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