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