionality meaning you may have a different number of objects a um different like or in particular the case that we have here is different number of camp so we actually are dealing with a different number of objects and different number of cameras and the query we for example may have a single camera and the database has multiple camera and so the question is how can you do this the without having to we compute a separate indexing for each scenario and some than the talk a a a a little bit about the invariance properties of the H of as U D and how to apply to the indexing retrieval problem and present some experimental result and so the basic scenario of using a a high order svd for indexing and retrieval consist of looking at multiple motion trajectory and of from yeah of multiple targets simultaneously and then i having a compact representation in the form of a tensor as and finally reducing the dimensionality and in this particular case but going to focus on a order is but a more more properly people refer to it as tucker decomposition that would be a more accurate in know processing that term a choice of D of becoming brain even though it's not use the terminology uh they origin of this is the following so if you look at a single trajectory we can model it to say to L usually X and Y coordinates of the trajectory over time if we have two trajectories we model it as a matrix if and we look at then i at the space of all of these pair of trajectories we get a tensor a three dimensional array and this is from what a single camera if we now want to extend that for looking at multiple cameras in particular and this case two cameras we have to three dimensional or rate or a four dimensional array and so it forms a higher-order tensor and you can continue this using multi modality you could like this same trick for doing indexing and retrieval yeah for having different modalities you can go higher dimension and higher dimension no the reason we wanna work with a choice is with is because of the following theorem and what i done the here is i've actually just the loosely paraphrase the the and words that precise mathematical description of the theory a paper and about uh um a page and a half of the paper devoted to the proof of the theorem but basically with the cr says is something which is quite into it a we are all familiar with the for a transform and if you have a multi the dimension of for a transform any now wanna take yeah the three dimensional for transform that thing and you now to take that two dimensional fourier transform only it's sufficient to just simply look at the corresponding to the mentioned they will have the the you can just take the inverse with respect to the third one and will have the right two dimensional fourier transform and the reason for that is because of the orthogonality property of the four yeah base and the same thing is true a here that is if i take a age of is he D and i decompose at it's decomposed into a tensor and in unitary matrices and so because of the a or orthogonality with the unitary property of those matrix if find out think the scene it's sub tensor so to get portion of the original tensor and i you can apply to a H of P D i will get the same corresponding unitary matrices for the dimensions of a in which i chosen for the subtensor tensor and i do not need to calculate them again from scratch which means of the corresponding indexing of the sub tensor would be identical a a of the same mold or the same unit are a major so if you want to precise mathematical description of what i just said and what's written here it's in the paper and a proof of it is in the paper and i should say one more thing this is uh a a result that was first oh for three the mention tensor yeah three order tensor by that change how how as part of is a P D as at university of london and what have done in this paper is extended to our bit-rate dimension the result it always true no matter what dimension but it is a critically important thing for us because if we were to work with a different type of decomposition like paris or parallel factor analysis or can a call or any of the other one a property fail and we would be unable to do anything that we're doing in this paper because you would have to we compute everything from scratch for each such that and so that that we have this property we can proceed along the lines of the original work that we did for tensor decomposition X this time we do it a lot a sub tensor is only so the indexing part and proceeds along the very same lines we have a H of ways P the we compute for the tensor in this case the four dimensional tensor and a with take the mode of the query and do it similar decomposition but this time we do it only along the M a modes if we choose and then yeah are we slice and a T have in index set tensor as and with the number of index tensor is is computed a the following for and for the retrieval procedure we simply and a compare the query index and yeah to the to the query tensor that we that we have obtained before and then a just simply do a frobenius norm between the two so the algorithm to be compute is essentially the same as we presented a uh several years back on tensor base a a comparison for indexing and retrieval of motion trajectory the main difference between this work and uh uh and our previous is in our previous work it was generic didn't care what tensor decomposition channel and it applied it on the same a dimensionality of then sir for the query and for the data and that's a a strong assumption yeah because we we have no control over the query size and this is especially true when you're dealing with multiple cameras and multiple camera tensor a queries because not all cameras have access to the same trajectory simultaneously and so of the main difference here is that we are only looking at the substance or for which they gave available and then comparing compare and then obtaining the corresponding a uh query representation from our original in which is index over all possible modality and so here the uh experimental results for work and uh these are collection of tensor is of a from the caviar datasets from in and these are from two cameras sets and this is the uh precision-recall recall curve corresponding and this is for complete queries and the resulting yeah uh these that the in matrix sizes and here are are are the indexing time and retrieval time and i should say that the uh indexing time is for a choice of be D are traditionally very good and where they suffer is a which remote time we do not remedy this and yeah we the of five well perform the retrieval times here and what we have to say is that we have to pay this price if we want to have the flexibility of dealing with different yeah size subtensor as in the query and a database and here we do the same thing but for partial queries so they query and the data size are not same size and these are the corresponding precision recall curve so short our our am am main messages a shows with D or type decomposition because of its sort the orthogonality is particularly useful in applications where you do not know in advance what are the dimensionality is and you need to make a mix and match it during query time and so we have applied this general principle in our case to motion trajectories but it can be applied to any higher order data an analysis with the retrieval or not and show that it actually yeah the very well thank you very much