morning everyone a um i'm sort from a little way many many jacob chicken as K i we present thing my work about the estimating uh functions on social graphs what the function represents uh and the preferences of the social network members for a specific multimedia content and that is how much should the social network members this like or like that particular content item i was start with a little bit of uh background and motivation uh to they we are aware that social a networking some we present on the web when the we show photos in the joe cells in creating user generated in content or discover cover or all the a high school friends with tend to carry out all these activities to the social networking sites that to happen a as part of this activity is you express our opinion of certain multimedia i for example we may yeah say how much we like up certain picture that the supposed to there or we may score uh a a specific movie in uh in addition with we tend to also leave such information is part of our user profile no is you can imagine that is the range of applications that can profit from knowing this user preferences and for instance uh when we do online shopping oh for a smart homes uh uh uh for entertainment targeted advertising uh a you a need to also that is there's is a range of applications information retrieval and search data mining and so forth for the more the data networks could also profit from knowing this information and in addition to for collaborative talks knowing go which person prefers uh has a prefers different types of uh uh task so could also be uh exploit so the high level uh abstraction of the problem that to look at is uh that of data very uh recovery where would have a function associated to with a small subset of the nodes are telling us how much these nodes the like a specific video for example and then we are interested in that term mean how much the other nodes texture like or these like this uh this specific item and mm the what we tend to exploit here is the phenomenon called a of philly which means that we tend to associate or conjugate with similar miller on there's so he is the roadmap for the rest of the talk uh we are close to being a social graph which uh can in addition uh carry out the set the weights describing the fee it is between the users how how much we are a similar of this email that with our specific neighbours see within the social network and then as a mentioned we we will assume that we know this preference of what a small subset of nodes now to estimate the the the missing um a preference is we will uh designed to algorithms one it's a descent L one and is base a message passing and it comprises two steps as people are familiar with the centre as algorithms were the first one is the bit take a local expectation in our own a but with and then we chain they uh and uh and information that is computed with our neighbours and then uh we also present uh a algorithm that lies in the class of sparse construction uh where a contrary to conventional a sparse reconstruction where we ten to i assist where we tend to a um constraint uh the form of the solution with some regularization term now we will have like multiple a regularization terms bold on the on the transform or the signal as well as in the signal domain which are described with these two summation and then we all that uh a problem with um at total file to make in the direction of multiple in this is with respect to related work this a been recent interest in the computer science community of of uh uh the turning this a user preferences and from the few words that to of a so far it's uh site it's to to represent once here but the or to simpler network or a correlation model the describes the correlation in user preferences between any two members of the network and then the odours also compute a certain set of features from the data that to together with the machine lower algorithm in this uh a network for to correlation model tries to compute the estimated the the um the missing preference i will be if show a comparison with this works it the end and talk about the the performance differences and and the related to direction of work is that on on opinion mining and sentiment analysis oh which also lies in the computer science community and now algorithms lie which in the brother field of a graphical models the descent of this algorithm that of present and uh i also cited one reference your and sparse the construction okay so with respect to the first algorithm is a mentioned that comprise two steps but the nose starts from an initial estimate bit could be an uninformed guess and so or and then the the notes uh to compute and normalized expectation using this weight it's um from the previous estimates of the neighbours so it's quite straightforward and there's we going to see to it actually works quite well uh a one analyse the performance of a good some really you use the a C N all the of the of the graph uh and then lisa goes as false oh we we compute the low class and the matrix is the difference between this may takes the in a where a represents the the weighted adjacency matrix of the social graph and these simply the uh and they are gonna make takes way H and they are gonna and three she's is the the some of the vertex decrease of each note and uh of i will i will need to be brief on these but so spectrogram could have to T we know that they will be as a set of eigenvalues associated with the solar plus and tricks and we study the convergence of a algorithm to equivalent to the markov chain that france on the graph and uh whose transition matrix a is given of this expression and it could be shown that oops i'm sorry um and that the the this transition matrix is a the related to the lip loss of the graph so that uh we was start the approximation that or or when we try to estimate the missing see is using this algorithm uh using this analysis of each uh iteration K we could show that the the error or the total variation at or of the oh the approximation is related to the i so the lip plus in matrix using this term and with some work we could show that the this error is is bounded but this exponential term uh times these uh ratio all of the maximum versus the meeting a node degree all of the of the graph where these uh lamb the subscript E um could be either the second smallest uh like a like in value or the be related to this the largest eigenvalue of a a class and matrix or or or or a as an alternative but they will not go in detail here we could the sure convergence analysis of this method using the uh the power matter at the which is you used to be totally compute and in the composition of a matrix now just an illustration of how does this work in terms of convergence rate i will show you we here uh uh to gauss uh which uh illustrate the the convergence of the algorithm as a function of the of the density of the matrix that is the well the that's it but graph as i'm sorry as a function of number of edges and um as a great no of core were just we have the the total variation distance on the X and we could show that uh your we observe the same slope uh is a function of these uh eigenvalue eigenvalue a a the sub E all the log option and i she show to good a house which uh or to by using a different threshold value at which point algorithm stops computing you words when the total the distance is below ten to the minus to for example we stop and then receive the is uh threshold is increase then we need the more iterations to converge i i for me to to mention that i'm sorry that we are using uh a small dog from the house which are typically encountered thirteen in uh examples also shown that networks one another interesting graph off is a how do we do with respect to a running the same algorithm one no one a random graph and it's interesting to show that uh when the graph is not so dance on the beginning we actually on the in terms of convergence speed and that is because small world graphs um uh we exhibit a but different uh a non uniform distribution of the node degree so that that G a small uh a large on the beginning we have a a number of know that have like a small number of neighbours and then that they actually a affect the convergence one i'll go is that not only for them but for for the neighbour says well now is the as density increases then things set down so we convert to almost as fast as running running the looks them the on a on them graph now with respect to sparse reconstruction a a as i mentioned conventionally uh when you try to estimate uh a function where that this function a a has the only a small number of file is that we know of we tend to put some regularization constraint on the solution to make life easier now this uh approach doesn't take into account that sometimes the solution to can candes it can require the shown number of constraints for instance here we would be to crowd is this content preferences sum up to one and to to all these we we generalise this approach by proposing is uh compound multi regularized the reconstruction well we place a number of additional a regularization terms boat on the solution itself that is in the signal the main and also on the on that the small value or that signal well these uh functions five i or for equalisation functions which are related to the constraints two additional constraint that we want to impose an solution now the them is quite good a complicated to to solve for X uh and i will briefly outline it here without going to the details uh what we to to to solve this problem of uh finding and but to minimize this so expression he's is uh a design all the algorithm based on alternating direction of multiple as where we do variable splitting and then alternating optimization and then re to to converges so they will be the three terms that they reader you'd update it and one is the the solution sell the other one is to the uh and the other two are related to the do dual variables that the used and specifically we could show that uh C is that to a first line related to we X he's is um a quadratic expression we could the we could do explicitly small with using the in the first uh expression on top here and then the second expression where we so for the for the you you for the dual variables that to introduce take actually that second line here it can be sure on it's in the paper decompose is into uh a set of independent the problems which could be sold in low unfortunately uh even with uh with the additional uh um and to go terms we don't do that well and this graph off loose raise that where on the x-axis axis showed the node in next we look at the fifteen a graph and then the y-axis a show these a function of the to you we are trying to estimate so the little but the red red to represent the know the getting the value that blue value what is and um the estimated value sort of function if you don't put any additional a constraint and uh a good red you represent the proposed solution where we can see that this function list can go a non-negative and you know they can sum up to one where uh we can see that that we have multiple uh content items of interest so we our preference actually present probabilities or or these a set of uh a content items tense so we can show that for some values we are we are doing well and we we we could be estimate the with the the function close we but for some well as we seem under perform significantly and even more noticeably is the fact that uh for example is a out line you of it this uh uh a conventional at the legalisation doesn't what because the without the extra constraints we could the estimate you one right is that the negative uh a as a transform here we use the graph a with transform uh uh from this uh paper or site each year we assume that to we on know the function value of twenty five percent of the nodes and then the rest of the nose do not have this function ready available but this is expected to because the you do doing these um the caff transform based estimation uh um there is an underlying assumption the spectrum of the function on the graph is moot that means that is a small number of coefficient that are significant and then the five the function of decays as a function of the coefficient index which is shown here so if you show the uh um a reconstructed value of the function using this graph based methods because see that the spectrum is quite small but we actually if little that they a look at the actual value well the spectrum uh it doesn't follow that behaviour so using all the shelf off graph transforms um doesn't provide a a can solution for this problem and i a thing is that the function is sent in the estimation is sensitive to the a choice of this subset V sub sub zero and that's because the function is of to normal and is not a redundant so down that line assumption that this uh a good off of let then any like a after as one uh uh uh price to takes a uh into account is that the function is node so i was like to conclude at this point um stating that i have presented to uh two algorithms for and uh recovery of signals some social and that also uh with a variety of implications i mentioned that uh will but a if you about how do we do compared to state-of-the-art in the computer science community uh we observe that the we do a twenty two eighty percent better in terms of break addiction error or and of a a a a at are forty yeah and the variation of that there relative to those works uh which has the set of features and use the net autocorrelation correlation model and we believe the that's due to two reasons the first one is the then to can see the the social influences the fact of all them with if liz is a factor um of of all the members of the social community which we believe can into use a certain amount of noise you know where estimation where is to if we do things locally which in each neighbourhood and computing features is not always easy and um i we i why believe that it is in flames alters of buying the performance so their algorithm to much to the the specific date that the the use in our case the conversion of while got them is uh simply in but the social good of that is it's spectrum a unfortunately this or when we do a sparse reconstruction and coming from the goal compressed sensing community we we are still lacking uh um a good graph transform to to do so this type of estimation and the we also need to figure out how to better map this function on the graph the take take for but the advantage of though that graph transform so i will conclude with the sum i the management thank you a no from oh i'm so i yes i yes i a oh yes yes yes at each iteration a i yes um um but uh uh it's it's normal to want so like uh uh i i take their preferences and i you know i say my but if an it's the like by to the preferences of my neighbours and there are also proportional to this way describing house see and we are or not no no no no no no i'm sorry i didn't yes yes yeah really matter okay