require(lattice)
require(XML)
require(quantreg)

# Single Item

rateSample = read.csv("rateSample.csv", header = TRUE, row.names = "ID")

# plot(1:400, apply(rateSample[, 2:6], 1, sum))

fit = lm(Y ~ . - 1, data = rateSample)  # couldn't reveal the truth
summary(fit)

parallel(~ rateSample[, 6:2], 
         alpha           = 0.1,   # alpha-blending
         aspect          = "xy",  # 45-degree banking
         horizontal.axis = FALSE)

# Douban Movie 250 List
# See http://en.wikipedia.org/wiki/Internet_Movie_Database
# C [6.0, 8.5],    step = 0.01, 251  nodes.
# m [1300, 25000], step = 10,   2371 nodes.

url = "http://movie.douban.com/top250?format=text"
topList = htmlTreeParse(url, useInternal = TRUE)

rateScore = as.numeric(iconv(sapply(getNodeSet(doc = topList,
            path = "//td[@headers='m_rating_score']"), xmlValue),
            from = 'UTF-8', to = ''))

rateNum = as.numeric(iconv(sapply(getNodeSet(doc = topList,
          path = "//td[@headers='m_rating_num']"), xmlValue),
          from = 'UTF-8', to = ''))

RV = rateScore * rateNum

cGrid = rep(seq(6.0, 8.5, 0.01), 2371)
mGrid = rep(seq(1300, 25000, 10), 251)

resMat = matrix(NA, nrow = 251 * 2371, ncol = 250)

for (i in 1:nrow(resMat)) {
     resMat[i, ] = sort(
     (RV + (cGrid[i] * mGrid[i]))/(rateNum + mGrid[i]), 
     index.return = TRUE, decreasing = TRUE)$ix
}

# L1-norm

resVec = rep(NA, nrow(resMat))
for (i in 1:length(resVec)) {
     resVec[i] = as.numeric(
     dist(rbind(1:250, resMat[i, ]), 
     method = "manhattan"))
}

which(resVec == min(resVec))  # GMT+8 2011/12/24 18:00
# [1] 28617 28618 161404 161406 161407 315515 315516 469626 469627
cGrid[which(resVec == min(resVec))]
# [1] 6.02 6.03 6.10 6.12 6.13 6.07 6.08 6.04 6.05
mGrid[which(resVec == min(resVec))]
# [1] 2940 2950 3050 3070 3080 3010 3020 2970 2980

# L2-norm
resVec = rep(NA, nrow(resMat))
for (i in 1:length(resVec)) {
     resVec[i] = as.numeric(
     dist(rbind(1:250, resMat[i, ]), 
     method = "euclidean"))
}

which(resVec == min(resVec))         # [1] 315515
cGrid[which(resVec == min(resVec))]  # [1] 6.07
mGrid[which(resVec == min(resVec))]  # [1] 3010


# Quantile Regression for Rank Shift
x = 1:250
y = abs(resMat[315515, ] - 1:250)
plot(x, y, cex = 0.25, 
     type = "n", ylim = c(0, 25),
     xlab = "Original Rank", 
     ylab = "Absolute Rank Shift")
points(x, y, cex = 0.5, col = "darkgrey")
abline(rq(y ~ x, tau = 0.5), col = "black")  # Median Est.
abline(lm(y ~ x), lty = 2, col = "red")      # Least Square Est.
taus = c(0.1, 0.25, 0.75, 0.90)
for(i in 1:length(taus)) {
    abline(rq(y ~ x, 
    tau = taus[i]), 
    col = "darkgrey")
}