Speech Transcript - REGULARIZED GRADIENT ALGORITHM FOR NON-NEGATIVE INDEPENDENT COMPONENT ANALYSIS

0:00:14	good morning everybody
0:00:17	i'm going to talk about regularized a the an algorithm for nonnegative independent component and
0:00:23	this C a general use
0:00:25	it made J then
0:00:27	and to sort of the arc and playstation then
0:00:31	my don't is divided in no
0:00:33	five part
0:00:35	i mean
0:00:35	first we we can be a a record but the
0:00:39	that's is to partition problem
0:00:40	and then right the nonnegative independent component analysis
0:00:44	after that i we describe the proposed a
0:00:46	exactly be the eyes like an algorithm for nonnegative independent component analysis
0:00:53	i we some simulation result before concluding
0:00:59	so
0:01:00	a a as we were that we we have uh
0:01:02	and mix
0:01:03	and
0:01:03	and motivation
0:01:05	of four
0:01:06	and sources
0:01:08	that a mixed by a matrix of a kind it uh
0:01:12	and the blind separation problem is to estimate do hide and sources and the mixing batteries
0:01:18	given given only the observation
0:01:21	some of recreation we walk on use for example
0:01:24	a
0:01:24	dynamic
0:01:25	a a point you an emission tomography
0:01:28	in these of question we have a
0:01:30	similar
0:01:31	a a construct it is the image
0:01:34	of the same hot again
0:01:36	and we we tried to estimate
0:01:38	the farm up in at the compartment
0:01:41	a a from the is uh from the image
0:01:44	in that application we or one is a a a a a a a it can mark to graph you
0:01:48	mass spectrum at three
0:01:49	we have
0:01:50	similar in my spectral
0:01:52	of the
0:01:53	same
0:01:54	a a a a a a a a solution
0:01:57	and we tried to identify the different more you that are composed
0:02:01	this distribution
0:02:03	oh these two application and in many or of application a source
0:02:07	the source is a nonnegative
0:02:09	so
0:02:10	this non negativity must be considered
0:02:12	when performing this separation
0:02:15	one way to detect
0:02:17	to take into account the the negativity easy do
0:02:21	that if independent component analysis
0:02:27	so
0:02:28	a is
0:02:29	i method
0:02:30	we have some
0:02:32	i i'd being it down classical a independent component and a like this
0:02:37	so you know the source it's uh as you need to be a a non-negative
0:02:42	independent
0:02:43	and when you that
0:02:45	and under this assumption
0:02:48	it is shown that this source can be actually estimate
0:02:52	by
0:02:53	firstly whitening the observation
0:02:55	for a about by rotating the right in that that to like them with the D
0:03:02	so the the right moves but
0:03:04	and and uh he
0:03:06	that
0:03:07	for example we can make a single but with the composition and all of the vision
0:03:12	and a do light a whitening metrics
0:03:15	but don't know the things that can be quite a more difficult
0:03:20	a so to to do so probably propose a creature on
0:03:24	that they should do do new that even nice of the output
0:03:29	and the problem because out
0:03:30	looking for the rotation
0:03:32	that we my a discrete and J D
0:03:36	so
0:03:37	i
0:03:38	do is a optimization is quite difficult to
0:03:42	to to that but glad than that me because
0:03:45	we have a
0:03:46	two
0:03:46	to to take or to take a four oh for maintaining
0:03:51	do the do you do it that when the metrics
0:03:54	and the rotation set
0:03:56	and we have to compute also the gradient
0:04:00	we one
0:04:03	so um
0:04:04	and have to a proposed that but that
0:04:09	i a way for keeping the orthogonality constraint is
0:04:12	having a penalty to
0:04:14	a a J orthogonal gonna
0:04:15	that in a with the deviation to a of gravity
0:04:19	and
0:04:20	we we can
0:04:21	we we we can are then
0:04:24	it from the coast to of addition to and in the bright
0:04:28	but
0:04:29	well i to the first that the first so that of the the and day
0:04:35	one mean not that it's content the disk you must function C
0:04:39	that
0:04:39	a the that the a T V two
0:04:42	that the that distribution
0:04:44	which i in italian you looking at it in of a method
0:04:48	and you just have to this
0:04:51	a
0:04:51	expression of the gradient
0:04:53	to overcome this problem
0:04:55	we propose a
0:04:56	to uh the press the of function
0:04:59	do the discontinuous will function by a control as well touch people you
0:05:04	oh one tension
0:05:05	well if
0:05:06	labs of the
0:05:08	a level that control
0:05:10	the accuracy also be of the C function approximation
0:05:13	do so used to them that the be to the approximation
0:05:18	so
0:05:19	we then introduce two
0:05:21	but it could to the J uh
0:05:23	which may to do
0:05:25	the approximate
0:05:27	you you could tell them
0:05:28	that that's to it from some them that and
0:05:31	the we have applied addition
0:05:36	also so we can
0:05:37	a do have a at
0:05:40	a question
0:05:42	a given by a
0:05:43	a a a a a a a a question
0:05:45	and do do the club and and be computer
0:05:49	a
0:05:51	and
0:05:53	you you leaving the um but not than the person in question can the computer
0:05:58	well for me to
0:06:00	but
0:06:01	the i the that anything about that
0:06:03	because
0:06:04	it is do i from the approximation
0:06:07	and then we show what is important
0:06:12	well i i'm i'm a a a good an expression computed from J T
0:06:16	and can are computed from
0:06:19	J number
0:06:20	one of note that
0:06:21	due to expansion differ from
0:06:24	beta
0:06:25	so
0:06:26	and one the people to but that becomes good
0:06:30	well will not come up to
0:06:33	for a a small value of you got
0:06:35	but
0:06:36	this value a i've i've mode
0:06:39	well conversion
0:06:40	so it is important to take a
0:06:43	the
0:06:44	all
0:06:45	a
0:06:46	you listen to the approximation
0:06:50	so
0:06:51	i move two
0:06:52	simulation result
0:06:57	for the relation a we use a synthetic source
0:07:01	the source is uh generated we've
0:07:03	special uniformly distributed and a matrix
0:07:06	a S
0:07:07	and we had a parameter
0:07:09	which can to
0:07:11	the sparsity of the source
0:07:14	so the parameter that a a a controlled the nonzero elements
0:07:18	in the source is metric
0:07:21	and the not the matrix a a a a a a a generic it using a a a a normal
0:07:26	is distributed and them and the marked metrics
0:07:29	a
0:07:31	for the for most measure and is
0:07:33	for all
0:07:34	a
0:07:35	the thing to do
0:07:37	the performance of the it
0:07:39	the one use
0:07:41	the cost function the we which you the content a will will look to minimize
0:07:46	the second one is in non blind there from us and a and X
0:07:50	which
0:07:50	a and the quality of this to partition
0:07:53	and the first create a turkey data and is the C P you time to converse
0:08:03	i we got a
0:08:04	we compare the them we also we have
0:08:07	of "'em" at that that that are already put point it for nonnegative independent component and i like this
0:08:12	the first one is the you did six a estimate of reported by probably
0:08:17	using a could turn and G P
0:08:19	this may
0:08:20	the the data to the retention to a in as the exponential of excuse semantic method
0:08:29	and the second method that is
0:08:31	the to spare method
0:08:33	and
0:08:34	this not well or also on the T and E use method
0:08:38	the attention is parameterized by a given as
0:08:41	rotation
0:08:43	the fact that are
0:08:45	we compared to use of the project
0:08:47	but then method
0:08:49	well can also and E P
0:08:51	it
0:08:51	do that are are on
0:08:53	i chance that
0:08:54	the first
0:08:55	that you to come to do collect then
0:08:57	and the second that is
0:08:59	two
0:08:59	we we
0:09:00	project do do you obtain but takes
0:09:03	on or set
0:09:06	the fact that the is look like to would do i am a dog it were on john
0:09:12	but as
0:09:12	the penalty term
0:09:20	so
0:09:20	you hmmm
0:09:22	the original source of it
0:09:23	and the source is a part of it by a at
0:09:26	for this simulation we use
0:09:28	and source as the number of simple is but
0:09:31	a two one one thousand
0:09:33	and they just passed to you is said
0:09:36	to zero point to zero one
0:09:39	is a a to correspond to
0:09:42	one that's sent of nonzero element
0:09:45	in the mixing matrix it is a very sparse might so
0:09:49	the is many zero
0:09:51	and
0:09:52	in these uh
0:09:55	so this metrics
0:09:57	and so on
0:09:58	the
0:10:00	separation that a and that the constriction little
0:10:03	the proposed and that are in the
0:10:05	oh is black land is
0:10:07	i that form
0:10:08	the the of an that are
0:10:15	and simulation read that
0:10:18	we we quote you know we can see that we we we close to that
0:10:22	to
0:10:23	mm a you greens
0:10:26	and we than ten monte
0:10:28	a
0:10:29	i meant what the colour and and a at the mean value or ten for
0:10:34	do do the you the that i present
0:10:38	and one way one may not that the you proposed in but that in the in these better than he's
0:10:44	so that
0:10:45	it's like
0:10:46	so i've done but what limit that
0:10:48	read
0:10:48	also so present
0:10:50	the bus
0:10:51	is so the constriction and separation
0:10:54	it
0:10:59	so last move to conclusion
0:11:03	so we we we propose a to be that i lead and murdered for nonnegative independent component and i
0:11:09	the is it on a creature don't it by probably in this method
0:11:13	we we had a a pin that be turn to maintain to
0:11:16	the orthogonality constraint
0:11:18	and we
0:11:20	so we approximate the discontinuous function C by you can is when you but will and for making a unknown
0:11:26	that compilation of the gradient
0:11:28	and similar shown on synthetic data so that the
0:11:31	with a difference but it's
0:11:33	do you so that do was in that but out there from existing one
0:11:38	so you should uh
0:11:41	we have to to
0:11:43	to to for thirty
0:11:44	only to cover convergence and i'm like these
0:11:47	for the in the the optimal parameter of the algorithm
0:11:51	this
0:11:51	this can help
0:11:52	is to have
0:11:54	the proposed with mid or
0:11:55	we are we have was to to consider the node in to for evaluating the a business
0:12:00	and a corporate the sparsity V
0:12:02	a priori
0:12:06	for for attention
0:12:07	time
0:12:11	i questions comments
0:12:14	so we have sometimes yes
0:12:20	having a can at that uh a high i present to any
0:12:24	and
0:12:25	re at that time
0:12:27	so
0:12:27	oh class
0:12:28	or music a spectrogram
0:12:30	uh
0:12:31	a a taking into account a priori
0:12:36	or
0:12:37	i
0:12:37	have that a a a a i and yeah yeah i one them to and the data for example a
0:12:43	music spectrograms
0:12:44	spectral on yeah yeah now i i i i used the data on to the application i i saw in
0:12:51	the first the first slide
0:12:53	do mass spectrum
0:12:54	yeah i to go back to the first slide and
0:13:01	yeah yeah my spectrum data is i it L
0:13:05	a a a a and and i use of a gimmick that
0:13:08	is solution
0:13:10	and the second one is a a a a a bit mission
0:13:15	then i'm be no emission tomography
0:13:17	but a
0:13:19	i i i i i i well i'd this time so i i a i don't have a desired to
0:13:23	see
0:13:24	to that a year and i
0:13:25	but also these applications
0:13:27	so that the mixing matrices a non and the data are also
0:13:31	yeah
0:13:32	but in this one
0:13:33	in the but of this application to meeting the mixing matrix and a day in the sources and a negative
0:13:39	but
0:13:39	the non negative independent component and i'll this
0:13:42	don't assume that the mixing that these a negative
0:13:45	a a a a up in the meeting but at exists C
0:13:49	or you the meeting that fixed uh you get to that can also exploit the fact that the and X
0:13:54	the matrix is a nonnegative
0:13:57	this that don't in it i'm yeah i do this information can a modify the method so then Q it's
0:14:04	exploited
0:14:04	yeah i to have a yes or or a i i
0:14:09	for example in no
0:14:14	hmmm
0:14:15	hmmm in performing the
0:14:17	do do do do the whitening
0:14:19	yeah
0:14:21	given to your
0:14:23	the writing the whitening matrix
0:14:25	in
0:14:27	the mixing matrix can the estimated from these two metrics
0:14:30	but
0:14:31	you the meeting you can do the meets the a
0:14:34	when we keep lying the
0:14:35	whitening that X interpretation
0:14:38	a we don't
0:14:40	a have this a we don't we we we web we are we are not sure to have
0:14:45	in a that too much excess
0:14:47	yeah
0:14:47	so you
0:14:49	a happy can in incorporate use information but uh
0:14:53	uh
0:14:54	i i i i i i don't know at maybe that they have picked and the every Q incorporate this
0:14:59	information to okay go back to the where do you that application
0:15:04	and that's P S sparsity degree and these applications because you at like one percent sparsity might of the E
0:15:09	mixing matrix in your in simulations
0:15:11	yeah in uh in uh
0:15:14	my spectrum from data
0:15:16	do the my spec and did that is in a very very sparse data this
0:15:21	i
0:15:23	yeah but that yeah that's that's possibly will like uh one percent one time uh a ten percent
0:15:28	matt my and that there is a a a approximately when per sent one send them nonzero element in do
0:15:35	you must big from the the
0:15:37	so not yeah one percent nonzero elements with these a very sparse fixed okay yeah so did this use why
0:15:43	we use or a
0:15:45	in simulation
0:15:47	a
0:15:49	you plastic this plastic could you please god
0:15:51	you quite a zero point zero one yeah that is point to one based and a zero yeah and hmmm
0:15:56	just a similar to a spectrum D to okay yeah that that the other application this position um position thing
0:16:03	and the speedy
0:16:05	as is an as is also sparse and that's also a spice mixing matrix or a in project or emission
0:16:11	tomography time one thing i C it is not sparse it's a just okay
0:16:15	so that that if the makes matrix is not sparse your then yeah great and doesn't have a really have
0:16:21	a big advantage of the others yeah
0:16:23	yeah the the source is are not sparse
0:16:25	uh_huh do
0:16:27	are have are way to use we work a
0:16:30	similar to what i yeah yeah but this would it is very sparse yeah it will be a a it
0:16:36	it you can you more interesting to use a and very yeah i i a plan to use that on
0:16:41	the data are also yeah
0:16:43	yeah okay yeah i'm trying now to use it in the mouth you did was picked from the
0:16:48	because yeah mentioned this on the uh on the look on the future works nine
0:16:51	okay
0:16:52	i a i just place
0:16:54	yes
0:16:54	and
0:17:00	yeah
0:17:00	yeah
0:17:03	uh i yeah
0:17:04	that that control is still
0:17:10	we
0:17:13	yeah
0:17:14	we approximate this of function by and the probably to and
0:17:18	so
0:17:19	number of the control do i could a C of the of the the approximation
0:17:23	the that she is them the
0:17:25	do be to a a you what dictation approximate the sign function
0:17:31	that's the performance depend on the choice of manner
0:17:34	yeah
0:17:35	yeah okay we have to do is to to to a large value of from that but you from that
0:17:40	used to large
0:17:41	a do the same to about all
0:17:43	C function we a pure in or uh you between attention
0:17:47	ah okay yeah
0:17:49	no common
0:17:50	question
0:17:52	thing to and that's again

REGULARIZED GRADIENT ALGORITHM FOR NON-NEGATIVE INDEPENDENT COMPONENT ANALYSIS

Signal Separation