Wednesday, February 25, 2015

Link Prediction using Network based Inference - A quick matrix based implementation

I explored a paper proposed by Zhou etal used Network based Inference(NBI) method to predict missing links in bipartite network and was thinking a lot how to implement using some simple matrix ways. I have taken the pic below from Zhou paper above  to explain the idea .Given the bipartite graph , a two phase resource transfer Information from  X(x,y,z) set of nodes gets distributed to Y set of nodes and then again goes back to resource X .  This process allows us to define a technique for the calculation of the weight matrix W.  In 2010 a modified version of this approach is proposed in Solving the apparent diversity-accuracy dilemma of recommender systems which used a modified Hybrid algorithm in which the functions defined in NBI and HeatS are combined in connection with a parameter called λ.

In this post i am going to implement the algorithm how does this work using simple matrix method in R. Interested readers must see those publications for the mathematical equations explained. Before going a bit further , if we are given a weight matrix W( which is calculated using the algorithms above) and the adjacency matrix A of the bipartite network, it is possible to compute the recommendation matrix R using the equation below, where W is n x n matrix and A is n x m matrix .

                                                                               R = W.A      (1)

The R list is then sorted in a descending order with respect to the score.

We use this kind of calculations in chemo-genomics predictions and also other bipartite type data. When doing Drug target prediction we can use W is as the sequence similarity matrix and A as the Drug target adjacency matrix to obtain recommendation of targets based on sequence similarity . Similarity W can be a compound similarity matrix and A the bipartite compound target matrix. Now we can use equation (1) above to get recommendations of compounds given a sequence of interest. This trick of using matrix just blowed my mind off !! Isn't it cool ?

Now for the functions here it goes below. If you are using the codes do let me know the results how does it work. My next post would be integrating similarity matrices information along with the degree information into W.

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