% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/lsh_probability.R
\name{lsh_probability}
\alias{lsh_probability}
\alias{lsh_threshold}
\title{Probability that a candidate pair will be detected with LSH}
\usage{
lsh_probability(h, b, s)

lsh_threshold(h, b)
}
\arguments{
\item{h}{The number of minhash signatures.}

\item{b}{The number of LSH bands.}

\item{s}{The Jaccard similarity.}
}
\description{
Functions to help choose the correct parameters for the \code{\link{lsh}} and
\code{\link{minhash_generator}} functions. Use \code{lsh_threshold} to
determine the minimum Jaccard similarity for two documents for them to likely
be considered a match. Use \code{lsh_probability} to determine the
probability that a pair of documents with a known Jaccard similarity will be
detected.
}
\details{
Locality sensitive hashing returns a list of possible matches for
similar documents. How likely is it that a pair of documents will be detected
as a possible match? If \code{h} is the number of minhash signatures,
\code{b} is the number of bands in the LSH function (implying then that the
number of rows \code{r = h / b}), and \code{s} is the actual Jaccard
similarity of the two documents, then the probability \code{p} that the two
documents will be marked as a candidate pair is given by this equation.

\deqn{p = 1 - (1 - s^{r})^{b}}

According to \href{http://infolab.stanford.edu/~ullman/mmds/book.pdf}{MMDS},
that equation approxmiates an S-curve. This implies that there is a threshold
(\code{t}) for \code{s} approximated by this equation.

\deqn{t = \frac{1}{b}^{\frac{1}{r}}}
}
\examples{
# Threshold for default values
lsh_threshold(h = 200, b = 40)

# Probability for varying values of s
lsh_probability(h = 200, b = 40, s = .25)
lsh_probability(h = 200, b = 40, s = .50)
lsh_probability(h = 200, b = 40, s = .75)
}
\references{
Jure Leskovec, Anand Rajaraman, and Jeff Ullman,
 \href{http://www.mmds.org/#book}{\emph{Mining of Massive Datasets}}
 (Cambridge University Press, 2011), ch. 3.
}

