Failed attempt at using holographic database for determining entry presence/absense

holo_fail.r

#define a function to generate a random vector
makeNewVector = function(vectorLength){
	#random normal
	x = rnorm(vectorLength)
	#normalize to length 1
	x/(sqrt(sum(x^2)))
}

#define a function to compute cosine similarity between two vectors
cosine <- function( x, y) {
	crossprod(x,y) / sqrt( crossprod(x)*crossprod(y) )
}


#set random seed
set.seed(1)

#set simulation parameters
vectorLength = 1e3
numVectors = 1e4

#generate entry vectors
vecList = list()
for(i in 1:numVectors){
	#each vector is a random normal with length 1
	vecList[[i]] = makeNewVector(vectorLength)
}

#generate database
db = rep(0,vectorLength)
for(i in 1:numVectors){
	#database is simply the superposition of its vectors
	db = db + vecList[[i]]
}

#compute resonance of each entry
sims = rep(NA,numVectors)
for(i in 1:numVectors){
	sims[i] = cosine(vecList[[i]],db)
}

#check against vectors not in database
newSims = rep(NA,numVectors)
for(i in 1:numVectors){
	#each vector is a random normal with length 1
	newVec = makeNewVector(vectorLength)
	newSims[i] = cosine(newVec,db)
}


#gather & vizualize the similarities
library(tidyverse)
tibble(
	newSims
	, sims
) %>% 
	tidyr::gather(
		key = class
		, value = value
	) %>% 
	ggplot()+
	facet_grid(
		class ~ .
	)+
	geom_histogram(
		mapping = aes(
			x = value
		)
	)