# READ AND DISPLAY DATA

bcw = read.csv("BCW/breast-cancer-wisconsin.data")
bcw[1,]
bcw[,1]

c(1,2,4)

names(bcw) = c("ID","ClumpThick","UCSize","UCShape","A5","A6","A7","A8","A9","A10","A11")

bcw[1,]
bcw[,"A7"]
bcw[1:30,1:10]

# BUILD FREQUENCY and CONTINGENCY TABLES

table(bcw[,2])
table(bcw[,2:3])

# basic statistics with built-in functions (mean, median, min, max, midrange, variance, standard deviation, quartiles, IQR, )

wdbc = read.csv("BCW/wdbc.data")
mean(wdbc[,3])
median(wdbc[,3])
min(wdbc[,3])
max(wdbc[,3])
max(wdbc[,3]) - min(wdbc[,3])
?var
var(wdbc[,3])
sqrt(var(wdbc[,3]))
var(wdbc[,3])^0.5
quantile(wdbc[,3])
#     0%     25%     50%     75%    100% 
# 6.9810 11.6975 13.3550 15.7800 28.1100 
quantile(wdbc[,3],0.11)
#    11% 
#10.4837 

# computation of the mode linking built-in functions

which.max(table(bcw[,6]))

# data visualization (histograms, boxplot, scatter plot)

boxplot(wdbc[,2:ncol(wdbc)])
boxplot(bcw[,2:ncol(bcw)])

plot(wdbc[,3])
plot(wdbc[,3:6])

hist(bcw[,2])

qqplot(wdbc[,3],wdbc[,4])

# - S programming: assignments, comparisons, conditional statements, loops

# handling vectors
v = wdbc[,3]
v = v - 10.0
v = v / 10.0
w = wdbc[,4]
v*w
v %*% w

# - S programming: definition of functions
# - Example: re-implementing the mean() function
# - Homework: re-implement mean, variance, standard deviation, median; implement

# SIMILARITY MEASURES
a = c(1,0,0,1)
b = c(1,0,0,0)
table(a,b)
jaccard(a,b)

table(t(bcw[1,]),t(bcw[2,]))
cat_d(t(bcw[1,]),t(bcw[2,]))

minkowski(t(wdbc[1,3:6]),t(wdbc[2,3:6]),2)

# PREPROCESSING

#  a replace(x,y,T) function to replace each occurrence of a value x with value y in table T 

myrepl <- function(X, a, b) {
  for (i in 1:length(X)){
    if (X[i] == a) X[i] = b;
  }
  X
}

mysrepl <- function(a, b) {
 f <- function(x) {
   v = x;
   if (x == a) v = b;
   v
 }
}

aapply <- function(X, f) {
  for (i in 1:length(X)) X[i] = f(X[i])
  X
}

# SEARCH FOR MISSING VALUES IN bcw

for(i in 1:ncol(bcw)) for(j in 1:nrow(bcw)) if (! is.numeric(bcw[j,i])) print(c(i,j,bcw[j,i]))

aapply(bcw[,7],mysrepl("?",0))

# correlation / covariance

# Chi square test
bt = table(bcw[,2:3])
a = table(bcw[,2])
b = table(bcw[,3])
N = sum(a)

e = matrix(nrow=length(a),ncol=length(b))
for(i in 1:nrow(e)) for (j in 1:ncol(e)) e[i,j] = a[i]*b[j]/N
for(i in 1:nrow(e)) for (j in 1:ncol(e)) chi = chi + (bt[i,j] - e[i,j])^2 / e[i,j]

# Correlation and Covariance on Real Data