Mining Massive Datasets - 7a LSH Family, Hash Functions

mmds-q7a.R

#
# Q1
# Suppose we have an LSH family h of (d1,d2,.6,.4) hash functions. We can use three functions from h and the AND-construction to form a (d1,d2,w,x) family, and we can use two functions from h and the OR-construction to form a (d1,d2,y,z) family. Calculate w, x, y, and z, and then identify the correct value of one of these in the list below.
#
val1 <- .6
val2 <- .4

# AND construction
w <- val1 ^ 3
x <- val2 ^ 3

# OR construction
y <- 1 - ((1 - val1) ^ 2)
z <- 1 - ((1 - val2) ^ 2)

c(w=w, x=x, y=y, z=z)

# w     x     y     z 
# 0.216 0.064 0.840 0.640