Data6012 project 1

1 Project 1

1.1 Hotel recommendation system

This system recommends the chain hotesl to travelers.

1.2 Dataset

#Using toy dataset
hotels <- matrix(c(4,4,4,3,5,4,4,3,3,5,2,3,3,4,2,4,3,4,5,4,5,5,2,5,4,NA,3,4,3,4,4,5,NA,2,2,3), ncol = 6, byrow = TRUE)
colnames(hotels)<- c("Marriott","Hilton","Best Western", "Hyatt", "Intercontinental","Wyndham")
rownames(hotels)<- c("user1","user2","user3","user4","user5","user6")
hotels

##       Marriott Hilton Best Western Hyatt Intercontinental Wyndham
## user1        4      4            4     3                5       4
## user2        4      3            3     5                2       3
## user3        3      4            2     4                3       4
## user4        5      4            5     5                2       5
## user5        4     NA            3     4                3       4
## user6        4      5           NA     2                2       3

1.3 Separating training and test datasets

training <- matrix(c(4,NA,4,3,5,4,4,3,NA,5,2,3,3,4,2,4,NA,4,NA,4,5,5,2,5,4,NA,3,NA,3,4,4,5,NA,2,2,NA),ncol = 6, byrow = TRUE)
colnames(training)<-c("Marriott","Hilton","Best Western", "Hyatt", "Intercontinental","Wyndham")
rownames(training)<- c("user1","user2","user3","user4","user5","user6")

test <- c(5,4,3,4,3,3)

1.4 Raw average (mean) rating

raw_average <- mean(training, na.rm=TRUE)
raw_average

## [1] 3.642857

1.5 Calculating the RMSE

RMSE - training dataset

rmse_training <- sqrt(mean((training-raw_average)^2, na.rm= TRUE))
rmse_training

## [1] 1.007624

RMSE - test dataset

rmse_test <- sqrt(mean((test-raw_average)^2))
rmse_test

## [1] 0.7457362

1.6 Calculating bias for each user and each item

training dataset

user bias

user_mean <- rowMeans(training, na.rm= TRUE)
user_bias <- user_mean-raw_average
user_bias

##      user1      user2      user3      user4      user5      user6 
##  0.3571429 -0.2428571 -0.2428571  0.5571429 -0.1428571 -0.3928571

item bias

item_mean <- colMeans(training, na.rm = TRUE)
item_bias <- item_mean- raw_average
item_bias

##         Marriott           Hilton     Best Western            Hyatt 
##        0.1571429        0.3571429       -0.1428571        0.1571429 
## Intercontinental          Wyndham 
##       -0.8428571        0.3571429

1.7 Calculating baseline predictors

every user-item combination.

baselineP <- function(n,m){
  3.5+ user_bias[n]+item_bias[m]
}
baseline_predictor <- data.frame(matrix(NA, ncol=6, nrow=6))
colnames(baseline_predictor)<- c("Marriott","Hilton","Best Western", "Hyatt", "Intercontinental","Wyndham")
rownames(baseline_predictor)<- c("user1","user2","user3","user4","user5","user6")
for (i in 1:6){
  for(j in 1:6){
    baseline_predictor[i,j] <- baselineP(i,j)
  }
}
baseline_predictor

##       Marriott   Hilton Best Western    Hyatt Intercontinental  Wyndham
## user1 4.014286 4.214286     3.714286 4.014286         3.014286 4.214286
## user2 3.414286 3.614286     3.114286 3.414286         2.414286 3.614286
## user3 3.414286 3.614286     3.114286 3.414286         2.414286 3.614286
## user4 4.214286 4.414286     3.914286 4.214286         3.214286 4.414286
## user5 3.514286 3.714286     3.214286 3.514286         2.514286 3.714286
## user6 3.264286 3.464286     2.964286 3.264286         2.264286 3.464286

1.8 Calculating RMSE for the baseline predictors

Test dataset

rmse_test_b <- sqrt(((test[1]-4.369565)^2 + (test[2]-4.369565)^2 +(test[3]-2.869565)^2 + (test[4]-3.536232)^2 +(test[5]-3.536232)^2 + (test[6]-3.569565)^2)/5)
rmse_test_b

## [1] 0.5249895

Training dataset

a<- (training -baseline_predictor)^2
a

##           Marriott    Hilton Best Western     Hyatt Intercontinental
## user1 0.0002040816        NA   0.08163265 1.0287755       3.94306122
## user2 0.3430612245 0.3773469           NA 2.5144898       0.17163265
## user3 0.1716326531 0.1487755   1.24163265 0.3430612               NA
## user4           NA 0.1716327   1.17877551 0.6173469       1.47448980
## user5 0.2359183673        NA   0.04591837        NA       0.23591837
## user6 0.5412755102 2.3584184           NA 1.5984184       0.06984694
##          Wyndham
## user1 0.04591837
## user2 0.37734694
## user3 0.14877551
## user4 0.34306122
## user5 0.08163265
## user6         NA

mean_a <- sum(colSums(a, na.rm=TRUE, dims= 1))/23
rmse_training_b <- sqrt(mean_a)
rmse_training_b

## [1] 0.9299369

1.9 Summurizing results

Percentage of improvement of test dataset - 29.6%

(1-(rmse_test_b/rmse_test))*100

## [1] 29.60118

Percentage of improvement of training dataset - 7.7%

(1-(rmse_training_b/rmse_training))*100

## [1] 7.709931