0:00:13a to now three money and
0:00:15it it can um
0:00:16you don't will have and
0:00:18uh_huh and silky key for so you know Q to assume karen's and come from japan
0:00:24and in in just present a and we will present the new the or boring with some four
0:00:29don't think it detection for two days and that you know that
0:00:31nick details of several is it didn't it
0:00:34is that the the ten send up to matters
0:00:37from thirty and you indicate that you have
0:00:39you have
0:00:40is ten so is not only um
0:00:43a two dimension
0:00:44um at least two maybe
0:00:46i two dimensions
0:00:50do would problem uh the the than the friend is about how well i with only that we we we
0:00:55we bold and with tom was this
0:00:57the and with them the cater
0:00:58but this
0:00:59a big three number of component
0:01:01it's that a a back on the common
0:01:03on in them first what in them
0:01:05that you less and the and uh the a thing with them well
0:01:09a best only one component in the uh huh uh he that's going last
0:01:12and what but what i went don't that to to to do to to dry but there are with them
0:01:21can a bit a bit number of component
0:01:23we we assume like uh we will present the
0:01:26this a we coding it is that
0:01:28and you we see that for coding it that
0:01:31more thank with them can can of
0:01:33fit the data L
0:01:34and we will as well
0:01:36in yeah present here the application
0:01:38with a easy data
0:01:40the real were application
0:01:43so just see here
0:01:44what is it ten so that so it's is that the moon to way and the
0:01:49a the F is this special case of them
0:01:51canonical polyadic is to compose and when we call
0:01:54we so on this one these the uh a five
0:01:58in the model it like this we have to so and we want to to compile ways to for symbol
0:02:02if just your time your data have that freedom are
0:02:05three dimensions
0:02:06and then we want to find three fact
0:02:10for the one and on the first dimension of the tool of but that's for the tree so on
0:02:14and the call that's a here
0:02:15is them
0:02:17you you have a very uh a special case but very special should die that's only
0:02:21that kernel that were not uh
0:02:24uh the and and only a on the diagonal of ten so
0:02:29so you see is it's worse than a in the mood the linear
0:02:31oh form
0:02:35and you know two is a at rate the our motivation we we you is here the first very simple
0:02:41it's sample
0:02:42assume that you have a ten so with side of one can dress by one can write my one hundred
0:02:47and a and just a so is composed by three from the value C yeah
0:02:52three dimensional so
0:02:53and one from a to have three
0:02:56and no one thought the have
0:02:59sparse common and
0:03:00and we we for the common to be called you we a not my symbol
0:03:04but simple modification like this
0:03:07you see uh
0:03:07the come of a symbol here if it um
0:03:10i go to you have a common and
0:03:12the come the second come
0:03:14by the first come plus the second and and with the scary is zero point five
0:03:19and if we use the less and with um
0:03:22the i less camp them can find a a a a way
0:03:24to not
0:03:25one to plop by and this and then pro
0:03:28proof was in two thousand
0:03:29to tell them
0:03:30and it cannot fit this like up we call it um
0:03:33you see here
0:03:34up the fruit ways and um
0:03:37a a there and the right the C
0:03:39in did not improve anymore
0:03:40even if we have here
0:03:44uh no five power than uh
0:03:47but are and i uh in interest
0:03:49and ask we
0:03:50which at
0:03:51this they that we are not able and a bit on this you see here the monte look at this
0:03:54and with some ball by so
0:03:57okay this i was is only fall for for and a map
0:04:00and has done in to tell than five
0:04:03he's ten this and an to uh and a no
0:04:07to at the for three dimensional
0:04:09symmetric and so
0:04:11and more of in two thousand six
0:04:13he also able
0:04:14it's then the multi this and we some bus
0:04:16with two
0:04:18to kind of and was some we have uh
0:04:20the multi cut the least square and with some i'm want to claremont moaned deeply is
0:04:25camilla but
0:04:26and we so
0:04:27and we chess here these want to plot this i L S
0:04:31this square and the in
0:04:32and this can okay is better that uh uh a less it with them but is still
0:04:37cannot be the
0:04:38the solution i decide yes
0:04:41you he use easy G "'em" ten minus five
0:04:44and the here at go and with them
0:04:46in a point to it out to two thousand nine
0:04:49it better but this to
0:04:51this this to and up that five one than five hundred and in into a recent
0:04:55and we paul than
0:04:57one and was a bit of the ten
0:04:59is but uh and is good up to five hundred into
0:05:05the when the this event that of the the clear less and was an that this D very similar to
0:05:11is a on the a less and some that's mean
0:05:13in me that this and with some
0:05:15to to a that the the fact that
0:05:17need to inverse of very last scale matters
0:05:19if you have a high dimensional so
0:05:21and you have high come and
0:05:23you have you have
0:05:24in the the number of common in this last
0:05:28you have to go out with them
0:05:31but on the that
0:05:32the idea but the the have go like with the with that you best only one component
0:05:36at it it's race and sell this at the hair the to go with them
0:05:40have a come that's in the cost but it
0:05:42it men
0:05:43a lot of
0:05:44the both trace and
0:05:45the clearly a the clear less and was a list
0:05:49but but up uh with free to a it's way and but is to have
0:05:53a hack "'em" with this in a cost
0:05:55and the and i was
0:05:56but what um
0:05:58well well that's
0:05:59but uh we propose a and with them that's have some
0:06:02in the in this reason that's
0:06:04the at the new and with a suit
0:06:07but that then the here that's going with them
0:06:10list can with this in cost than that yeah you're like a resume
0:06:14this is the new
0:06:15this our motivation
0:06:17and of of we don't we also have a here the whole one it was on for some the P
0:06:20M F three and so
0:06:22and we some but by but the row and that that doesn't
0:06:25no uh
0:06:26no but it that T seven and the but see if to get a
0:06:29okay again to it's is
0:06:31um but uh to F P and to but now screen
0:06:34we best in two thousand than a to of than ten in nice gas
0:06:39and we we we'd
0:06:42we don't
0:06:43present all of this and with them
0:06:45it's could be that the second
0:06:48or is that a sum
0:06:49so we see here
0:06:51well in a in order to derive a new entry time we consider again the
0:06:56problem the nonnegative
0:06:58the nonacoustic a trip this programming
0:07:01it's like this we will abide is fun so
0:07:04uh with three D the
0:07:06it's square matrix a policy nonnegative symmetric
0:07:09as i was to different methods and be the best that with item one
0:07:13and we propose the the recursive approach to solve this problem
0:07:18first what it uh we have
0:07:20it at this step one we compute that's
0:07:22solution of this
0:07:23but this gradient
0:07:24so it on the element of this vector is
0:07:29so this orders distill it at you know we'll be the solution of this but
0:07:34oh difference and
0:07:36usually it's it could be like this we
0:07:38that's this they have some
0:07:40the estimated date
0:07:43element in this vector and we we have to
0:07:45two set
0:07:46one is
0:07:47i i by
0:07:48with the in des up normally it like
0:07:51and they negative
0:07:52uh as due da
0:07:54a to
0:07:55and this it uh this this as a
0:07:58a well up but an only uh this this these negative and this see it says nonnegative
0:08:05we on
0:08:07and not a a small problem that's model uh i P be problem with a a what
0:08:12by a a K and K way it
0:08:15where K the number of active
0:08:17and one here
0:08:18and was on this one
0:08:19in the read seas
0:08:21a pro
0:08:22the egg with them like this
0:08:23you see yeah
0:08:24a compute the solution and then five
0:08:28a remove
0:08:29give only the
0:08:30you only the non at
0:08:33am and and then on again
0:08:34so on
0:08:35this re would be the will bit this real and to yeah
0:08:39this that i M T
0:08:43so you see here
0:08:44that the eye or less and the clear less of that on the component
0:08:48the here at school i are let the that the two that only one component
0:08:51and we're new act we will be the new it with them in this
0:08:54the and we dedicate possible we that they K come
0:08:58and we assume that
0:09:01and the
0:09:03yes i and i and these it
0:09:05it the fact that and but with
0:09:08"'kay" come and
0:09:09to be estimated
0:09:11and we
0:09:12so the the the the C P i got easy the and F model into two points
0:09:18one these that the um
0:09:20one part composed Y
0:09:22by like come around but it not
0:09:24in this test
0:09:26and then not about it does
0:09:27compose Y
0:09:29a component
0:09:30like this
0:09:32and we define the the to do or
0:09:34but that's a the the used as a
0:09:36it you see here the dress you that's so is
0:09:38we we
0:09:40planned and pressed by
0:09:42and and T a model
0:09:44an net of model but with a low
0:09:47come than is only take a component
0:09:49is that a
0:09:50is is only K can is that a a common
0:09:53so you see here and we
0:09:56from the cost function fall
0:09:57for these ten so we uh we we see here
0:10:00with we want to spend the conference
0:10:03and we will we convert this cost person to
0:10:08to this
0:10:09to this
0:10:09to just fall
0:10:11to this song what we do
0:10:13okay you C
0:10:16so if it better why the vector i best the
0:10:18but but the we if you better why the fact that i i and
0:10:22i and R
0:10:24uh a when we've press and we can from but this but for sent to this fall
0:10:29this the and be form and then we can use the egg be
0:10:32the because see a problem
0:10:34we at i as and
0:10:35oh at to just on this problem
0:10:37and and with them like this
0:10:42oh okay
0:10:43oh sorry
0:10:44the that's that be like this
0:10:47but the but to be here you see the vet to be here
0:10:49is is uh by on
0:10:52rest of you ten so
0:10:54multiplied with
0:10:55a cocker our products of on the animal
0:10:57a on the fact that it's set the fact and
0:11:00and it's K we for the paul high dimensional a so we need to be love
0:11:04this takes so
0:11:05and it could demand high and with a an that file
0:11:07and the one we we we one he that's we
0:11:10we don't want to to be a to time so
0:11:12we don't want to be the rest you ten so
0:11:17and how to how to remove this
0:11:19we spread that the feedback vector
0:11:20the fire stress
0:11:24the if you
0:11:25we the different nice enough
0:11:27the was you ten
0:11:28and we we had
0:11:29uh if
0:11:31the is present for the fire matters here
0:11:34C you raw data
0:11:35and this i
0:11:37this it the
0:11:39i agree is bounded location here
0:11:41but for here
0:11:42use the case and these uh
0:11:44do not the high how to mark broader and this
0:11:47you know the card to dot product is step
0:11:49all four on the fact that it's of the father and
0:11:52and this also
0:11:54on this you how to mark
0:11:55or or fall on the fact that but is that the from and
0:11:58so you have a is present fall
0:12:00it decide for first and for the for a part of a that
0:12:04five matches
0:12:06and a
0:12:07and that we play
0:12:11and i could be a problem for
0:12:13and we from a with a place that there the with some four
0:12:16to press
0:12:18uh i
0:12:18"'kay" can it is that the on component
0:12:22and you see here
0:12:23but it's it's rice sent to look at the that and we select
0:12:27that's of says
0:12:28from a component
0:12:29and then compute like to
0:12:31yeah my two
0:12:33oh U
0:12:37free fine here and then we hope that the fact the
0:12:41i and a
0:12:42you in the
0:12:44and can and
0:12:46and and do this
0:12:47and to the
0:12:48will be replicate into a common would be okay that is
0:12:56okay i will explain
0:12:59and the egg with them these
0:13:00in this okay if the right within five
0:13:04would be to um
0:13:05problem for the problem of that for the the and with them alive live it becomes easier
0:13:10the uh this the the identity matrix with I
0:13:13uh i think and
0:13:16the uh going to control of the the this and then they met with with the amount
0:13:21with this garment maker
0:13:22and the size of this
0:13:24this product with that though
0:13:26and by
0:13:28by well i se and by a
0:13:31and no i by by K
0:13:33and then in it K of
0:13:35this i and he's ready last are
0:13:37this in also very locked the you C
0:13:39the problem is
0:13:41uh the problem that is points and
0:13:43this step maybe
0:13:45you might high can be and the problem i
0:13:47we want to
0:13:47you do this
0:13:48this that
0:13:50how to do this
0:13:52we define this one
0:13:54is that little back on that
0:13:56on the role we back only one row by row
0:13:59and established
0:14:03the top with new the new and before i three problem paul
0:14:07one role
0:14:08for one rows
0:14:09in this case you have
0:14:12a silly a fast
0:14:14he's only four gram uh and easy four
0:14:16is the only for gamma we we already removed that acted out border no cortical product
0:14:22oh wow identity matrix
0:14:23a sigh i
0:14:25i se and
0:14:26active and here
0:14:30and the nice nest i next next i we will present how to to
0:14:34"'kay" command from its of set up
0:14:36a common
0:14:39normally we we would that
0:14:41we than there
0:14:42normally you see here
0:14:43the this real we we have that and do you on the common
0:14:48like this
0:14:50this can be certified
0:14:52the and
0:14:54the number
0:14:55the number of them
0:14:56the number of i you numbers of the case is that you
0:15:00the number of combination
0:15:04"'kay" we taken from that
0:15:06a set of site
0:15:07so i i
0:15:08false and if you have take "'em" and and you best only to common
0:15:12it just K you have
0:15:13mm forty five
0:15:16yes just used
0:15:21a D oh okay K you we have to us another give high up a bit of i know guy
0:15:26of so that's less than like this we divide that says i'll from one to octave in
0:15:31into a into to separate into
0:15:33it is the fact but
0:15:35this is that it's to be
0:15:36a a normal less all i'll L a possible
0:15:41and and and of the K and not a a a to that we
0:15:44we select
0:15:45"'kay" highly colour already
0:15:47correlated component
0:15:48from a component
0:15:50from a common or
0:15:51we can see a
0:15:52we have many guys select
0:15:54a but a and
0:15:56"'kay" K K E
0:15:57come on from a common a
0:16:00we to here for
0:16:01a coding data
0:16:03and it would be you
0:16:05the fine fine ten so a to so ten so
0:16:07with side one hundred fall
0:16:09for every four on the dimension
0:16:11and the what on it
0:16:13if we have here ten component
0:16:15i don't we also for to the common to be calling yeah
0:16:18and here you see
0:16:19uh the
0:16:20what deep look at effect of them is not
0:16:24in of fit the data of or what
0:16:25you the also
0:16:27problem for the a less
0:16:29here here you have to a
0:16:31you have here the the
0:16:33here here the your with them
0:16:35and here these the
0:16:37with K
0:16:38is weak a four we have this for this can wasn't
0:16:41and we we K seven we have
0:16:45and we K ten we had this line
0:16:47and the clear less we have
0:16:50this i
0:16:52so you using we will put pop here and with them
0:16:56but that then the are you less
0:16:58but are better than the to go ahead with "'em" of got better than the light and them
0:17:02uh sometime time is also but than than the pls and and we some
0:17:07easy to a bit own application for easy day that i we take can they that from
0:17:12uh from a of
0:17:13from the two not from model
0:17:15and he the the data i like this you you
0:17:18the data
0:17:19it you you you recall of from
0:17:21when you put on you audio how your hands
0:17:24a a yeah or right hand or left hand then you accommodate that
0:17:28and more of a can be the uh
0:17:30in that's in that of fate go
0:17:32the that they could and
0:17:34from forty it's of less and we have to task for left and right
0:17:38for left and right hand
0:17:40and you have to thirty T for channel
0:17:42can we have D for yeah sin for channel
0:17:45so T type time frame rate T one frequency bin from the to estimate the hot
0:17:50and here we had twenty four
0:17:51eight mister one
0:17:53jen before we have we have fourteen subjects
0:17:56and two task
0:17:57and we we want to five
0:17:59for the dominant for this data
0:18:01you see here
0:18:03because this late that have really needed
0:18:05spectral and temporal component
0:18:08using it
0:18:09we you
0:18:10our algorithm weekly
0:18:12this is not hand
0:18:14it uh
0:18:16we here
0:18:17and we
0:18:18with K by
0:18:20week at yeah you go to a three
0:18:23we see here
0:18:26we see here the to and in the spectrogram and to common and in them
0:18:31for a common of sex two gram and for common in this uh and the temporal program
0:18:35uh in in and
0:18:36not did D spectral and and is a temporal come and you see
0:18:39calling it because is very similar
0:18:42yes and we
0:18:44we already ready i is that lead the component
0:18:48this for a is at the get the yeah man "'em" and is a be that we don't
0:18:52i for the query less about the query less the also what for the data
0:18:56but you see the for the multi the F
0:18:59K L can of well for this they now be go
0:19:02the we we can see though clean near common an here
0:19:06a no so for the the same
0:19:08problem for them one look at this
0:19:12come and that this
0:19:13here is not
0:19:15it's red
0:19:16well the um
0:19:18the coding a common and
0:19:20and the the the data
0:19:22and i L S the so
0:19:25and the next that we close the
0:19:28the easy this at six no from
0:19:30by on the feature we attracted
0:19:33by and F
0:19:34and the and light we see here it we
0:19:38with the multi that the
0:19:39K K with the multi that if L west
0:19:42it's only seventy five also so eighties
0:19:46at this a i not seventy five here
0:19:49and to what the i he's of yeah and with our you of the we we have ten I
0:19:53to but i ninety two or ninety three
0:19:57sending about greasy
0:20:04we conclude this uh present a we already propose is then
0:20:08the new the new and with some of that
0:20:10uh a between them oh component
0:20:12but you on the it could be a problem
0:20:14and we so
0:20:16it's ten this and want to of this row by row
0:20:19and we were well here some set so on
0:20:22so approximate or to select the number of common and to be attracted to be a that
0:20:27thank you