Přepis řeči - NOVEL HIERARCHICAL ALS ALGORITHM FOR NONNEGATIVE TENSOR FACTORIZATION

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

NOVEL HIERARCHICAL ALS ALGORITHM FOR NONNEGATIVE TENSOR FACTORIZATION

Non-negative Tensor Factorization and Blind Separation

Přednášející: Anh-Huy Phan, Autoři: Anh-Huy Phan, Andrzej Cichocki, Brain Science Institue, Japan; Kiyotoshi Matsuoka, Kyushu University of Technology, Japan; Jianting Cao, Brain Science Institue, Japan