31:T522,md`# Collaborative Filtering One of the simplest recommender systems imaginable is user-based colaborative filtering. The concept is to find users with similar tastes and then recommend items that they also liked. There are many variations of this algorithm and more advanced approaches. See for example this [tutorial](http://technocalifornia.blogspot.com/2014/08/introduction-to-recommender-systems-4.html?m=1&from=singlemessage&isappinstalled=0). For this simple implementation we will use Pearson correlation as the measure of similarity between users. This is defined as: ${tex.block`sim(a, b) = {\sum_{m \in movies} (r_{a,m}- \overline{r}_a ) (r_{b,m}- \overline{r}_b ) \over \sqrt{ \sum_{m \in movies} (r_{a,m}- \overline{r}_a )^2} \sqrt{ \sum_{m \in movies} (r_{b,m}- \overline{r}_b )^2}}`} where ${tex`r_{a,m}`} is the rating of movie ${tex`m`} by user ${tex`a`}. We will give an unrated movie a recommendation score by finding the most similar user that has rated the movie and use this rating. For a larger example it would make sense to use a weighted average of a group of similar users. It is also possible to make adjustment for the bias of users - some users tend to give higher ratings than others. Choose which user to see recommendation for. The red numbers are the recommendation scores: `32:T4a5,pearson = { var pearson=[]; for(let i=0; ix.title==movies[j])[0].ratings; if(user in movie_ratings && selectedUser in movie_ratings) { pairs.push([movie_ratings[user], movie_ratings[selectedUser] ]); } } if(pairs.length>2) { var mean_user=0; var mean_selecteduser=0; for(var j=0; jx.title==movies[j])[0].imgurl+"' />" t+=movies[j]; t+="
("+data.filter(x=>x.title==movies[j])[0].year+")"; t+=""; } t+="Pearson
Corr."; t+=""; for(var i=0; i"+user+""; for(var j=0; j"; if(user in data.filter(x=>x.title==movie)[0].ratings) { t+=data.filter(x=>x.title==movie)[0].ratings[user]; } else if (selectedUser==user) { var prediction=null; var best_correlation=-1000; for(var k=0; kx.title==movie)[0].ratings) { if(pearson[k] != null && !isNaN(pearson[k]) && pearson[k]>best_correlation) { prediction=data.filter(x=>x.title==movie)[0].ratings[users[k]]; best_correlation=pearson[k]; } } } if(prediction) { t+=""+prediction+""; } } t+=""; } if(pearson[i]) { t+=""+(pearson[i]).toFixed(2)+""; } else { t+=""; } t+=""; } t+=""; return t; }34:T860,data = [{ title: "West Side Story", year: 1961, imgurl: "https://m.media-amazon.com/images/M/MV5BMTM0NDAxOTI5MF5BMl5BanBnXkFtZTcwNjI4Mjg3NA@@._V1_UX140_CR0,0,140,209_AL_.jpg", ratings: {A: 2, D:1, H: 5, B: 1, C:2, I: 5, J: 4, G: 5} }, { title: "Rocky", year: 1976, imgurl: "https://m.media-amazon.com/images/M/MV5BMTY5MDMzODUyOF5BMl5BanBnXkFtZTcwMTQ3NTMyNA@@._V1_UX140_CR0,0,140,209_AL_.jpg", ratings: {B: 2, D: 2, E: 3, H: 5, J: 5} }, { title: "Jaws", year: 1975, imgurl: "https://m.media-amazon.com/images/M/MV5BMmVmODY1MzEtYTMwZC00MzNhLWFkNDMtZjAwM2EwODUxZTA5XkEyXkFqcGdeQXVyNTAyODkwOQ@@._V1_UX140_CR0,0,140,209_AL_.jpg", ratings: {B: 2, D:3, A: 2, I: 3, J: 3, C: 3, H: 5, G: 4} }, { title: "Jurassic Park", year: 1993, imgurl: "https://m.media-amazon.com/images/M/MV5BMjM2MDgxMDg0Nl5BMl5BanBnXkFtZTgwNTM2OTM5NDE@._V1_UX140_CR0,0,140,209_AL_.jpg", ratings: {B: 2, D: 1, F: 2, E: 2, J: 4, C: 2, I: 5} }, { title: "Inception", year: 2010, imgurl: "https://m.media-amazon.com/images/M/MV5BMjAxMzY3NjcxNF5BMl5BanBnXkFtZTcwNTI5OTM0Mw@@._V1_UY209_CR0,0,140,209_AL_.jpg", ratings: {A: 4, F: 2, D: 3, E: 3, C: 5, F: 4, G: 3} }, { title: "Gravity", year: 2013, imgurl: "https://m.media-amazon.com/images/M/MV5BNjE5MzYwMzYxMF5BMl5BanBnXkFtZTcwOTk4MTk0OQ@@._V1_UY209_CR0,0,140,209_AL_.jpg", ratings: {F: 3, B: 4, D: 5, G: 1, C: 4, F: 2} }, { title: "Interstellar", year: 2014, imgurl: "https://m.media-amazon.com/images/M/MV5BZjdkOTU3MDktN2IxOS00OGEyLWFmMjktY2FiMmZkNWIyODZiXkEyXkFqcGdeQXVyMTMxODk2OTU@._V1_UY209_CR0,0,140,209_AL_.jpg", ratings: {A: 5, B: 5, G: 3, H: 1, C: 5, F: 3} }, { title: "Ex Machina", year: 2014, imgurl: "https://m.media-amazon.com/images/M/MV5BMTUxNzc0OTIxMV5BMl5BanBnXkFtZTgwNDI3NzU2NDE@._V1_UY209_CR0,0,140,209_AL_.jpg", ratings: {A: 4, B: 5, I: 3, E: 4, J: 1, F: 3} } ]35:[] 2f:{"title":"Collaborative Filtering","cells":[{"id":0,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":91,"value":"viewof selectedUser=html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":35,"value":"html`${t}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":108,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":26,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":27,"value":"movies={\n return data.map(x => x.title).sort();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"users={\n var userset=new Set();\n for(let i=0; i