DATA 612 - Project 3 : Matrix Factorization methods

# Normalize the matrix (replace NAs with 0 and normalize ratings)
movieMatrix <- as.matrix(normalize(movieRealMatrix)@data)

# Perform SVD
movieSVD <- svd(movieMatrix)
rownames(movieSVD$u) <- rownames(movieMatrix)
rownames(movieSVD$v) <- colnames(movieMatrix)

# Extract singular values
Sigmak <- movieSVD$d 
Uk <- movieSVD$u 
Vk <- t(as.matrix(movieSVD$v))

# Calculate cumulative proportion of variance explained
cumulative_variance <- cumsum(Sigmak^2) / sum(Sigmak^2)

# Plot the cumulative variance explained by the first n components
plot(cumulative_variance, type = "b", pch = 19, col = "blue", 
     xlab = "Number of Components", ylab = "Cumulative Variance Explained",
     main = "Cumulative Variance Explained by SVD Components")

# Add lines for 80% and 90% of the variance explained
abline(h = 0.80, col = "red", lty = 2)
abline(h = 0.90, col = "green", lty = 2)

# Annotate the points where 80% and 90% are reached
text(which(cumulative_variance >= 0.80)[1], 0.80, labels = "80%", pos = 4, col = "red")
text(which(cumulative_variance >= 0.90)[1], 0.90, labels = "90%", pos = 4, col = "green")

# Convert realRatingMatrix to a regular matrix
ratingmat <- as(movieRealMatrix, "matrix")

ratingmat[is.na(ratingmat)] <- 0
ratingmat[is.infinite(ratingmat)] <- 0
ratingmat <- ratingmat[1:100, 1:100]

s <- svd(ratingmat)

k <- 20
U_k <- s$u[, 1:k]
D_k <- diag(s$d[1:k])
V_k <- s$v[, 1:k]

predmat <- U_k %*% D_k %*% t(V_k)

# Plot (adjust size if matrix has fewer rows/columns)
par(mfrow = c(1, 2))  # side-by-side plots
image(ratingmat, main = "Original Ratings Matrix")
image(predmat, main = "Reconstructed Ratings Matrix (SVD)")

# Reduce dimensions
n <- length(movieSVD$d)
total_energy <- sum(movieSVD$d^2)
for (i in (n-1):1) {
  energy <- sum(movieSVD$d[1:i]^2)
  if (energy/total_energy<0.9) {
    n_dims <- i+1
    break
  }
}

trim_mov_D <- movieSVD$d[1:n_dims]
trim_mov_U <- movieSVD$u[, 1:n_dims]
trim_mov_V <- movieSVD$v[, 1:n_dims]

trimMovies <- as.data.frame(trim_mov_V) %>% select(V1, V2)
trimMovies$movieId <- as.integer(rownames(trimMovies))

movieSample <- trimMovies %>% arrange(V1) %>% head(5)
movieSample <- rbind(movieSample, trimMovies %>% arrange(desc(V1)) %>% head(5))
movieSample <- rbind(movieSample, trimMovies %>% arrange(V2) %>% head(5))
movieSample <- rbind(movieSample, trimMovies %>% arrange(desc(V2)) %>% head(5))

movieSample <- movieSample %>%
  inner_join(Movies, by = "movieId") %>%
  select(Movie = title, Concept1 = V1, Concept2 = V2)

movieSample$Concept1 <- round(movieSample$Concept1, 4)
movieSample$Concept2 <- round(movieSample$Concept2, 4)

knitr::kable(movieSample, booktabs = TRUE, caption = "Top and Bottom Movies by SVD Concept Values") %>%
  kableExtra::kable_styling(latex_options = c("striped", "hold_position"))

# Plot labels without overlapping
library(ggrepel)

ggplot(movieSample, aes(Concept1, Concept2, label=Movie)) + 
  geom_point() +
  geom_text_repel(aes(label=Movie), hjust=-0.1, vjust=-0.1, size = 3) +
  scale_x_continuous(limits = c(-0.2, 0.2)) +
  scale_y_continuous(limits = c(-0.1, 0.1))