was not critical. We choose a value of 100 because this is the The Als is considered stable after iterating for ten maximum overlap expected iterations without changing in size. Stabilisation thus means hat a sufficient number of good neighbours have been Neighbourhood Selection identified and therefore a prediction can be made. Poor For a Simple Pearson predictor, neighbourhood selection neighbours would be expected to drop out of the Als after a means simply choosing the best k(absolute) correlation few iterations scores,where k is the neighbourhood size. Not every Once the als has stabilised using the above algorithm, w potential neighbour will have rated the film to be predicted. use the antibody concentration to weigh the neighbours Reviewers who did not vote on the film are not added to the However, early experiments showed that the most recently neighbourhood dded antibodies were at a disadvantage compared to earlier antibodies. This is because they have had no time to mature For the Als predictor, a more involved procedure is required: (i.e. increase in concentration). Likewise, the earliest antibodies had saturated. To overcome this we reset the Initialise AIs concentrations and allow a limited run of the ais to Encode user for whom to make predictions as ar differentiate the concentrations. WHILE(AIS not stabilised )&( Reviewers avai Add next user as an antibody ab Reset al Calculate matching scores between Ab and Ag all antibodies to initial concentrations) WHILE Calculate matching scores between Ab and other antibodies ntibody at maximum concentration) DO WHILE (AIS at full size)&(AlS not stable)DO OD Iterate AIs OD Prediction We predict a rating P, by using a weighted average over N, Dur AIS behaves as follows: At each step (iteration)an the neighbourhood of u, which was taken as the entire AIS antibodys concentration is increased by an amount amount which depends on its matching to other antibodies In p,=i+R n(v-F) y (4) bsence of either, an antibodys concentration will slowly decrease over time. Antibodies with a sufficiently low concentration are removed from the system, whereas wom=Ia, r, (NB relative not absolute) antibodies with a high concentration may saturate. An AIs iteration is governed by the following equation: Where Wu is the weight between users u and 1, ran is the correlation score between u and v, and xr is the concentration tibody death of the antibody corresponding to user v. dh stimulation)(su pression)(rate allanton kmxy-∑mxx一kx (3) Prediction Accuracy: We take the mean absolute error number of pre k ,= Stimulation, ka k, Death rate ∑ actual- predicted N= Number antibodies MAE= (5) x or y)=concentration of antibody (or antigen) Mean number of recommendations: This is the tota This is a slightly modified version of Farmer Is number of unique films rated by the neighbours quation [ 8]. In particular, the first term is simplified as we only have one antigen, and we normalise the suppression Mean overlap size: This is the number of recommendations term to allow a 'like for like'comparison between the that the user has also seen different rate constants. k, and k, were varied as described in the next section. k, was fixed at 0. 1, while the concentration Mean accuracy of recommendations: Each overlapped film range was set at 0-100 (initially 10). We fixed N at 100. The has an actual vote(from the antigen) and a predicted vote matching function is the absolute value of the Pearson (from the neighbours). The overlapped films were ranked or correlation measure. This allows us to have both positively both actual and predicted vote, breaking ties by movie ID and negatively correlated users in our neighbourhood, which The two ranked lists were compared using Kendalls Tau t increases the pool of neighbours available to us This measure reflects the level of concordance in the lists bywas not critical. We choose a value of 100 because this is the maximum overlap expected. Neighbourhood Selection For a Simple Pearson predictor, neighbourhood selection means simply choosing the best k (absolute) correlation scores, where k is the neighbourhood size. Not every potential neighbour will have rated the film to be predicted. Reviewers who did not vote on the film are not added to the neighbourhood. For the AIS predictor, a more involved procedure is required: Initialise AIS Encode user for whom to make predictions as antigen Ag WHILE (AIS not stabilised) & (Reviewers available) DO Add next user as an antibody Ab Calculate matching scores between Ab and Ag Calculate matching scores between Ab and other antibodies WHILE (AIS at full size) & (AIS not stable) DO Iterate AIS OD OD Our AIS behaves as follows: At each step (iteration) an antibody’s concentration is increased by an amount dependent on its matching to the antigen and decreased by an amount which depends on its matching to other antibodies. In absence of either, an antibody’s concentration will slowly decrease over time. Antibodies with a sufficiently low concentration are removed from the system, whereas antibodies with a high concentration may saturate. An AIS iteration is governed by the following equation: ( ) ( ) , , )3( 1 2 3 3 1 2 1 x or y concentration of antibody or antigen N Number antibodies k Stimulation k Suppression k Death Rate m r m x x k x N k k m x y rate death su ppression antibody stimulation antigen dt dx i ij i N j i i ij i j i = = = = = = = − −         −        −        = ∑− This is a slightly modified version of Farmer et al’s equation [8]. In particular, the first term is simplified as we only have one antigen, and we normalise the suppression term to allow a ‘like for like’ comparison between the different rate constants. k1 and k2 were varied as described in the next section. k3 was fixed at 0.1, while the concentration range was set at 0–100 (initially 10). We fixed N at 100. The matching function is the absolute value of the Pearson correlation measure. This allows us to have both positively and negatively correlated users in our neighbourhood, which increases the pool of neighbours available to us. The AIS is considered stable after iterating for ten iterations without changing in size. Stabilisation thus means that a sufficient number of ‘good’ neighbours have been identified and therefore a prediction can be made. ‘Poor’ neighbours would be expected to drop out of the AIS after a few iterations. Once the AIS has stabilised using the above algorithm, we use the antibody concentration to weigh the neighbours. However, early experiments showed that the most recently added antibodies were at a disadvantage compared to earlier antibodies. This is because they have had no time to mature (i.e. increase in concentration). Likewise, the earliest antibodies had saturated. To overcome this, we reset the concentrations and allow a limited run of the AIS to differentiate the concentrations: Reset AIS (set all antibodies to initial concentrations) WHILE (No antibody at maximum concentration) DO Iterate AIS OD Prediction We predict a rating pi by using a weighted average over N, the neighbourhood of u, which was taken as the entire AIS. ( ) ( ) )4( w r x NB relative not absolute w w v v p u uv uv v v N uv v N uv i i = − = + ∑ ∑ ∈ ∈ Where wuv is the weight between users u and v, ruv is the correlation score between u and v, and xv is the concentration of the antibody corresponding to user v. Evaluation Prediction Accuracy: We take the mean absolute error, where np is the number of predictions: )5( np actual predicted MAE ∑ − = Mean number of recommendations: This is the total number of unique films rated by the neighbours. Mean overlap size: This is the number of recommendations that the user has also seen. Mean accuracy of recommendations: Each overlapped film has an actual vote (from the antigen) and a predicted vote (from the neighbours). The overlapped films were ranked on both actual and predicted vote, breaking ties by movie ID. The two ranked lists were compared using Kendall’s Tau τ. This measure reflects the level of concordance in the lists by