movie-recommendation-system-using-r.ipynb

{"metadata":{"kernelspec":{"name":"ir","display_name":"R","language":"R"},"language_info":{"name":"R","codemirror_mode":"r","pygments_lexer":"r","mimetype":"text/x-r-source","file_extension":".r","version":"4.0.5"}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"markdown","source":"# What Is a Recommendation System?\n- A recommendation system is an artificial intelligence or AI algorithm, usually associated with machine learning, that uses Big Data to suggest or recommend additional products to consumers. These can be based on various criteria, including past purchases, search history, demographic information, and other factors. Recommender systems are highly useful as they help users discover products and services they might otherwise have not found on their own.\n\n- Recommender systems are trained to understand the preferences, previous decisions, and characteristics of people and products using data gathered about their interactions. These include impressions, clicks, likes, and purchases. Because of their capability to predict consumer interests and desires on a highly personalized level, recommender systems are a favorite with content and product providers. They can drive consumers to just about any product or service that interests them, from books to videos to health classes to clothing.\n\n# What is a product recommendation\n- In the product discovery phase, you can use more than one tool to show the consumer the most suitable options, offer the right personalized products, and design a satisfying experience. Product recommendations are one of the most powerful of these tools.\n\n# Advantage of product recommendations\n- Recommendations for related products: \n    - Provides a list of related products that are similar to the chosen one, either in use or in price which creates a cross-selling opportunity. For example at the cart step, offering complementary products to the ones already added to the cart, you can encourage your customer to shop a little bit more.\n- Recommendations based on past purchases: \n    - If you already bought a digital camera, a recommendation of its lenses might make sense.\n- Recommendations based on search: \n    - Product recommendation engines may look at search history to suggest products based on terms consumers have used.\n\n# Types of Recommendation Systems:\n- **Collaborative filtering** algorithms recommend items (this is the filtering part) based on preference information from many users (this is the collaborative part). \n\n- **Content filtering**, by contrast, uses the attributes or features of an item  (this is the content part) to recommend other items similar to the user’s preferences. \n\n- **Hybrid recommender systems** combine the advantages of the types above to create a more comprehensive recommending system.\n\n- **Context filtering** includes users’ contextual information in the recommendation process. \n\n# Recommendation Engine Benefits\n- Drive Traffic\n    - Through personalized email messages and targeted blasts, a recommendation engine can encourage elevated amounts of traffic to your site, thus increasing the opportunity to scoop up more data to further enrich a customer profile.\n\n- Deliver Relevant Content\n    - By analyzing the customer’s current site usage and previous browsing history, a recommendation engine can deliver relevant product recommendations as he or she shops based on said profile. The data is collected in real time so the software can react as shopping habits change on the fly.\n\n- Engage Shoppers\n    - Shoppers become more engaged when personalized product recommendations are made to them across the customer journey. Through individualized product recs, customers are able to delve more deeply into your product line without having to dive into (and very likely get lost in) an ecommerce rabbit hole.\n\n- Convert Shoppers to Customers\n    - Converting shoppers into customers takes a special touch. Personalized interactions from a recommendation engine show your customer that he or she is valued as an individual, in turn, engendering long-term loyalty.\n\n- Increase Average Order Value\n    - Average order values typically go up when an engine is leveraged to display personalized options as shoppers are more willing to spend generously on items they thoroughly covet.\n\n- Increase Number of Items per Order\n    - In addition to the average order value rising, the number of items per order also typically rises when an engine is employed. When the customer is shown options that meet his or her interest, they are far more likely to add items to to their active purchase cart.\n\n- Control Merchandising and Inventory Rules\n    - A recommendation engine can add your marketing and inventory control directives to a customer’s profile to feature products that are on clearance or overstocked so as to avoid unnecessary shopping friction and tone deafness.\n\n- Reduce Workload and Overhead\n    - The volume of data required to create a personal shopping experience for each customer is usually far too large to be managed manually. Using an engine automates this process, easing the workload for your IT staff.\n\n- A Recommendation Engine Provides Reports\n    - Detailed reports are an integral part of a personalization system. Accurate and up-to-the-minute reporting will allow you to make informed decisions about the direction of a campaign or the structure of a product page.\n\n- Offer Advice and Direction\n    - An experienced recommendation provider like Kibo can offer advice on how to use the data collected from your recommendation engine. Acting as a partner and a consultant, the provider should have the industry know-how needed to help guide you and your ecommerce site to a prosperous future.\n\n\nDataset: [MovieLens](https://grouplens.org/datasets/movielens/)\n\n### The main goal of this machine learning project is to build a recommendation system that recommends movies to users.","metadata":{"_uuid":"051d70d956493feee0c6d64651c6a088724dca2a","_execution_state":"idle"}},{"cell_type":"markdown","source":"# Importing Libraries","metadata":{}},{"cell_type":"code","source":"library(recommenderlab)  # Lab for Developing and Testing Recommender Algorithms\nlibrary(ggplot2)   # ggplot2 is a system for declaratively creating graphics, based on The Grammar of Graphics.                  \nlibrary(data.table)  # data.table is an R package that provides an enhanced version of data.frames, which are the standard data structure for storing data in base R.\nlibrary(reshape2)  # reshape2 is an R package written by Hadley Wickham that makes it easy to transform data between wide and long formats.","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:16:55.861619Z","iopub.execute_input":"2023-02-08T07:16:55.867693Z","iopub.status.idle":"2023-02-08T07:16:58.645494Z"},"trusted":true},"execution_count":1,"outputs":[{"name":"stderr","text":"Loading required package: Matrix\n\nLoading required package: arules\n\n\nAttaching package: ‘arules’\n\n\nThe following objects are masked from ‘package:base’:\n\n    abbreviate, write\n\n\nLoading required package: proxy\n\n\nAttaching package: ‘proxy’\n\n\nThe following object is masked from ‘package:Matrix’:\n\n    as.matrix\n\n\nThe following objects are masked from ‘package:stats’:\n\n    as.dist, dist\n\n\nThe following object is masked from ‘package:base’:\n\n    as.matrix\n\n\nLoading required package: registry\n\nRegistered S3 methods overwritten by 'registry':\n  method               from \n  print.registry_field proxy\n  print.registry_entry proxy\n\n\nAttaching package: ‘reshape2’\n\n\nThe following objects are masked from ‘package:data.table’:\n\n    dcast, melt\n\n\n","output_type":"stream"}]},{"cell_type":"markdown","source":"# Retrieving the Data","metadata":{}},{"cell_type":"code","source":"movie_data <- read.csv(\"/kaggle/input/movielens-dataset-movies/movies.csv\",stringsAsFactors=FALSE)\nrating_data <- read.csv(\"/kaggle/input/movielens-dataset-for-recommendation-system/ratings.csv\")\nstr(movie_data)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:16:58.647134Z","iopub.execute_input":"2023-02-08T07:16:58.670119Z","iopub.status.idle":"2023-02-08T07:16:58.985747Z"},"trusted":true},"execution_count":2,"outputs":[{"name":"stdout","text":"'data.frame':\t10329 obs. of  3 variables:\n $ movieId: int  1 2 3 4 5 6 7 8 9 10 ...\n $ title  : chr  \"Toy Story (1995)\" \"Jumanji (1995)\" \"Grumpier Old Men (1995)\" \"Waiting to Exhale (1995)\" ...\n $ genres : chr  \"Adventure|Animation|Children|Comedy|Fantasy\" \"Adventure|Children|Fantasy\" \"Comedy|Romance\" \"Comedy|Drama|Romance\" ...\n","output_type":"stream"}]},{"cell_type":"code","source":"summary(movie_data)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:16:58.987497Z","iopub.execute_input":"2023-02-08T07:16:58.988548Z","iopub.status.idle":"2023-02-08T07:16:59.003520Z"},"trusted":true},"execution_count":3,"outputs":[{"output_type":"display_data","data":{"text/plain":"    movieId          title              genres         \n Min.   :     1   Length:10329       Length:10329      \n 1st Qu.:  3240   Class :character   Class :character  \n Median :  7088   Mode  :character   Mode  :character  \n Mean   : 31924                                        \n 3rd Qu.: 59900                                        \n Max.   :149532                                        "},"metadata":{}}]},{"cell_type":"code","source":"head(movie_data)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:16:59.005362Z","iopub.execute_input":"2023-02-08T07:16:59.006367Z","iopub.status.idle":"2023-02-08T07:16:59.027331Z"},"trusted":true},"execution_count":4,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 3</caption>\n<thead>\n\t<tr><th></th><th scope=col>movieId</th><th scope=col>title</th><th scope=col>genres</th></tr>\n\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>1</td><td>Toy Story (1995)                  </td><td>Adventure|Animation|Children|Comedy|Fantasy</td></tr>\n\t<tr><th scope=row>2</th><td>2</td><td>Jumanji (1995)                    </td><td>Adventure|Children|Fantasy                 </td></tr>\n\t<tr><th scope=row>3</th><td>3</td><td>Grumpier Old Men (1995)           </td><td>Comedy|Romance                             </td></tr>\n\t<tr><th scope=row>4</th><td>4</td><td>Waiting to Exhale (1995)          </td><td>Comedy|Drama|Romance                       </td></tr>\n\t<tr><th scope=row>5</th><td>5</td><td>Father of the Bride Part II (1995)</td><td>Comedy                                     </td></tr>\n\t<tr><th scope=row>6</th><td>6</td><td>Heat (1995)                       </td><td>Action|Crime|Thriller                      </td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 3\n\n| <!--/--> | movieId &lt;int&gt; | title &lt;chr&gt; | genres &lt;chr&gt; |\n|---|---|---|---|\n| 1 | 1 | Toy Story (1995)                   | Adventure|Animation|Children|Comedy|Fantasy |\n| 2 | 2 | Jumanji (1995)                     | Adventure|Children|Fantasy                  |\n| 3 | 3 | Grumpier Old Men (1995)            | Comedy|Romance                              |\n| 4 | 4 | Waiting to Exhale (1995)           | Comedy|Drama|Romance                        |\n| 5 | 5 | Father of the Bride Part II (1995) | Comedy                                      |\n| 6 | 6 | Heat (1995)                        | Action|Crime|Thriller                       |\n\n","text/latex":"A data.frame: 6 × 3\n\\begin{tabular}{r|lll}\n  & movieId & title & genres\\\\\n  & <int> & <chr> & <chr>\\\\\n\\hline\n\t1 & 1 & Toy Story (1995)                   & Adventure\\textbar{}Animation\\textbar{}Children\\textbar{}Comedy\\textbar{}Fantasy\\\\\n\t2 & 2 & Jumanji (1995)                     & Adventure\\textbar{}Children\\textbar{}Fantasy                 \\\\\n\t3 & 3 & Grumpier Old Men (1995)            & Comedy\\textbar{}Romance                             \\\\\n\t4 & 4 & Waiting to Exhale (1995)           & Comedy\\textbar{}Drama\\textbar{}Romance                       \\\\\n\t5 & 5 & Father of the Bride Part II (1995) & Comedy                                     \\\\\n\t6 & 6 & Heat (1995)                        & Action\\textbar{}Crime\\textbar{}Thriller                      \\\\\n\\end{tabular}\n","text/plain":"  movieId title                             \n1 1       Toy Story (1995)                  \n2 2       Jumanji (1995)                    \n3 3       Grumpier Old Men (1995)           \n4 4       Waiting to Exhale (1995)          \n5 5       Father of the Bride Part II (1995)\n6 6       Heat (1995)                       \n  genres                                     \n1 Adventure|Animation|Children|Comedy|Fantasy\n2 Adventure|Children|Fantasy                 \n3 Comedy|Romance                             \n4 Comedy|Drama|Romance                       \n5 Comedy                                     \n6 Action|Crime|Thriller                      "},"metadata":{}}]},{"cell_type":"code","source":"summary(rating_data)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:16:59.029094Z","iopub.execute_input":"2023-02-08T07:16:59.030128Z","iopub.status.idle":"2023-02-08T07:16:59.067580Z"},"trusted":true},"execution_count":5,"outputs":[{"output_type":"display_data","data":{"text/plain":"     userId         movieId           rating        timestamp        \n Min.   :  1.0   Min.   :     1   Min.   :0.500   Min.   :8.286e+08  \n 1st Qu.:192.0   1st Qu.:  1073   1st Qu.:3.000   1st Qu.:9.711e+08  \n Median :383.0   Median :  2497   Median :3.500   Median :1.115e+09  \n Mean   :364.9   Mean   : 13381   Mean   :3.517   Mean   :1.130e+09  \n 3rd Qu.:557.0   3rd Qu.:  5991   3rd Qu.:4.000   3rd Qu.:1.275e+09  \n Max.   :668.0   Max.   :149532   Max.   :5.000   Max.   :1.452e+09  "},"metadata":{}}]},{"cell_type":"code","source":"head(rating_data)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:16:59.069330Z","iopub.execute_input":"2023-02-08T07:16:59.070375Z","iopub.status.idle":"2023-02-08T07:16:59.088294Z"},"trusted":true},"execution_count":6,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 4</caption>\n<thead>\n\t<tr><th></th><th scope=col>userId</th><th scope=col>movieId</th><th scope=col>rating</th><th scope=col>timestamp</th></tr>\n\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>1</td><td> 16</td><td>4.0</td><td>1217897793</td></tr>\n\t<tr><th scope=row>2</th><td>1</td><td> 24</td><td>1.5</td><td>1217895807</td></tr>\n\t<tr><th scope=row>3</th><td>1</td><td> 32</td><td>4.0</td><td>1217896246</td></tr>\n\t<tr><th scope=row>4</th><td>1</td><td> 47</td><td>4.0</td><td>1217896556</td></tr>\n\t<tr><th scope=row>5</th><td>1</td><td> 50</td><td>4.0</td><td>1217896523</td></tr>\n\t<tr><th scope=row>6</th><td>1</td><td>110</td><td>4.0</td><td>1217896150</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 4\n\n| <!--/--> | userId &lt;int&gt; | movieId &lt;int&gt; | rating &lt;dbl&gt; | timestamp &lt;int&gt; |\n|---|---|---|---|---|\n| 1 | 1 |  16 | 4.0 | 1217897793 |\n| 2 | 1 |  24 | 1.5 | 1217895807 |\n| 3 | 1 |  32 | 4.0 | 1217896246 |\n| 4 | 1 |  47 | 4.0 | 1217896556 |\n| 5 | 1 |  50 | 4.0 | 1217896523 |\n| 6 | 1 | 110 | 4.0 | 1217896150 |\n\n","text/latex":"A data.frame: 6 × 4\n\\begin{tabular}{r|llll}\n  & userId & movieId & rating & timestamp\\\\\n  & <int> & <int> & <dbl> & <int>\\\\\n\\hline\n\t1 & 1 &  16 & 4.0 & 1217897793\\\\\n\t2 & 1 &  24 & 1.5 & 1217895807\\\\\n\t3 & 1 &  32 & 4.0 & 1217896246\\\\\n\t4 & 1 &  47 & 4.0 & 1217896556\\\\\n\t5 & 1 &  50 & 4.0 & 1217896523\\\\\n\t6 & 1 & 110 & 4.0 & 1217896150\\\\\n\\end{tabular}\n","text/plain":"  userId movieId rating timestamp \n1 1       16     4.0    1217897793\n2 1       24     1.5    1217895807\n3 1       32     4.0    1217896246\n4 1       47     4.0    1217896556\n5 1       50     4.0    1217896523\n6 1      110     4.0    1217896150"},"metadata":{}}]},{"cell_type":"markdown","source":"# Data Pre-processing\n\n- From the above table, we observe that the userId column, as well as the movie I'd column, consists of integers. Furthermore, we need to convert the genres present in the movie_data data frame into a more usable format for the users. In order to do so, we will first create a one-hot encoding to create a matrix that comprises corresponding genres for each of the films.","metadata":{}},{"cell_type":"code","source":"movie_genre <- as.data.frame(movie_data$genres, stringsAsFactors=FALSE)\nlibrary(data.table)\nmovie_genre2 <- as.data.frame(tstrsplit(movie_genre[,1], '[|]', \n                                   type.convert=TRUE), \n                         stringsAsFactors=FALSE)\ncolnames(movie_genre2) <- c(1:10)\nlist_genre <- c(\"Action\", \"Adventure\", \"Animation\", \"Children\", \n                \"Comedy\", \"Crime\",\"Documentary\", \"Drama\", \"Fantasy\",\n                \"Film-Noir\", \"Horror\", \"Musical\", \"Mystery\",\"Romance\",\n                \"Sci-Fi\", \"Thriller\", \"War\", \"Western\")\ngenre_mat1 <- matrix(0,10330,18)\ngenre_mat1[1,] <- list_genre\ncolnames(genre_mat1) <- list_genre\nfor (index in 1:nrow(movie_genre2)) {\n  for (col in 1:ncol(movie_genre2)) {\n    gen_col = which(genre_mat1[1,] == movie_genre2[index,col]) \n    genre_mat1[index+1,gen_col] <- 1\n}\n}\ngenre_mat2 <- as.data.frame(genre_mat1[-1,], stringsAsFactors=FALSE) #remove first row, which was the genre list\nfor (col in 1:ncol(genre_mat2)) {\n  genre_mat2[,col] <- as.integer(genre_mat2[,col]) #convert from characters to integers\n} \nstr(genre_mat2)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:16:59.089961Z","iopub.execute_input":"2023-02-08T07:16:59.090934Z","iopub.status.idle":"2023-02-08T07:17:01.291998Z"},"trusted":true},"execution_count":7,"outputs":[{"name":"stdout","text":"'data.frame':\t10329 obs. of  18 variables:\n $ Action     : int  0 0 0 0 0 1 0 0 1 1 ...\n $ Adventure  : int  1 1 0 0 0 0 0 1 0 1 ...\n $ Animation  : int  1 0 0 0 0 0 0 0 0 0 ...\n $ Children   : int  1 1 0 0 0 0 0 1 0 0 ...\n $ Comedy     : int  1 0 1 1 1 0 1 0 0 0 ...\n $ Crime      : int  0 0 0 0 0 1 0 0 0 0 ...\n $ Documentary: int  0 0 0 0 0 0 0 0 0 0 ...\n $ Drama      : int  0 0 0 1 0 0 0 0 0 0 ...\n $ Fantasy    : int  1 1 0 0 0 0 0 0 0 0 ...\n $ Film-Noir  : int  0 0 0 0 0 0 0 0 0 0 ...\n $ Horror     : int  0 0 0 0 0 0 0 0 0 0 ...\n $ Musical    : int  0 0 0 0 0 0 0 0 0 0 ...\n $ Mystery    : int  0 0 0 0 0 0 0 0 0 0 ...\n $ Romance    : int  0 0 1 1 0 0 1 0 0 0 ...\n $ Sci-Fi     : int  0 0 0 0 0 0 0 0 0 0 ...\n $ Thriller   : int  0 0 0 0 0 1 0 0 0 1 ...\n $ War        : int  0 0 0 0 0 0 0 0 0 0 ...\n $ Western    : int  0 0 0 0 0 0 0 0 0 0 ...\n","output_type":"stream"}]},{"cell_type":"code","source":"# Create a ‘search matrix’ that will allow us to perform an easy search of the films by specifying the genre present in our list.\nSearchMatrix <- cbind(movie_data[,1:2], genre_mat2[])\nhead(SearchMatrix)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:01.294545Z","iopub.execute_input":"2023-02-08T07:17:01.295969Z","iopub.status.idle":"2023-02-08T07:17:01.328790Z"},"trusted":true},"execution_count":8,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 20</caption>\n<thead>\n\t<tr><th></th><th scope=col>movieId</th><th scope=col>title</th><th scope=col>Action</th><th scope=col>Adventure</th><th scope=col>Animation</th><th scope=col>Children</th><th scope=col>Comedy</th><th scope=col>Crime</th><th scope=col>Documentary</th><th scope=col>Drama</th><th scope=col>Fantasy</th><th scope=col>Film-Noir</th><th scope=col>Horror</th><th scope=col>Musical</th><th scope=col>Mystery</th><th scope=col>Romance</th><th scope=col>Sci-Fi</th><th scope=col>Thriller</th><th scope=col>War</th><th scope=col>Western</th></tr>\n\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>1</td><td>Toy Story (1995)                  </td><td>0</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n\t<tr><th scope=row>2</th><td>2</td><td>Jumanji (1995)                    </td><td>0</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n\t<tr><th scope=row>3</th><td>3</td><td>Grumpier Old Men (1995)           </td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n\t<tr><th scope=row>4</th><td>4</td><td>Waiting to Exhale (1995)          </td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n\t<tr><th scope=row>5</th><td>5</td><td>Father of the Bride Part II (1995)</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr>\n\t<tr><th scope=row>6</th><td>6</td><td>Heat (1995)                       </td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 20\n\n| <!--/--> | movieId &lt;int&gt; | title &lt;chr&gt; | Action &lt;int&gt; | Adventure &lt;int&gt; | Animation &lt;int&gt; | Children &lt;int&gt; | Comedy &lt;int&gt; | Crime &lt;int&gt; | Documentary &lt;int&gt; | Drama &lt;int&gt; | Fantasy &lt;int&gt; | Film-Noir &lt;int&gt; | Horror &lt;int&gt; | Musical &lt;int&gt; | Mystery &lt;int&gt; | Romance &lt;int&gt; | Sci-Fi &lt;int&gt; | Thriller &lt;int&gt; | War &lt;int&gt; | Western &lt;int&gt; |\n|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n| 1 | 1 | Toy Story (1995)                   | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n| 2 | 2 | Jumanji (1995)                     | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n| 3 | 3 | Grumpier Old Men (1995)            | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |\n| 4 | 4 | Waiting to Exhale (1995)           | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |\n| 5 | 5 | Father of the Bride Part II (1995) | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n| 6 | 6 | Heat (1995)                        | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |\n\n","text/latex":"A data.frame: 6 × 20\n\\begin{tabular}{r|llllllllllllllllllll}\n  & movieId & title & Action & Adventure & Animation & Children & Comedy & Crime & Documentary & Drama & Fantasy & Film-Noir & Horror & Musical & Mystery & Romance & Sci-Fi & Thriller & War & Western\\\\\n  & <int> & <chr> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int> & <int>\\\\\n\\hline\n\t1 & 1 & Toy Story (1995)                   & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n\t2 & 2 & Jumanji (1995)                     & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n\t3 & 3 & Grumpier Old Men (1995)            & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n\t4 & 4 & Waiting to Exhale (1995)           & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\\\\n\t5 & 5 & Father of the Bride Part II (1995) & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\\n\t6 & 6 & Heat (1995)                        & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\\\\n\\end{tabular}\n","text/plain":"  movieId title                              Action Adventure Animation\n1 1       Toy Story (1995)                   0      1         1        \n2 2       Jumanji (1995)                     0      1         0        \n3 3       Grumpier Old Men (1995)            0      0         0        \n4 4       Waiting to Exhale (1995)           0      0         0        \n5 5       Father of the Bride Part II (1995) 0      0         0        \n6 6       Heat (1995)                        1      0         0        \n  Children Comedy Crime Documentary Drama Fantasy Film-Noir Horror Musical\n1 1        1      0     0           0     1       0         0      0      \n2 1        0      0     0           0     1       0         0      0      \n3 0        1      0     0           0     0       0         0      0      \n4 0        1      0     0           1     0       0         0      0      \n5 0        1      0     0           0     0       0         0      0      \n6 0        0      1     0           0     0       0         0      0      \n  Mystery Romance Sci-Fi Thriller War Western\n1 0       0       0      0        0   0      \n2 0       0       0      0        0   0      \n3 0       1       0      0        0   0      \n4 0       1       0      0        0   0      \n5 0       0       0      0        0   0      \n6 0       0       0      1        0   0      "},"metadata":{}}]},{"cell_type":"markdown","source":"### For the movie recommendation system to make sense of our ratings through recommended labs, we have to convert our matrix into a sparse matrix. This new matrix is of the class ‘realRatingMatrix’:","metadata":{}},{"cell_type":"code","source":"ratingMatrix <- dcast(rating_data, userId~movieId, value.var = \"rating\", na.rm=FALSE)\nratingMatrix <- as.matrix(ratingMatrix[,-1]) #remove userIds\n#Convert rating matrix into a recommenderlab sparse matrix\nratingMatrix <- as(ratingMatrix, \"realRatingMatrix\")\nratingMatrix","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:01.330618Z","iopub.execute_input":"2023-02-08T07:17:01.331717Z","iopub.status.idle":"2023-02-08T07:17:03.383208Z"},"trusted":true},"execution_count":9,"outputs":[{"output_type":"display_data","data":{"text/plain":"668 x 10325 rating matrix of class ‘realRatingMatrix’ with 105339 ratings."},"metadata":{}}]},{"cell_type":"markdown","source":"### Overview of some of the important parameters that provide us with various options for building recommendation systems for movies:","metadata":{}},{"cell_type":"code","source":"recommendation_model <- recommenderRegistry$get_entries(dataType = \"realRatingMatrix\")\nnames(recommendation_model)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:03.385038Z","iopub.execute_input":"2023-02-08T07:17:03.386096Z","iopub.status.idle":"2023-02-08T07:17:03.406733Z"},"trusted":true},"execution_count":10,"outputs":[{"output_type":"display_data","data":{"text/html":"<style>\n.list-inline {list-style: none; margin:0; padding: 0}\n.list-inline>li {display: inline-block}\n.list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n</style>\n<ol class=list-inline><li>'HYBRID_realRatingMatrix'</li><li>'ALS_realRatingMatrix'</li><li>'ALS_implicit_realRatingMatrix'</li><li>'IBCF_realRatingMatrix'</li><li>'LIBMF_realRatingMatrix'</li><li>'POPULAR_realRatingMatrix'</li><li>'RANDOM_realRatingMatrix'</li><li>'RERECOMMEND_realRatingMatrix'</li><li>'SVD_realRatingMatrix'</li><li>'SVDF_realRatingMatrix'</li><li>'UBCF_realRatingMatrix'</li></ol>\n","text/markdown":"1. 'HYBRID_realRatingMatrix'\n2. 'ALS_realRatingMatrix'\n3. 'ALS_implicit_realRatingMatrix'\n4. 'IBCF_realRatingMatrix'\n5. 'LIBMF_realRatingMatrix'\n6. 'POPULAR_realRatingMatrix'\n7. 'RANDOM_realRatingMatrix'\n8. 'RERECOMMEND_realRatingMatrix'\n9. 'SVD_realRatingMatrix'\n10. 'SVDF_realRatingMatrix'\n11. 'UBCF_realRatingMatrix'\n\n\n","text/latex":"\\begin{enumerate*}\n\\item 'HYBRID\\_realRatingMatrix'\n\\item 'ALS\\_realRatingMatrix'\n\\item 'ALS\\_implicit\\_realRatingMatrix'\n\\item 'IBCF\\_realRatingMatrix'\n\\item 'LIBMF\\_realRatingMatrix'\n\\item 'POPULAR\\_realRatingMatrix'\n\\item 'RANDOM\\_realRatingMatrix'\n\\item 'RERECOMMEND\\_realRatingMatrix'\n\\item 'SVD\\_realRatingMatrix'\n\\item 'SVDF\\_realRatingMatrix'\n\\item 'UBCF\\_realRatingMatrix'\n\\end{enumerate*}\n","text/plain":" [1] \"HYBRID_realRatingMatrix\"       \"ALS_realRatingMatrix\"         \n [3] \"ALS_implicit_realRatingMatrix\" \"IBCF_realRatingMatrix\"        \n [5] \"LIBMF_realRatingMatrix\"        \"POPULAR_realRatingMatrix\"     \n [7] \"RANDOM_realRatingMatrix\"       \"RERECOMMEND_realRatingMatrix\" \n [9] \"SVD_realRatingMatrix\"          \"SVDF_realRatingMatrix\"        \n[11] \"UBCF_realRatingMatrix\"        "},"metadata":{}}]},{"cell_type":"code","source":"lapply(recommendation_model, \"[[\", \"description\")\n# lapply() is a function that takes a vector,list or data frame as input and gives the output as list by appplying a certain operation on it.","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:03.408491Z","iopub.execute_input":"2023-02-08T07:17:03.409518Z","iopub.status.idle":"2023-02-08T07:17:03.426454Z"},"trusted":true},"execution_count":11,"outputs":[{"output_type":"display_data","data":{"text/html":"<dl>\n\t<dt>$HYBRID_realRatingMatrix</dt>\n\t\t<dd>'Hybrid recommender that aggegates several recommendation strategies using weighted averages.'</dd>\n\t<dt>$ALS_realRatingMatrix</dt>\n\t\t<dd>'Recommender for explicit ratings based on latent factors, calculated by alternating least squares algorithm.'</dd>\n\t<dt>$ALS_implicit_realRatingMatrix</dt>\n\t\t<dd>'Recommender for implicit data based on latent factors, calculated by alternating least squares algorithm.'</dd>\n\t<dt>$IBCF_realRatingMatrix</dt>\n\t\t<dd>'Recommender based on item-based collaborative filtering.'</dd>\n\t<dt>$LIBMF_realRatingMatrix</dt>\n\t\t<dd>'Matrix factorization with LIBMF via package recosystem (https://cran.r-project.org/web/packages/recosystem/vignettes/introduction.html).'</dd>\n\t<dt>$POPULAR_realRatingMatrix</dt>\n\t\t<dd>'Recommender based on item popularity.'</dd>\n\t<dt>$RANDOM_realRatingMatrix</dt>\n\t\t<dd>'Produce random recommendations (real ratings).'</dd>\n\t<dt>$RERECOMMEND_realRatingMatrix</dt>\n\t\t<dd>'Re-recommends highly rated items (real ratings).'</dd>\n\t<dt>$SVD_realRatingMatrix</dt>\n\t\t<dd>'Recommender based on SVD approximation with column-mean imputation.'</dd>\n\t<dt>$SVDF_realRatingMatrix</dt>\n\t\t<dd>'Recommender based on Funk SVD with gradient descend (https://sifter.org/~simon/journal/20061211.html).'</dd>\n\t<dt>$UBCF_realRatingMatrix</dt>\n\t\t<dd>'Recommender based on user-based collaborative filtering.'</dd>\n</dl>\n","text/markdown":"$HYBRID_realRatingMatrix\n:   'Hybrid recommender that aggegates several recommendation strategies using weighted averages.'\n$ALS_realRatingMatrix\n:   'Recommender for explicit ratings based on latent factors, calculated by alternating least squares algorithm.'\n$ALS_implicit_realRatingMatrix\n:   'Recommender for implicit data based on latent factors, calculated by alternating least squares algorithm.'\n$IBCF_realRatingMatrix\n:   'Recommender based on item-based collaborative filtering.'\n$LIBMF_realRatingMatrix\n:   'Matrix factorization with LIBMF via package recosystem (https://cran.r-project.org/web/packages/recosystem/vignettes/introduction.html).'\n$POPULAR_realRatingMatrix\n:   'Recommender based on item popularity.'\n$RANDOM_realRatingMatrix\n:   'Produce random recommendations (real ratings).'\n$RERECOMMEND_realRatingMatrix\n:   'Re-recommends highly rated items (real ratings).'\n$SVD_realRatingMatrix\n:   'Recommender based on SVD approximation with column-mean imputation.'\n$SVDF_realRatingMatrix\n:   'Recommender based on Funk SVD with gradient descend (https://sifter.org/~simon/journal/20061211.html).'\n$UBCF_realRatingMatrix\n:   'Recommender based on user-based collaborative filtering.'\n\n\n","text/latex":"\\begin{description}\n\\item[\\$HYBRID\\_realRatingMatrix] 'Hybrid recommender that aggegates several recommendation strategies using weighted averages.'\n\\item[\\$ALS\\_realRatingMatrix] 'Recommender for explicit ratings based on latent factors, calculated by alternating least squares algorithm.'\n\\item[\\$ALS\\_implicit\\_realRatingMatrix] 'Recommender for implicit data based on latent factors, calculated by alternating least squares algorithm.'\n\\item[\\$IBCF\\_realRatingMatrix] 'Recommender based on item-based collaborative filtering.'\n\\item[\\$LIBMF\\_realRatingMatrix] 'Matrix factorization with LIBMF via package recosystem (https://cran.r-project.org/web/packages/recosystem/vignettes/introduction.html).'\n\\item[\\$POPULAR\\_realRatingMatrix] 'Recommender based on item popularity.'\n\\item[\\$RANDOM\\_realRatingMatrix] 'Produce random recommendations (real ratings).'\n\\item[\\$RERECOMMEND\\_realRatingMatrix] 'Re-recommends highly rated items (real ratings).'\n\\item[\\$SVD\\_realRatingMatrix] 'Recommender based on SVD approximation with column-mean imputation.'\n\\item[\\$SVDF\\_realRatingMatrix] 'Recommender based on Funk SVD with gradient descend (https://sifter.org/\\textasciitilde{}simon/journal/20061211.html).'\n\\item[\\$UBCF\\_realRatingMatrix] 'Recommender based on user-based collaborative filtering.'\n\\end{description}\n","text/plain":"$HYBRID_realRatingMatrix\n[1] \"Hybrid recommender that aggegates several recommendation strategies using weighted averages.\"\n\n$ALS_realRatingMatrix\n[1] \"Recommender for explicit ratings based on latent factors, calculated by alternating least squares algorithm.\"\n\n$ALS_implicit_realRatingMatrix\n[1] \"Recommender for implicit data based on latent factors, calculated by alternating least squares algorithm.\"\n\n$IBCF_realRatingMatrix\n[1] \"Recommender based on item-based collaborative filtering.\"\n\n$LIBMF_realRatingMatrix\n[1] \"Matrix factorization with LIBMF via package recosystem (https://cran.r-project.org/web/packages/recosystem/vignettes/introduction.html).\"\n\n$POPULAR_realRatingMatrix\n[1] \"Recommender based on item popularity.\"\n\n$RANDOM_realRatingMatrix\n[1] \"Produce random recommendations (real ratings).\"\n\n$RERECOMMEND_realRatingMatrix\n[1] \"Re-recommends highly rated items (real ratings).\"\n\n$SVD_realRatingMatrix\n[1] \"Recommender based on SVD approximation with column-mean imputation.\"\n\n$SVDF_realRatingMatrix\n[1] \"Recommender based on Funk SVD with gradient descend (https://sifter.org/~simon/journal/20061211.html).\"\n\n$UBCF_realRatingMatrix\n[1] \"Recommender based on user-based collaborative filtering.\"\n"},"metadata":{}}]},{"cell_type":"markdown","source":"### Based Collaborative Filtering","metadata":{}},{"cell_type":"code","source":"recommendation_model$IBCF_realRatingMatrix$parameters","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:03.428076Z","iopub.execute_input":"2023-02-08T07:17:03.429037Z","iopub.status.idle":"2023-02-08T07:17:03.447232Z"},"trusted":true},"execution_count":12,"outputs":[{"output_type":"display_data","data":{"text/html":"<dl>\n\t<dt>$k</dt>\n\t\t<dd>30</dd>\n\t<dt>$method</dt>\n\t\t<dd>'cosine'</dd>\n\t<dt>$normalize</dt>\n\t\t<dd>'center'</dd>\n\t<dt>$normalize_sim_matrix</dt>\n\t\t<dd>FALSE</dd>\n\t<dt>$alpha</dt>\n\t\t<dd>0.5</dd>\n\t<dt>$na_as_zero</dt>\n\t\t<dd>FALSE</dd>\n</dl>\n","text/markdown":"$k\n:   30\n$method\n:   'cosine'\n$normalize\n:   'center'\n$normalize_sim_matrix\n:   FALSE\n$alpha\n:   0.5\n$na_as_zero\n:   FALSE\n\n\n","text/latex":"\\begin{description}\n\\item[\\$k] 30\n\\item[\\$method] 'cosine'\n\\item[\\$normalize] 'center'\n\\item[\\$normalize\\_sim\\_matrix] FALSE\n\\item[\\$alpha] 0.5\n\\item[\\$na\\_as\\_zero] FALSE\n\\end{description}\n","text/plain":"$k\n[1] 30\n\n$method\n[1] \"cosine\"\n\n$normalize\n[1] \"center\"\n\n$normalize_sim_matrix\n[1] FALSE\n\n$alpha\n[1] 0.5\n\n$na_as_zero\n[1] FALSE\n"},"metadata":{}}]},{"cell_type":"markdown","source":"# Exploring Similar Data\n- Collaborative Filtering involves suggesting movies to the users that are based on collecting preferences from many other users. For example, if user A likes to watch action films and so does user B, then the movies that user B will watch in the future will be recommended to A and vice-versa. Therefore, recommending movies is dependent on creating a relationship of similarity between the two users. With the help of recommended lab, we can compute similarities using various operators like cosine, Pearson as well as Jaccard.","metadata":{}},{"cell_type":"markdown","source":"## User's Similarities","metadata":{}},{"cell_type":"code","source":"similarity_mat <- similarity(ratingMatrix[1:4, ],\n                               method = \"cosine\",\n                               which = \"users\")\nas.matrix(similarity_mat)\nimage(as.matrix(similarity_mat), main = \"User's Similarities\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:03.450293Z","iopub.execute_input":"2023-02-08T07:17:03.452031Z","iopub.status.idle":"2023-02-08T07:17:03.773513Z"},"trusted":true},"execution_count":13,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A matrix: 4 × 4 of type dbl</caption>\n<thead>\n\t<tr><th></th><th scope=col>1</th><th scope=col>2</th><th scope=col>3</th><th scope=col>4</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>       NA</td><td>0.9880430</td><td>0.9820862</td><td>0.9957199</td></tr>\n\t<tr><th scope=row>2</th><td>0.9880430</td><td>       NA</td><td>0.9962866</td><td>0.9687126</td></tr>\n\t<tr><th scope=row>3</th><td>0.9820862</td><td>0.9962866</td><td>       NA</td><td>0.9944484</td></tr>\n\t<tr><th scope=row>4</th><td>0.9957199</td><td>0.9687126</td><td>0.9944484</td><td>       NA</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA matrix: 4 × 4 of type dbl\n\n| <!--/--> | 1 | 2 | 3 | 4 |\n|---|---|---|---|---|\n| 1 |        NA | 0.9880430 | 0.9820862 | 0.9957199 |\n| 2 | 0.9880430 |        NA | 0.9962866 | 0.9687126 |\n| 3 | 0.9820862 | 0.9962866 |        NA | 0.9944484 |\n| 4 | 0.9957199 | 0.9687126 | 0.9944484 |        NA |\n\n","text/latex":"A matrix: 4 × 4 of type dbl\n\\begin{tabular}{r|llll}\n  & 1 & 2 & 3 & 4\\\\\n\\hline\n\t1 &        NA & 0.9880430 & 0.9820862 & 0.9957199\\\\\n\t2 & 0.9880430 &        NA & 0.9962866 & 0.9687126\\\\\n\t3 & 0.9820862 & 0.9962866 &        NA & 0.9944484\\\\\n\t4 & 0.9957199 & 0.9687126 & 0.9944484 &        NA\\\\\n\\end{tabular}\n","text/plain":"  1         2         3         4        \n1        NA 0.9880430 0.9820862 0.9957199\n2 0.9880430        NA 0.9962866 0.9687126\n3 0.9820862 0.9962866        NA 0.9944484\n4 0.9957199 0.9687126 0.9944484        NA"},"metadata":{}},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nS1USFPlKhgAAAABJRU5ErkJggg=="},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"- In the above matrix, each row and column represents a user. We have taken four users and each cell in this matrix represents the similarity that is shared between the two users.","metadata":{}},{"cell_type":"markdown","source":"### Delineate the similarity that is shared between the films:","metadata":{}},{"cell_type":"markdown","source":"## Movies similarity","metadata":{}},{"cell_type":"code","source":"movie_similarity <- similarity(ratingMatrix[, 1:4], method =\n                                 \"cosine\", which = \"items\")\nas.matrix(movie_similarity)\nimage(as.matrix(movie_similarity), main = \"Movies similarity\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:03.775232Z","iopub.execute_input":"2023-02-08T07:17:03.776207Z","iopub.status.idle":"2023-02-08T07:17:03.907025Z"},"trusted":true},"execution_count":14,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A matrix: 4 × 4 of type dbl</caption>\n<thead>\n\t<tr><th></th><th scope=col>1</th><th scope=col>2</th><th scope=col>3</th><th scope=col>4</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>1</th><td>       NA</td><td>0.9834866</td><td>0.9779671</td><td>0.9550638</td></tr>\n\t<tr><th scope=row>2</th><td>0.9834866</td><td>       NA</td><td>0.9829378</td><td>0.9706208</td></tr>\n\t<tr><th scope=row>3</th><td>0.9779671</td><td>0.9829378</td><td>       NA</td><td>0.9932438</td></tr>\n\t<tr><th scope=row>4</th><td>0.9550638</td><td>0.9706208</td><td>0.9932438</td><td>       NA</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA matrix: 4 × 4 of type dbl\n\n| <!--/--> | 1 | 2 | 3 | 4 |\n|---|---|---|---|---|\n| 1 |        NA | 0.9834866 | 0.9779671 | 0.9550638 |\n| 2 | 0.9834866 |        NA | 0.9829378 | 0.9706208 |\n| 3 | 0.9779671 | 0.9829378 |        NA | 0.9932438 |\n| 4 | 0.9550638 | 0.9706208 | 0.9932438 |        NA |\n\n","text/latex":"A matrix: 4 × 4 of type dbl\n\\begin{tabular}{r|llll}\n  & 1 & 2 & 3 & 4\\\\\n\\hline\n\t1 &        NA & 0.9834866 & 0.9779671 & 0.9550638\\\\\n\t2 & 0.9834866 &        NA & 0.9829378 & 0.9706208\\\\\n\t3 & 0.9779671 & 0.9829378 &        NA & 0.9932438\\\\\n\t4 & 0.9550638 & 0.9706208 & 0.9932438 &        NA\\\\\n\\end{tabular}\n","text/plain":"  1         2         3         4        \n1        NA 0.9834866 0.9779671 0.9550638\n2 0.9834866        NA 0.9829378 0.9706208\n3 0.9779671 0.9829378        NA 0.9932438\n4 0.9550638 0.9706208 0.9932438        NA"},"metadata":{}},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nzvr4DOIFc56f/dp72W37XXrTqPqNF9w7v8nPf+HQHnU3q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QcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJYQcAEAlhBwAQCWEHABAJ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\nABHCDgAgQtgBAET8BU1dFeM5r8SnAAAAAElFTkSuQmCC"},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"### Extract the most unique ratings:","metadata":{}},{"cell_type":"code","source":"rating_values <- as.vector(ratingMatrix@data)\nunique(rating_values) # extracting unique ratings","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:03.908889Z","iopub.execute_input":"2023-02-08T07:17:03.909928Z","iopub.status.idle":"2023-02-08T07:17:04.368959Z"},"trusted":true},"execution_count":15,"outputs":[{"output_type":"display_data","data":{"text/html":"<style>\n.list-inline {list-style: none; margin:0; padding: 0}\n.list-inline>li {display: inline-block}\n.list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n</style>\n<ol class=list-inline><li>0</li><li>5</li><li>4</li><li>3</li><li>4.5</li><li>1.5</li><li>2</li><li>3.5</li><li>1</li><li>2.5</li><li>0.5</li></ol>\n","text/markdown":"1. 0\n2. 5\n3. 4\n4. 3\n5. 4.5\n6. 1.5\n7. 2\n8. 3.5\n9. 1\n10. 2.5\n11. 0.5\n\n\n","text/latex":"\\begin{enumerate*}\n\\item 0\n\\item 5\n\\item 4\n\\item 3\n\\item 4.5\n\\item 1.5\n\\item 2\n\\item 3.5\n\\item 1\n\\item 2.5\n\\item 0.5\n\\end{enumerate*}\n","text/plain":" [1] 0.0 5.0 4.0 3.0 4.5 1.5 2.0 3.5 1.0 2.5 0.5"},"metadata":{}}]},{"cell_type":"markdown","source":"### Create a table of ratings that will display the most unique ratings:","metadata":{}},{"cell_type":"code","source":"Table_of_Ratings <- table(rating_values) # creating a count of movie ratings\nTable_of_Ratings","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:04.370584Z","iopub.execute_input":"2023-02-08T07:17:04.371595Z","iopub.status.idle":"2023-02-08T07:17:07.585081Z"},"trusted":true},"execution_count":16,"outputs":[{"output_type":"display_data","data":{"text/plain":"rating_values\n      0     0.5       1     1.5       2     2.5       3     3.5       4     4.5 \n6791761    1198    3258    1567    7943    5484   21729   12237   28880    8187 \n      5 \n  14856 "},"metadata":{}}]},{"cell_type":"markdown","source":"# Most Viewed Movies Visualization\n - In this section of the machine learning project, we will explore the most viewed movies in our dataset. We will first count the number of views in a film and then organize them in a table that would group them in descending order.","metadata":{}},{"cell_type":"code","source":"movie_views <- colCounts(ratingMatrix) # count views for each movie\ntable_views <- data.frame(movie = names(movie_views),\n                          views = movie_views) # create dataframe of views\ntable_views <- table_views[order(table_views$views,\n                                 decreasing = TRUE), ] # sort by number of views\ntable_views$title <- NA\nfor (index in 1:10325){\n  table_views[index,3] <- as.character(subset(movie_data,\n                                         movie_data$movieId == table_views[index,1])$title)\n}\ntable_views[1:6,]","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:07.587074Z","iopub.execute_input":"2023-02-08T07:17:07.588229Z","iopub.status.idle":"2023-02-08T07:17:32.087105Z"},"trusted":true},"execution_count":17,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 6 × 3</caption>\n<thead>\n\t<tr><th></th><th scope=col>movie</th><th scope=col>views</th><th scope=col>title</th></tr>\n\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>296</th><td>296</td><td>325</td><td>Pulp Fiction (1994)                      </td></tr>\n\t<tr><th scope=row>356</th><td>356</td><td>311</td><td>Forrest Gump (1994)                      </td></tr>\n\t<tr><th scope=row>318</th><td>318</td><td>308</td><td>Shawshank Redemption, The (1994)         </td></tr>\n\t<tr><th scope=row>480</th><td>480</td><td>294</td><td>Jurassic Park (1993)                     </td></tr>\n\t<tr><th scope=row>593</th><td>593</td><td>290</td><td>Silence of the Lambs, The (1991)         </td></tr>\n\t<tr><th scope=row>260</th><td>260</td><td>273</td><td>Star Wars: Episode IV - A New Hope (1977)</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 6 × 3\n\n| <!--/--> | movie &lt;chr&gt; | views &lt;int&gt; | title &lt;chr&gt; |\n|---|---|---|---|\n| 296 | 296 | 325 | Pulp Fiction (1994)                       |\n| 356 | 356 | 311 | Forrest Gump (1994)                       |\n| 318 | 318 | 308 | Shawshank Redemption, The (1994)          |\n| 480 | 480 | 294 | Jurassic Park (1993)                      |\n| 593 | 593 | 290 | Silence of the Lambs, The (1991)          |\n| 260 | 260 | 273 | Star Wars: Episode IV - A New Hope (1977) |\n\n","text/latex":"A data.frame: 6 × 3\n\\begin{tabular}{r|lll}\n  & movie & views & title\\\\\n  & <chr> & <int> & <chr>\\\\\n\\hline\n\t296 & 296 & 325 & Pulp Fiction (1994)                      \\\\\n\t356 & 356 & 311 & Forrest Gump (1994)                      \\\\\n\t318 & 318 & 308 & Shawshank Redemption, The (1994)         \\\\\n\t480 & 480 & 294 & Jurassic Park (1993)                     \\\\\n\t593 & 593 & 290 & Silence of the Lambs, The (1991)         \\\\\n\t260 & 260 & 273 & Star Wars: Episode IV - A New Hope (1977)\\\\\n\\end{tabular}\n","text/plain":"    movie views title                                    \n296 296   325   Pulp Fiction (1994)                      \n356 356   311   Forrest Gump (1994)                      \n318 318   308   Shawshank Redemption, The (1994)         \n480 480   294   Jurassic Park (1993)                     \n593 593   290   Silence of the Lambs, The (1991)         \n260 260   273   Star Wars: Episode IV - A New Hope (1977)"},"metadata":{}}]},{"cell_type":"markdown","source":"### Visualize a bar plot for the total number of views of the top films. We will carry this out using ggplot2:","metadata":{}},{"cell_type":"code","source":"ggplot(table_views[1:6, ], aes(x = title, y = views)) +\n  geom_bar(stat=\"identity\", fill = 'steelblue') +\n  geom_text(aes(label=views), vjust=-0.3, size=3.5) +\n  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +\n  ggtitle(\"Total Views of the Top Films\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:32.088846Z","iopub.execute_input":"2023-02-08T07:17:32.089910Z","iopub.status.idle":"2023-02-08T07:17:32.399808Z"},"trusted":true},"execution_count":18,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nP/grTdN2TmgpIj7GgGbtOj7UuUPdqpE+xsDuo8e436LPgEHpTpf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nxPvPzV1/suegwf1CHZ++unj88Ky1rw5yH0XMZQrImyfG/F9oteE7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CJ6NmZNGdkXwj9ZWIjrXOlxVXVY/PXLj7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\n++lLovQ+Ihh6cuGtbN++CKHG4qzAGzWT1NXhCQD/kEWUvPfsN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qJEV9RZyKgZWXRnxEZHt863A+D/AsEOAPBHU9a37oXyoqKi3iLZ1H2B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\npCG96M4r2ppb3QuDCb8FTGW/saKx/Ey09+ZU0+lBK75/dZTJ44vr3dYXxu3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CJZLb1w/sJkMIMbTXjIr/xadUr6LwuvmMDRpsPIQF+Dic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\nxMT/ASEeSmR/RWNJAAAAAElFTkSuQmCC"},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"- From the above bar-plot, we observe that Pulp Fiction is the most-watched film followed by Forrest Gump.","metadata":{}},{"cell_type":"markdown","source":"# Heatmap of Movie Ratings\n- Visualize a heatmap of the movie ratings. This heatmap will contain the first 25 rows and 25 columns as follows ","metadata":{}},{"cell_type":"code","source":"image(ratingMatrix[1:20, 1:25], axes = FALSE, main = \"Heatmap of the first 25 rows and 25 columns\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:32.402619Z","iopub.execute_input":"2023-02-08T07:17:32.404166Z","iopub.status.idle":"2023-02-08T07:17:32.553384Z"},"trusted":true},"execution_count":19,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nHt2WfwKK1u8hc6O8we5PfcFXf9KvfGBuN32ElHuVWVOBYKdSO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1ud8nr84sDhr9wTOWnp8y+f3rbytbFd0+pfXHp/3ZLrE+xqkmbNmnXp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\ninLZP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Mn6MKV/34VnuH49/1tzV2nrnH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\nAAAAKvH/WCU3W8g6tf8AAAAASUVORK5CYII="},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"# Performing Data Preparation\n## We will conduct data preparation in the following three steps:\n\n- Selecting useful data.\n- Normalizing data.\n- Binarizing the data.\n\n### For finding useful data in our dataset, we have set the threshold for the minimum number of users who have rated a film as 50. This is also same for minimum number of views that are per film. This way, we have filtered a list of watched films from least-watched ones.","metadata":{}},{"cell_type":"code","source":"movie_ratings <- ratingMatrix[rowCounts(ratingMatrix) > 50,\n                             colCounts(ratingMatrix) > 50]\nmovie_ratings","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:32.556137Z","iopub.execute_input":"2023-02-08T07:17:32.557416Z","iopub.status.idle":"2023-02-08T07:17:32.580639Z"},"trusted":true},"execution_count":20,"outputs":[{"output_type":"display_data","data":{"text/plain":"420 x 447 rating matrix of class ‘realRatingMatrix’ with 38341 ratings."},"metadata":{}}]},{"cell_type":"markdown","source":"- From the above output of ‘movie_ratings’, we observe that there are 420 users and 447 films as opposed to the previous 668 users and 10325 films.","metadata":{}},{"cell_type":"markdown","source":"###  We can now delineate our matrix of relevant users as follows:","metadata":{}},{"cell_type":"code","source":"minimum_movies<- quantile(rowCounts(movie_ratings), 0.98)\nminimum_users <- quantile(colCounts(movie_ratings), 0.98)\nimage(movie_ratings[rowCounts(movie_ratings) > minimum_movies,\n                     colCounts(movie_ratings) > minimum_users],\nmain = \"Heatmap of the top users and movies\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:32.582320Z","iopub.execute_input":"2023-02-08T07:17:32.583288Z","iopub.status.idle":"2023-02-08T07:17:32.749079Z"},"trusted":true},"execution_count":21,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\n8J6C56K5BgaotVnsHM7qa8t8lNrm7NV9kF/+Wbrjnwwd/97OzD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XoX9pVc8YOAACg7GJiYoo3GgyGgQMH6vX64ov+fGfIgqNNj2wfc+b+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\nAABAJQh2AAAAKkGwAwAAUIn/B2QHuR+aQRMbAAAAAElFTkSuQmCC"},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"### Visualize the distribution of the average ratings per user:","metadata":{}},{"cell_type":"code","source":"average_ratings <- rowMeans(movie_ratings)\nqplot(average_ratings, fill=I(\"steelblue\"), col=I(\"red\")) +\n  ggtitle(\"Distribution of the average rating per user\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:32.751877Z","iopub.execute_input":"2023-02-08T07:17:32.753257Z","iopub.status.idle":"2023-02-08T07:17:33.065671Z"},"trusted":true},"execution_count":22,"outputs":[{"name":"stderr","text":"Warning message:\n“\u001b[1m\u001b[22m`qplot()` was deprecated in ggplot2 3.4.0.”\n\u001b[1m\u001b[22m`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n","output_type":"stream"},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nkYTdwN8fvvHS01/yL/8dQpj3lR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gEgI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\nJ6Ldm0xEagAAAABJRU5ErkJggg=="},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"# Data Normalization\n- In the case of some users, there can be high ratings or low ratings provided to all of the watched films. This will act as a bias while implementing our model. In order to remove this, we normalize our data. Normalization is a data preparation procedure to standardize the numerical values in a column to a common scale value. This is done in such a way that there is no distortion in the range of values. Normalization transforms the average value of our rating column to 0. We then plot a heatmap that delineates our normalized ratings.","metadata":{}},{"cell_type":"code","source":"normalized_ratings <- normalize(movie_ratings)\nsum(rowMeans(normalized_ratings) > 0.00001)\nimage(normalized_ratings[rowCounts(normalized_ratings) > minimum_movies,\n                          colCounts(normalized_ratings) > minimum_users],\nmain = \"Normalized Ratings of the Top Users\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:33.068501Z","iopub.execute_input":"2023-02-08T07:17:33.069746Z","iopub.status.idle":"2023-02-08T07:17:33.207859Z"},"trusted":true},"execution_count":23,"outputs":[{"output_type":"display_data","data":{"text/html":"0","text/markdown":"0","text/latex":"0","text/plain":"[1] 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h2AAAAkiDYAQAASIJgBwAAIAmCHQAAgCQIdgAAAJIg2AEAAEiCYAcAACAJ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\nYII="},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"# Performing Data Binarization\n- Binarizing the data means that we have two discrete values 1 and 0, which will allow our recommendation systems to work more efficiently. We will define a matrix that will consist of 1 if the rating is above 3 otherwise it will be 0.","metadata":{}},{"cell_type":"code","source":"binary_minimum_movies <- quantile(rowCounts(movie_ratings), 0.95)\nbinary_minimum_users <- quantile(colCounts(movie_ratings), 0.95)\n#movies_watched <- binarize(movie_ratings, minRating = 1)\ngood_rated_films <- binarize(movie_ratings, minRating = 3)\nimage(good_rated_films[rowCounts(movie_ratings) > binary_minimum_movies,\ncolCounts(movie_ratings) > binary_minimum_users],\nmain = \"Heatmap of the top users and movies\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:33.209552Z","iopub.execute_input":"2023-02-08T07:17:33.210577Z","iopub.status.idle":"2023-02-08T07:17:33.339303Z"},"trusted":true},"execution_count":24,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nt76ir0xt1c+zXMM/3l73R5DOuj/KZ481S8vWp+l7rVkDtPhHbt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LT4j0aAACAqSxf7IRIuOfDsh43XPfEvBsf2lCdPXDQ1Dkvz7vur/Ge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\n5Dy/sLmcVCixqPsyV82+zSuO9SZrYtDW7hWJSG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3jXphXNDfc0j9s59SOjQbPfpajklj5rDxxb3NoL50+/voxqweN1bw+P27oQ4WqxG2k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\nAAAA8MT/Adn5ws4y7QAaAAAAAElFTkSuQmCC"},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"# Collaborative Filtering System\n- In this section of the project, we will develop our very own Item Based Collaborative Filtering System. This type of collaborative filtering finds similarity in the items based on the people’s ratings of them. The algorithm first builds a similar-items table of the customers who have purchased them into a combination of similar items. This is then fed into the recommendation system.\n\n- The similarity between single products and related products can be determined with the following algorithm:\n    - For each Item i1 present in the product catalog, purchased by customer C.\n    - And, for each item, i2 was also purchased by customer C.\n    - Create a record that the customer purchased items i1 and i2.\n    - Calculate the similarity between i1 and i2.\n\n- We will build this filtering system by splitting the dataset into an 80% training set and a 20% test set.","metadata":{}},{"cell_type":"code","source":"sampled_data<- sample(x = c(TRUE, FALSE),\n                      size = nrow(movie_ratings),\n                      replace = TRUE,\n                      prob = c(0.8, 0.2))\ntraining_data <- movie_ratings[sampled_data, ]\ntesting_data <- movie_ratings[!sampled_data, ]","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:33.342072Z","iopub.execute_input":"2023-02-08T07:17:33.343595Z","iopub.status.idle":"2023-02-08T07:17:33.367231Z"},"trusted":true},"execution_count":25,"outputs":[]},{"cell_type":"markdown","source":"# Building the Recommendation System\n- We will now explore the various parameters of our Item Based Collaborative Filter. These parameters are default in nature. In the first step, k denotes the number of items for computing their similarities. Here, k is equal to 30. Therefore, the algorithm will now identify the k most similar items and store their number. We use the cosine method which is the default one but you can also use the Pearson method.","metadata":{}},{"cell_type":"code","source":"recommendation_system <- recommenderRegistry$get_entries(dataType =\"realRatingMatrix\")\nrecommendation_system$IBCF_realRatingMatrix$parameters","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:33.369336Z","iopub.execute_input":"2023-02-08T07:17:33.370375Z","iopub.status.idle":"2023-02-08T07:17:33.385168Z"},"trusted":true},"execution_count":26,"outputs":[{"output_type":"display_data","data":{"text/html":"<dl>\n\t<dt>$k</dt>\n\t\t<dd>30</dd>\n\t<dt>$method</dt>\n\t\t<dd>'cosine'</dd>\n\t<dt>$normalize</dt>\n\t\t<dd>'center'</dd>\n\t<dt>$normalize_sim_matrix</dt>\n\t\t<dd>FALSE</dd>\n\t<dt>$alpha</dt>\n\t\t<dd>0.5</dd>\n\t<dt>$na_as_zero</dt>\n\t\t<dd>FALSE</dd>\n</dl>\n","text/markdown":"$k\n:   30\n$method\n:   'cosine'\n$normalize\n:   'center'\n$normalize_sim_matrix\n:   FALSE\n$alpha\n:   0.5\n$na_as_zero\n:   FALSE\n\n\n","text/latex":"\\begin{description}\n\\item[\\$k] 30\n\\item[\\$method] 'cosine'\n\\item[\\$normalize] 'center'\n\\item[\\$normalize\\_sim\\_matrix] FALSE\n\\item[\\$alpha] 0.5\n\\item[\\$na\\_as\\_zero] FALSE\n\\end{description}\n","text/plain":"$k\n[1] 30\n\n$method\n[1] \"cosine\"\n\n$normalize\n[1] \"center\"\n\n$normalize_sim_matrix\n[1] FALSE\n\n$alpha\n[1] 0.5\n\n$na_as_zero\n[1] FALSE\n"},"metadata":{}}]},{"cell_type":"code","source":"recommen_model <- Recommender(data = training_data,\n                          method = \"IBCF\",\n                          parameter = list(k = 30))\nrecommen_model","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:33.387019Z","iopub.execute_input":"2023-02-08T07:17:33.388191Z","iopub.status.idle":"2023-02-08T07:17:33.595461Z"},"trusted":true},"execution_count":27,"outputs":[{"output_type":"display_data","data":{"text/plain":"Recommender of type ‘IBCF’ for ‘realRatingMatrix’ \nlearned using 341 users."},"metadata":{}}]},{"cell_type":"code","source":"class(recommen_model)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:33.597285Z","iopub.execute_input":"2023-02-08T07:17:33.598311Z","iopub.status.idle":"2023-02-08T07:17:33.612198Z"},"trusted":true},"execution_count":28,"outputs":[{"output_type":"display_data","data":{"text/html":"'Recommender'","text/markdown":"'Recommender'","text/latex":"'Recommender'","text/plain":"[1] \"Recommender\"\nattr(,\"package\")\n[1] \"recommenderlab\""},"metadata":{}}]},{"cell_type":"markdown","source":"### Now explore our data science recommendation system model as follows:\n\n- Using the getModel() function, we will retrieve the recommen_model. We will then find the class and dimensions of our similarity matrix that is contained within model_info. Finally, we will generate a heatmap, that will contain the top 20 items and visualize the similarity shared between them.","metadata":{}},{"cell_type":"code","source":"model_info <- getModel(recommen_model)\nclass(model_info$sim)\ndim(model_info$sim)\ntop_items <- 20\nimage(model_info$sim[1:top_items, 1:top_items],\n   main = \"Heatmap of the first rows and columns\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:33.614837Z","iopub.execute_input":"2023-02-08T07:17:33.616063Z","iopub.status.idle":"2023-02-08T07:17:33.722585Z"},"trusted":true},"execution_count":29,"outputs":[{"output_type":"display_data","data":{"text/html":"'dgCMatrix'","text/markdown":"'dgCMatrix'","text/latex":"'dgCMatrix'","text/plain":"[1] \"dgCMatrix\"\nattr(,\"package\")\n[1] \"Matrix\""},"metadata":{}},{"output_type":"display_data","data":{"text/html":"<style>\n.list-inline {list-style: none; margin:0; padding: 0}\n.list-inline>li {display: inline-block}\n.list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n</style>\n<ol class=list-inline><li>447</li><li>447</li></ol>\n","text/markdown":"1. 447\n2. 447\n\n\n","text/latex":"\\begin{enumerate*}\n\\item 447\n\\item 447\n\\end{enumerate*}\n","text/plain":"[1] 447 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+6t3Gzf+7KvvuumSj+V6VgAA7SDsmiQKR1xceefFrX84BgBgO+A9dgAAkRB2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"},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"### In the next step of ML project, we will carry out the sum of rows and columns with the similarity of the objects above 0. We will visualize the sum of columns through a distribution as follows:","metadata":{}},{"cell_type":"markdown","source":"# Distribution of the column count","metadata":{}},{"cell_type":"code","source":"sum_rows <- rowSums(model_info$sim > 0)\ntable(sum_rows)\nsum_cols <- colSums(model_info$sim > 0)\nqplot(sum_cols, fill=I(\"steelblue\"), col=I(\"red\"))+ ggtitle(\"Distribution of the column count\")","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:33.724234Z","iopub.execute_input":"2023-02-08T07:17:33.725209Z","iopub.status.idle":"2023-02-08T07:17:33.971649Z"},"trusted":true},"execution_count":30,"outputs":[{"output_type":"display_data","data":{"text/plain":"sum_rows\n 30 \n447 "},"metadata":{}},{"name":"stderr","text":"\u001b[1m\u001b[22m`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n","output_type":"stream"},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nrSmdyrRM3GvOX/z1F7/9682v8t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dDrJ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\nAElFTkSuQmCC"},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"# Build Recommender System on the dataset\n- We will create a top_recommendations variable which will be initialized to 10, specifying the number of films to each user. We will then use the predict() function that will identify similar items and will rank them appropriately. Here, each rating is used as a weight. Each weight is multiplied with related similarities. Finally, everything is added in the end.:","metadata":{}},{"cell_type":"code","source":"top_recommendations <- 10 # the number of items to recommend to each user\npredicted_recommendations <- predict(object = recommen_model,\n                          newdata = testing_data,\n                          n = top_recommendations)\npredicted_recommendations","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:33.974463Z","iopub.execute_input":"2023-02-08T07:17:33.975724Z","iopub.status.idle":"2023-02-08T07:17:34.049841Z"},"trusted":true},"execution_count":31,"outputs":[{"output_type":"display_data","data":{"text/plain":"Recommendations as ‘topNList’ with n = 10 for 79 users. "},"metadata":{}}]},{"cell_type":"code","source":"user1 <- predicted_recommendations@items[[1]] # recommendation for the first user\nmovies_user1 <- predicted_recommendations@itemLabels[user1]\nmovies_user2 <- movies_user1\nfor (index in 1:10){\n  movies_user2[index] <- as.character(subset(movie_data,\n                                         movie_data$movieId == movies_user1[index])$title)\n}\nmovies_user2","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:34.051539Z","iopub.execute_input":"2023-02-08T07:17:34.052542Z","iopub.status.idle":"2023-02-08T07:17:34.098339Z"},"trusted":true},"execution_count":32,"outputs":[{"output_type":"display_data","data":{"text/html":"<style>\n.list-inline {list-style: none; margin:0; padding: 0}\n.list-inline>li {display: inline-block}\n.list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n</style>\n<ol class=list-inline><li>'Toy Story (1995)'</li><li>'Casino (1995)'</li><li>'Twelve Monkeys (a.k.a. 12 Monkeys) (1995)'</li><li>'Taxi Driver (1976)'</li><li>'Like Water for Chocolate (Como agua para chocolate) (1992)'</li><li>'Vertigo (1958)'</li><li>'North by Northwest (1959)'</li><li>'Casablanca (1942)'</li><li>'Fish Called Wanda, A (1988)'</li><li>'Reservoir Dogs (1992)'</li></ol>\n","text/markdown":"1. 'Toy Story (1995)'\n2. 'Casino (1995)'\n3. 'Twelve Monkeys (a.k.a. 12 Monkeys) (1995)'\n4. 'Taxi Driver (1976)'\n5. 'Like Water for Chocolate (Como agua para chocolate) (1992)'\n6. 'Vertigo (1958)'\n7. 'North by Northwest (1959)'\n8. 'Casablanca (1942)'\n9. 'Fish Called Wanda, A (1988)'\n10. 'Reservoir Dogs (1992)'\n\n\n","text/latex":"\\begin{enumerate*}\n\\item 'Toy Story (1995)'\n\\item 'Casino (1995)'\n\\item 'Twelve Monkeys (a.k.a. 12 Monkeys) (1995)'\n\\item 'Taxi Driver (1976)'\n\\item 'Like Water for Chocolate (Como agua para chocolate) (1992)'\n\\item 'Vertigo (1958)'\n\\item 'North by Northwest (1959)'\n\\item 'Casablanca (1942)'\n\\item 'Fish Called Wanda, A (1988)'\n\\item 'Reservoir Dogs (1992)'\n\\end{enumerate*}\n","text/plain":" [1] \"Toy Story (1995)\"                                          \n [2] \"Casino (1995)\"                                             \n [3] \"Twelve Monkeys (a.k.a. 12 Monkeys) (1995)\"                 \n [4] \"Taxi Driver (1976)\"                                        \n [5] \"Like Water for Chocolate (Como agua para chocolate) (1992)\"\n [6] \"Vertigo (1958)\"                                            \n [7] \"North by Northwest (1959)\"                                 \n [8] \"Casablanca (1942)\"                                         \n [9] \"Fish Called Wanda, A (1988)\"                               \n[10] \"Reservoir Dogs (1992)\"                                     "},"metadata":{}}]},{"cell_type":"code","source":"recommendation_matrix <- sapply(predicted_recommendations@items,\n                      function(x){ as.integer(colnames(movie_ratings)[x]) }) # matrix with the recommendations for each user\n#dim(recc_matrix)\nrecommendation_matrix[,1:4]","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:34.100142Z","iopub.execute_input":"2023-02-08T07:17:34.101127Z","iopub.status.idle":"2023-02-08T07:17:34.121669Z"},"trusted":true},"execution_count":33,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A matrix: 10 × 4 of type int</caption>\n<thead>\n\t<tr><th scope=col>0</th><th scope=col>1</th><th scope=col>2</th><th scope=col>3</th></tr>\n</thead>\n<tbody>\n\t<tr><td>   1</td><td> 17</td><td> 25</td><td> 39</td></tr>\n\t<tr><td>  16</td><td> 21</td><td> 62</td><td>110</td></tr>\n\t<tr><td>  32</td><td>235</td><td>223</td><td>112</td></tr>\n\t<tr><td> 111</td><td>261</td><td>474</td><td>158</td></tr>\n\t<tr><td> 265</td><td>357</td><td>508</td><td>236</td></tr>\n\t<tr><td> 903</td><td>364</td><td>541</td><td>293</td></tr>\n\t<tr><td> 908</td><td>440</td><td>590</td><td>350</td></tr>\n\t<tr><td> 912</td><td>539</td><td>908</td><td>355</td></tr>\n\t<tr><td>1079</td><td>708</td><td>913</td><td>357</td></tr>\n\t<tr><td>1089</td><td>785</td><td>923</td><td>442</td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA matrix: 10 × 4 of type int\n\n| 0 | 1 | 2 | 3 |\n|---|---|---|---|\n|    1 |  17 |  25 |  39 |\n|   16 |  21 |  62 | 110 |\n|   32 | 235 | 223 | 112 |\n|  111 | 261 | 474 | 158 |\n|  265 | 357 | 508 | 236 |\n|  903 | 364 | 541 | 293 |\n|  908 | 440 | 590 | 350 |\n|  912 | 539 | 908 | 355 |\n| 1079 | 708 | 913 | 357 |\n| 1089 | 785 | 923 | 442 |\n\n","text/latex":"A matrix: 10 × 4 of type int\n\\begin{tabular}{llll}\n 0 & 1 & 2 & 3\\\\\n\\hline\n\t    1 &  17 &  25 &  39\\\\\n\t   16 &  21 &  62 & 110\\\\\n\t   32 & 235 & 223 & 112\\\\\n\t  111 & 261 & 474 & 158\\\\\n\t  265 & 357 & 508 & 236\\\\\n\t  903 & 364 & 541 & 293\\\\\n\t  908 & 440 & 590 & 350\\\\\n\t  912 & 539 & 908 & 355\\\\\n\t 1079 & 708 & 913 & 357\\\\\n\t 1089 & 785 & 923 & 442\\\\\n\\end{tabular}\n","text/plain":"      0    1   2   3  \n [1,]    1  17  25  39\n [2,]   16  21  62 110\n [3,]   32 235 223 112\n [4,]  111 261 474 158\n [5,]  265 357 508 236\n [6,]  903 364 541 293\n [7,]  908 440 590 350\n [8,]  912 539 908 355\n [9,] 1079 708 913 357\n[10,] 1089 785 923 442"},"metadata":{}}]},{"cell_type":"markdown","source":"# Distribution of the Number of Items for IBCF","metadata":{}},{"cell_type":"code","source":"number_of_items <- factor(table(recommendation_matrix))\n\nchart_title <- \"Distribution of the Number of Items for IBCF\"\n\nqplot(number_of_items, fill=I(\"steelblue\"), col=I(\"red\")) + ggtitle(chart_title)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:34.123365Z","iopub.execute_input":"2023-02-08T07:17:34.124368Z","iopub.status.idle":"2023-02-08T07:17:34.343044Z"},"trusted":true},"execution_count":34,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAIAAAByhViMAAAABmJLR0QA/wD/AP+gvaeTAAAg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\n3O5bfzzzU08d/XrvznzKWh+RjnR8l1irYTtxJyz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QdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAAkRB2AACREHYAAJEQdgAA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\nAQD0XD30EbsQwtAvT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39f65rH2p/Ylo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\nOwAAAACOQGEHAAAAwBH/Af9n92F6q1A9AAAAAElFTkSuQmCC"},"metadata":{"image/png":{"width":420,"height":420}}}]},{"cell_type":"markdown","source":"# Movie Title, No. of Items","metadata":{}},{"cell_type":"code","source":"number_of_items_sorted <- sort(number_of_items, decreasing = TRUE)\nnumber_of_items_top <- head(number_of_items_sorted, n = 4)\ntable_top <- data.frame(as.integer(names(number_of_items_top)),\nnumber_of_items_top)\nfor(i in 1:4) {\ntable_top[i,1] <- as.character(subset(movie_data,\nmovie_data$movieId == table_top[i,1])$title)\n}\n\ncolnames(table_top) <- c(\"Movie Title\", \"No. of Items\")\nhead(table_top)","metadata":{"execution":{"iopub.status.busy":"2023-02-08T07:17:34.344670Z","iopub.execute_input":"2023-02-08T07:17:34.345674Z","iopub.status.idle":"2023-02-08T07:17:34.381865Z"},"trusted":true},"execution_count":35,"outputs":[{"output_type":"display_data","data":{"text/html":"<table class=\"dataframe\">\n<caption>A data.frame: 4 × 2</caption>\n<thead>\n\t<tr><th></th><th scope=col>Movie Title</th><th scope=col>No. of Items</th></tr>\n\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n</thead>\n<tbody>\n\t<tr><th scope=row>110</th><td>Braveheart (1995)                        </td><td>11</td></tr>\n\t<tr><th scope=row>260</th><td>Star Wars: Episode IV - A New Hope (1977)</td><td>11</td></tr>\n\t<tr><th scope=row>745</th><td><span style=white-space:pre-wrap>Wallace &amp; Gromit: A Close Shave (1995)   </span></td><td>9 </td></tr>\n\t<tr><th scope=row>21</th><td>Get Shorty (1995)                        </td><td>8 </td></tr>\n</tbody>\n</table>\n","text/markdown":"\nA data.frame: 4 × 2\n\n| <!--/--> | Movie Title &lt;chr&gt; | No. of Items &lt;fct&gt; |\n|---|---|---|\n| 110 | Braveheart (1995)                         | 11 |\n| 260 | Star Wars: Episode IV - A New Hope (1977) | 11 |\n| 745 | Wallace &amp; Gromit: A Close Shave (1995)    | 9  |\n| 21 | Get Shorty (1995)                         | 8  |\n\n","text/latex":"A data.frame: 4 × 2\n\\begin{tabular}{r|ll}\n  & Movie Title & No. of Items\\\\\n  & <chr> & <fct>\\\\\n\\hline\n\t110 & Braveheart (1995)                         & 11\\\\\n\t260 & Star Wars: Episode IV - A New Hope (1977) & 11\\\\\n\t745 & Wallace \\& Gromit: A Close Shave (1995)    & 9 \\\\\n\t21 & Get Shorty (1995)                         & 8 \\\\\n\\end{tabular}\n","text/plain":"    Movie Title                               No. of Items\n110 Braveheart (1995)                         11          \n260 Star Wars: Episode IV - A New Hope (1977) 11          \n745 Wallace & Gromit: A Close Shave (1995)    9           \n21  Get Shorty (1995)                         8           "},"metadata":{}}]}]}