0:00:13 | oh to more late |
---|---|

0:00:14 | that kind of behaviour in other works |

0:00:16 | we have used a diffusion adaptation to model for example |

0:00:21 | a flight formations symbols |

0:00:23 | to models warming of be is moving from one place to another |

0:00:28 | to uh to model bacteria more to two we had then the a people in this conference on a in |

0:00:32 | how but T search for four |

0:00:34 | or hell fish just want to go that is of four |

0:00:38 | to move to the than insertion of food so these are all examples of highly dynamic environments with the agents |

0:00:43 | some moving the topology of the network is changing of time |

0:00:47 | your neighbours are changing all the time |

0:00:49 | okay |

0:00:50 | so |

0:00:50 | nodes need to do adaptation in all the to learn |

0:00:54 | what's happening at on them and all that also to says what the neighbours think about the situation |

0:00:59 | okay |

0:01:00 | so before i start let me just evade be talk to day i'm going to show a video of it's |

0:01:05 | not my you to download it from the internet |

0:01:07 | and this a figure illustrates the behavior that i'm going to model today use see |

0:01:14 | and a a a group of fish lots of fish being |

0:01:17 | right |

0:01:18 | uh followed by a a group of shot |

0:01:21 | now |

0:01:21 | i'm going to model of is as two separate networks called in a thing we've each other be sharks form |

0:01:26 | a network of nodes to are in eighteen with each other |

0:01:29 | and the purpose is to encircle |

0:01:32 | a a group of fish and the fish is on the network of feature |

0:01:35 | that are call the meeting with each other and the purpose is to try to get away way and also |

0:01:39 | find before for done go dollars |

0:01:41 | before the locations of these are two separate networks |

0:01:44 | they have their on an object is but at the same time |

0:01:47 | they have |

0:01:48 | some form of a competitive interaction between each other okay so that we show you this C behaviour in in |

0:01:54 | nature of forced you see here it is |

0:01:58 | you see how we we shocks is a fish |

0:02:01 | and then they are back them one at a time that's have they |

0:02:04 | and they a function |

0:02:06 | okay so that it is they all have a code in a of this some not shocks the thing this |

0:02:10 | the all phones |

0:02:11 | no okay so |

0:02:13 | if five |

0:02:14 | you want to see if again |

0:02:16 | so that's what they do okay |

0:02:18 | that's how they |

0:02:20 | they play for four days circle circle the fish and then they are dark at one at a time okay |

0:02:24 | case of course this is this |

0:02:26 | a small example the |

0:02:27 | but i i'm sure that |

0:02:29 | there are more |

0:02:30 | complex examples in nature are okay so now let's come back to the math okay to new method |

0:02:36 | and to that modeling i'm going to do |

0:02:42 | to model that kind of behave and i'm going to use a call diffusion adaptation algorithms |

0:02:46 | so that we force motive the algorithms for you |

0:02:49 | by and that's what i need and that's for that consists of a collection of notes these nodes have a |

0:02:54 | adaptation and learning abilities select me motivated for us assume you have a collection of and know |

0:02:59 | that collected to each other through neighbourhoods circuits so you have a topology and this topology can change with time |

0:03:05 | because "'cause" and going to use it for the application |

0:03:07 | at hand |

0:03:08 | and that's assume |

0:03:09 | i'm not going to both |

0:03:11 | in the case the movie the deviations and the arguments of come just going to highlight the main ideas is |

0:03:15 | friend interested in the details the references |

0:03:18 | well help you with that of kid just because but i don't have time here to go through all the |

0:03:21 | deviations |

0:03:23 | but i going to highlight the main ideas |

0:03:26 | we set of nodes they have a model objective and that object of for example is that you all effect |

0:03:31 | of W O |

0:03:32 | this this down real all could the present the location of for all of them would like to know what |

0:03:36 | the food is |

0:03:37 | or it would represent the location of the are all of them would like to know with the shock is |

0:03:41 | an avoid it right |

0:03:43 | so a so you have a collection of a with the common object and each node each node |

0:03:49 | has an index K each node has access to some measurements |

0:03:52 | but related to that the objective for example each node |

0:03:55 | can sense it distance |

0:03:57 | do that objective and noisy distance and is noise |

0:04:01 | and can also sense in what that action that the object of its i know the distance and i of |

0:04:05 | the direction but all of this is up to now |

0:04:08 | okay okay because you are innovative noisy environment then each node in the network has access to that kind of |

0:04:13 | information |

0:04:14 | now how do they work together so that the local or the nation of from local cooperation they can improve |

0:04:21 | the estimate of word |

0:04:22 | V four days or of where the but a is all |

0:04:25 | improve the estimate of what have a parameter the network is trying to estimate a cam just using |

0:04:30 | the fish as an example in this context okay |

0:04:33 | and now you can formulate a global optimisation problem like this which says |

0:04:38 | a i have and nodes |

0:04:39 | all these nodes would like to find a weight vector |

0:04:42 | data you or the location of what that were for them looking for in order to minimize the sum of |

0:04:47 | the squares |

0:04:48 | okay this could be one cost function K |

0:04:50 | of course this is a global optimisation problem and we don't want to solve |

0:04:54 | it in a global man and we would like to solve it in a distributed manner okay because |

0:04:59 | every node K only has access to information coming from its in egypt neighbours okay so how do for that |

0:05:05 | problem in a distributed manner and we have started this problem in late data several publications only earlier |

0:05:10 | and we motivate the algorithms and we started its performance convergence performance times and performance is that is the performance |

0:05:17 | okay so he i'm just summarising the algorithm and all the set and done |

0:05:21 | this is one of the algorithms that you have one |

0:05:25 | that performs very very well okay and why i mean these algorithms we also insisted on coming up with a |

0:05:31 | good things that are simple to implement |

0:05:33 | because i believe that in applications like we one i'm showing you hear and i'd these agents i'm not very |

0:05:39 | sophisticated bill might be able to be implementing very complex |

0:05:42 | algorithm so we would like to see if you can him late |

0:05:45 | these kinds of complex behaviour through simple procedure is okay so this is one of the algorithms we have i |

0:05:51 | call it the at the diffusion fusion algorithm had that then combine "'cause" it consists of two steps |

0:05:57 | okay okay each node note K the first think it does it starts with an estimate of for that |

0:06:03 | that's see think of it as the location of the predator or four |

0:06:07 | a first think it does it uses a a measurements it has for example it's S estimate of the this |

0:06:12 | that's and the direction |

0:06:14 | it uses that |

0:06:15 | information to try to improve one its current estimate |

0:06:18 | that we give it an improved in to need to estimate and then it costs also with its neighbours it |

0:06:23 | combines |

0:06:24 | for the convex combination here the estimates from its neighbours |

0:06:28 | two and up with it improved estimates so this is a two-step procedure |

0:06:32 | the D there's of the must not math methods don't matter what matters is the process the process is |

0:06:37 | you know |

0:06:38 | for example |

0:06:40 | this is a very different from consensus type solutions in consensus step solutions if a it's just if you are |

0:06:45 | a way if a are familiar with that |

0:06:47 | you try to |

0:06:49 | a you require a agents to reach consensus about some something to agree |

0:06:54 | i something a kiss all over that each each node is essentially a averaging the information from its neighbours |

0:07:00 | in these kind of applications that they showed you the example that i showed you you can not to require |

0:07:05 | you you should not expect be nodes to reach consensus |

0:07:08 | because the fish that's closest to the shot should behave in a different manner than the fish that's as to |

0:07:13 | the for don't far away from the shore |

0:07:15 | you have to allow for individual that's estimate of the situation as well |

0:07:19 | so that's why |

0:07:20 | these diffusion algorithms algorithms always consist of two steps one of them is con thought and with the neighbours let |

0:07:26 | me see what the neighbours think about with four days |

0:07:29 | but before i take that for granted that also want to says it from my perspective |

0:07:33 | okay |

0:07:34 | uh uh where the shark is a with before is |

0:07:36 | relative to me so you always have personal assessment |

0:07:40 | okay a local processing local adaptation and learning in addition to |

0:07:45 | collaboration with your neighbours okay so this is always there okay you always have these two steps |

0:07:50 | and this is called adapt then combine adaptation comes before combination you also have combined then at that |

0:07:55 | and you have several different variations of these algorithms this one works very well okay |

0:08:00 | and these coefficients they always add up to one |

0:08:03 | over the neighbours on these graph they are just a last what i just |

0:08:06 | yeah explain okay |

0:08:08 | now in nature there are many many examples of source stick kate organise behaviour that are right |

0:08:14 | okay from local interactions between you node you in one is the the fish |

0:08:18 | behave like it's forming this very but for geometric figure |

0:08:22 | right |

0:08:23 | but is not sense brain telling them sitting here on this side and telling and you position yourself at this |

0:08:29 | particular location right |

0:08:30 | this is happening this is the result of highly localised processing okay |

0:08:34 | the diffusion adaptation algorithm i showed you is one example of high localised processing because every node is only coordinating |

0:08:41 | with that in you jet neighbours |

0:08:43 | you also have this kind of behaviour of the fish |

0:08:45 | but i D S to of the boats fine in V formation i again that is more central |

0:08:50 | bad board telling them sitting on the side and telling them this is what you okay to cells okay so |

0:08:55 | these are examples of highly complex |

0:08:57 | so self organized behavior that the result from local processing at the local level look |

0:09:03 | so the algorithm i just described to you the diffusion algorithm that i described use one example of |

0:09:08 | localise processing that leads to this kind of behaviour in and i'm going to illustrate it do you to |

0:09:14 | but showing you how |

0:09:15 | this algorithm can in more the behaviour of sharks all for putting on face |

0:09:21 | in the case when you have two networks competing against each other right and trying to get the out that |

0:09:25 | and the other trying to get away from |

0:09:27 | from the forced okay |

0:09:29 | is so now |

0:09:30 | uh uh uh |

0:09:31 | so |

0:09:33 | oh this is known that for example here this kind of behaviour is known and uh in a at if |

0:09:37 | you have let's say the shock yet trying but are a group of fish that have force in moving together |

0:09:43 | in harmony the ford and then start the me a shot peers |

0:09:47 | now the fish is known to behave in this manner they have this found and effect behaviour at they turn |

0:09:52 | around |

0:09:52 | they do not on |

0:09:54 | okay and can almost a long this and shots so they turn around and come back from behind |

0:09:59 | okay so they are known to behave in that manner so about going to model |

0:10:03 | that behaviour so that you |

0:10:05 | okay and then he are also i shall video the we do that i show here you see it in |

0:10:10 | a different man that here you have the collection |

0:10:13 | a sharp sold bill things and you have some fish she and you see the end up in so |

0:10:17 | if a fish and then they start at back them one at a time but to side |

0:10:21 | and in the video "'cause" this are just illustrations from the which are this is from the I B B |

0:10:25 | ball you to the and other kind sent this and the this we goes from scientific american and this it |

0:10:30 | is it's from some other |

0:10:31 | or or go shown down |

0:10:33 | and down here a can now again like i said before don't to much about the math okay because we |

0:10:38 | don't have time to go through the D as but let me explain in high level |

0:10:41 | a big use the algorithm i should do before that's all you need to to in more like that kind |

0:10:45 | of behaviour |

0:10:47 | okay |

0:10:47 | i to think about that like this okay you have a group of fish they don't know where the four |

0:10:52 | days so that's one object objective they have an mind i need to find with the four days |

0:10:56 | they can use the diffusion adaptation algorithm to estimate where the location of before this is to local cooperation number |

0:11:02 | one |

0:11:03 | no but to they also need to stay away at i'm where |

0:11:05 | the shot are |

0:11:07 | right so they have a that estimation problem that they need to solve a need to know where the shocks |

0:11:11 | are |

0:11:12 | so you have to |

0:11:13 | diffusion adaptation process is that they need to do and right in a distributed manner |

0:11:18 | the sharks they need to know where the group of fish is so they need to track for example with |

0:11:23 | the centre of gravity of a group of fish is |

0:11:26 | uh uh that estimation problem i they can also use a themselves the diffusion adaptation algorithm of the form i |

0:11:32 | showed you to estimate with the centre of gravity of the |

0:11:35 | group of fish is and track at that i'd because they need to follow that |

0:11:38 | and this so open so you can see that at the core of solving this problem you have to fall |

0:11:43 | for the or four |

0:11:45 | estimation problems all of them distributed estimation problems each one of them can be solved exactly in the same and |

0:11:51 | that okay so you see the uniformity here so one of these things is to try to show that with |

0:11:56 | this thing classifier algorithms with this same type of processing you can in one eight different kinds of behaviour |

0:12:01 | know because if you think about it this is something very very interesting |

0:12:05 | you see you you with think that to to model the uh the a flight formation in boards of the |

0:12:09 | the way but to a move you would need different kinds of algorithms and models those for each scenario and |

0:12:16 | interesting thing is with this same general kind of a with them they want a should do before you kind |

0:12:20 | of produce these different kinds of behaviour |

0:12:22 | okay |

0:12:23 | so here what you have just a a a a high level description you can divide the region at i |

0:12:28 | around the shark to for regions |

0:12:31 | region and one up here use the up here each in one |

0:12:33 | if if if is is region one T to means he's far away from the shot okay you defined this |

0:12:38 | C is in terms of a at I if it's away from the shock if you stay if you just |

0:12:42 | want to use |

0:12:43 | tracking where the for this and continues moving was before |

0:12:46 | no okay that's what it means |

0:12:47 | if if if fish finds itself so if if fish find itself |

0:12:57 | more |

0:13:03 | if a fish finds itself in region two |

0:13:06 | which means he's calls to or okay |

0:13:08 | then what you would do a double take it own i perpendicular to the direction of motion of the shot |

0:13:13 | so that's why he also needs to track where the shark is okay |

0:13:16 | so i'm telling you how they we use the information they get from the estimation process okay they |

0:13:21 | i get this information to do something with it they have to a decision with it's so well this fish |

0:13:26 | is tracking from local cooperation with the other fish with the shark is |

0:13:30 | if they that out they are to close to the shock that one move along a direction they would take |

0:13:34 | get to a like a should before the found in effect |

0:13:37 | they won't take a turn perpendicular to that that action this is what this not they me okay |

0:13:42 | if they are for example to to close to be we and one hundred eighty degree turn and move away |

0:13:47 | a okay |

0:13:47 | so essentially what this at is thing and what these conditions are telling you is how the fish use the |

0:13:52 | information they get from the solution of the distributed estimation problem okay they use it to evaluate how close they |

0:13:58 | are to a shock and then what decision they should make should they move |

0:14:02 | one you moving to the for should they |

0:14:04 | for all the found an effect well should they divorce and move back that that's actually what it means okay |

0:14:10 | and what that means is they are going to set their velocity vector that how long this uh and direction |

0:14:14 | of P |

0:14:14 | so the result of the estimation process affect how they said the velocity vector or okay |

0:14:20 | now |

0:14:21 | after the fish set but it like used for in the found an effect beta group with fish usually group |

0:14:26 | work "'cause" a how do they re group okay again |

0:14:29 | what they do is eight that for example and this step but it they become separate networks and that's what's |

0:14:33 | nice about that now you have set but at network |

0:14:36 | so one can say the out |

0:14:38 | okay i so one of them for example of this network can find which |

0:14:42 | one is which i if that is a net will close to it and which fish she's cost to it |

0:14:46 | and move in that direction so that they group |

0:14:49 | okay |

0:14:50 | so these sub networks can also track each other through local cooperation |

0:14:54 | and then take an action in the uh i i i uh uh |

0:14:57 | i um |

0:15:00 | a the act to that and move or or other subnet will give this one a we these sub networks |

0:15:05 | to group okay |

0:15:09 | so sing |

0:15:12 | yeah this fall all week is not working well here it's |

0:15:15 | chomping thing over several slides that |

0:15:17 | ones |

0:15:18 | the is |

0:15:28 | and a let me show the yeah as this we you before i come to you this is the case |

0:15:31 | of K using the kind of a bit they should you hit it is you have a group of fish |

0:15:35 | trying to find a for would okay it will be and then a shot at |

0:15:39 | so you can think that the fish they don't know what the for is they are called than eighteen to |

0:15:43 | find with the four days and moving in that direction but there was a of for the shot is |

0:15:48 | and the track it and then use see the found an effect and they group one on in you |

0:15:52 | continue their right you see so a this is all to produce with a kind of a with them i |

0:15:57 | showed you |

0:15:57 | however in this example i only have one network the fish networks so it's only the fish that's doing diffusion |

0:16:02 | adaptation |

0:16:03 | the problem i discussing today i'm showing to the case where you have to a networks a group of shocks |

0:16:08 | and facial case i'm going to show you that very so on |

0:16:11 | so what do they shot to do what do this shot do with the result of the estimation process with |

0:16:15 | a is out of tracking well the centre of gravity of a group of fish a |

0:16:19 | well where the closest fish is to sam what do they do with the result of that distributed estimation problem |

0:16:24 | the shocks they have a |

0:16:26 | several decisions to make |

0:16:27 | okay i'm not going to go again for all the mathematics but they have several say it's one of them |

0:16:31 | is chase if the fish just to a way they decide |

0:16:34 | that's just move towards the centre of gravity of that group |

0:16:37 | so they are tracking the centre of gravity that they set of the lost a vector do that that actually |

0:16:41 | are okay |

0:16:43 | once they get calls to it within a certain date as they decide to is or call it so they |

0:16:47 | move not a the attention or K they move along that that it's of that is to what the fish |

0:16:52 | were building but okay |

0:16:53 | so once they get close with it's or and they just they say a let me now is so call |

0:16:57 | it okay let's nice is it and and one at that time they take to are |

0:17:02 | you like that wide leans in and so the fish case so essentially they have a state machine that they |

0:17:07 | fall |

0:17:09 | and based on based on the estimation of sell the use the they transition from one state to another depending |

0:17:15 | on how close they are to the centre of mass okay so this is just a producing |

0:17:20 | in figures and equations what i just explained in plain in plain walls okay so i'm not going to both |

0:17:25 | a all of these the there's of course that is |

0:17:27 | and that is small in that will not that behaviour so if if the shock as far away he just |

0:17:31 | keeps moving towers the centre of gravity |

0:17:34 | okay once to gets that he starts so |

0:17:36 | that group |

0:17:38 | can and not only that if if fish moves for that i they would like to keep the fish within |

0:17:42 | a circle of the fish of one of them moves away from the so they will track that vision bring |

0:17:46 | came back okay |

0:17:47 | so all of that |

0:17:49 | so all of that requires that you use the distributed estimation problem okay i'm i don't have much time to |

0:17:55 | both a the uh sort of these small in but you are that to get an idea i would like |

0:17:58 | to show you |

0:17:59 | no i would like to show you V uh defined assimilation simulation than at break for |

0:18:03 | here you see this example now you have to network |

0:18:06 | right |

0:18:06 | you see how the shots since so fish |

0:18:09 | okay |

0:18:11 | let me let you watch it and then and makes some comments |

0:18:14 | you see and then they at that one at that time |

0:18:17 | okay now think about this to you see this is an example of a highly dynamic network okay and that |

0:18:23 | network that's moving all the time |

0:18:25 | your neighbour are changing all the time feelings of bit topologies changing all the time |

0:18:30 | number one number two each one of these networks you have to networks each one of them has an objective |

0:18:35 | the fish wants to find a way before it's |

0:18:38 | but it the estimation process |

0:18:40 | what do for exactly for that's would would be moving as well |

0:18:43 | the shocks would like to know what the centre of gravity of the fish and want to track that and |

0:18:47 | in tap that |

0:18:48 | and also the fish would like to avoid the sharks okay |

0:18:51 | so you have several object is okay in a high dynamic environment and a highly caught productive |

0:18:57 | and competitive environment like and you end up with a high and and a network that's able to adapt and |

0:19:03 | learn |

0:19:03 | a in real time okay so this is |

0:19:06 | an example of adaptation at the higher level and learning at a high level and then usual and you can |

0:19:11 | see just simply using that diffusion algorithm that i expect you before you are able to reproduce the be here |

0:19:16 | that i showed do before uh in the video and a lot a like to the other the real example |

0:19:20 | of how shocked friends |

0:19:22 | i go off to fisher okay |

0:19:24 | and you i hope i conveyed the main idea okay of of this kind of behaviour i again this is |

0:19:29 | all signal processing what you're saying here |

0:19:31 | all generated using |

0:19:33 | a diffusion adaptation algorithm i showed you before and using the result of the distributed estimation process to make decisions |

0:19:39 | should they move closer or should i so oh that's essential the kind of the decisions you make a okay |

0:19:44 | so and we this of some reference if you are interested in more to learn more about this some going |

0:19:48 | to stop S so that we stay on time okay so if you have any quick questions |

0:19:52 | before i move on to the second part yes please |

0:20:03 | i |

0:20:04 | yes |

0:20:09 | they don't have a job from the for the uh |

0:20:13 | so okay in any of the like take advantage of the behavior have your of other one of knowing that |

0:20:18 | be have your of other one to to maximise its proof |

0:20:21 | a i okay in this in this particular the model that i have here the information that's shared between the |

0:20:26 | network is the positions of the centre of gravity of the large network and the position of the there's in |

0:20:32 | this small a network so they know essentially a deep but they don't know this strategy that the other group |

0:20:38 | is falling they just know where the locations are and they spun |

0:20:41 | according to be process you that explain you before T that you move away well you D for or you |

0:20:46 | take an i two degrees is uh okay so that's the this strategy to they use in this particular example |

0:20:51 | okay |

0:20:52 | now if they knew exactly what strategy each other group or i would assume that you got but have to |

0:20:57 | do better yeah that's a good question but that we haven't done that |

0:21:01 | okay yes |

0:21:05 | i |

0:21:06 | a yes okay right that's a very good question of course C M just showing a very uh uh the |

0:21:11 | networks behaving but then you need to study the steady-state behavior of these kinds of networks the converge and we |

0:21:17 | have done that and other walks okay we have shown we have a derived expressions for the mean squared error |

0:21:22 | in steady-state state okay |

0:21:24 | how how close they get to the location of if we have done that in previous works yeah |

0:21:29 | of course for small step-size a the step size have to be small amount |

0:21:32 | for them to converge |

0:21:35 | oh can maybe one more question just so that we stay on time yes |

0:21:38 | here you assume that the sharks for example have the same state machine in each of them right let's say |

0:21:43 | for example there are different groups of sharks right which like to like if an state machines very but but |

0:21:49 | i is a tight so |

0:21:51 | is |

0:21:51 | right which might apps |

0:21:53 | behaving hating using a different types of machines as i a good question we haven't done that but you know |

0:21:58 | this are all generalisations that are possible to pursue so okay yeah and and and see what kind of behave |

0:22:03 | that emerges from that kind of of assumption what you thing about the real life i mean i R D's |

0:22:09 | i mean it's state machines are |

0:22:11 | well already very uh i mean somehow |

0:22:14 | or the or already in the sharks or or yeah that i think we have to ask an animal behaviour |

0:22:19 | expert okay yeah all we all yeah or they are knowing okay we'll it would it some of the lead |

0:22:24 | to channel and they explain about |

0:22:26 | be thinking process that these animals both through these state machines and are trying to see if you can to |

0:22:30 | produce that kind of behaviour |

0:22:32 | using the signal processing algorithms and models that we have a okay but this are all good questions okay but |

0:22:37 | to and so then you have to get deeper into a right to how and most be uh you know |

0:22:41 | i want to be fit to the other because i don't want okay maybe we should move one i would |

0:22:45 | be glad to talk to you i your questions after this session okay sorry for that just because they have |

0:22:50 | to move on to the second |