hpcbio_mash_minhash_jun_2016.Rnw

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  56
  57 \title[MASH]{Mash: fast genome and metagenome distance estimation}
  58 \author[Don Armstrong]{Don L. Armstrong}
  59 \institute[IGB]{Institute for Genomic Biology, Computing Genomes
  60   for Reproductive Health, University of Illinois, Urbana-Champaign}
  61
  62 \begin{document}
  63
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  70 options(digits=2)
  71 library("data.table")
  72 library("ggplot2")
  73 library("reshape2")
  74 library("grid")
  75 library("xtable")
  76
  77 @
  78
  79 \IfFileExists{figures/relevant_xkcd.png}{\frame[plain]{\centering \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{figures/relevant_xkcd.png}
  80
  81     \url{https://xkcd.com/1691/}}}
  82
  83 \frame[plain]{\titlepage
  84   \begin{center}
  85     Code and slides are here:
  86
  87     \qrcode[padding]{http://dla2.us/p/mashminhash2016}
  88
  89     \url{http://dla2.us/p/mashminhash2016}
  90    \end{center}
  91  }
  92
  93
  94 \frame[plain]{
  95   \begin{center}
  96   \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/paper_frontpage}
  97 \end{center}
  98 }
  99
 100 \begin{frame}{MinHash Algorithm}
 101   \begin{columns}
 102     \column{0.3\textwidth}
 103     \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/fig_1.png}
 104     \column{0.7\textwidth}
 105     \begin{itemize}
 106     \item Decompose dataset into k-mers
 107       \only<2>{
 108         \begin{digression}{What about strandedness}
 109           \begin{itemize}
 110           \item Take lexically lowest sequence
 111             \begin{itemize}
 112             \item Given 7-mers 5'-ACTGCAC-3' and its reverse complement, 5'-GTGCAGT-3'
 113             \item A $\lt$ G
 114             \item Use ACTGCAC
 115             \end{itemize}
 116           \item Because $S(A \cup B)$ is a random sample of $A \cup B$
 117             the fraction of elements in $S(A \cup B)$ which are shared
 118             by $S(A)$ and $S(B)$ is an unbiased estimate of $J(A,B)$
 119           \item $J(A,B) \approx \frac{|S(A \cup B) \cap S(A) \cap (B)}{|S(A \cup B)|}$
 120           \end{itemize}
 121         \end{digression}
 122       }
 123     \item Hash k-mers (32/64bit)
 124     \item Estimate Jaccard Index $J(A,B)$
 125       \only<3>{
 126         \begin{digression}{Estimating Jaccard Index}
 127           $J(A,B) = \frac{|A \cap B|}{|A \cup B|}$
 128           \begin{itemize}
 129           \item Sample randomly from $A$ and $B$
 130           \item Because $S(A \cup B)$ is a random sample of $A \cup B$
 131             the fraction of elements in $S(A \cup B)$ which are shared
 132             by $S(A)$ and $S(B)$ is an unbiased estimate of $J(A,B)$
 133           \item $J(A,B) \approx \frac{|S(A \cup B) \cap S(A) \cap (B)}{|S(A \cup B)|}$
 134           \end{itemize}
 135         \end{digression}
 136       }
 137     \item<3-> How can we randomly sample?
 138     \item<3-> Properties of the hash!
 139     \end{itemize}
 140   \end{columns}
 141 \end{frame}
 142
 143 \begin{frame}{Hash functions}
 144
 145 \end{frame}
 146
 147 \begin{frame}{MurmerHash3 -- properties}
 148 \end{frame}
 149
 150 \begin{frame}
 151   \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/fig_2.png}
 152 \end{frame}
 153
 154 \begin{frame}
 155   \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/fig_3.png}
 156 \end{frame}
 157
 158 \begin{frame}
 159   \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/fig_4.png}
 160 \end{frame}
 161
 162 \begin{frame}
 163   \includegraphics[width=\textwidth,height=0.8\textheight,keepaspectratio]{mash_minhash_paper/fig_5.png}
 164 \end{frame}
 165
 166
 167 \section*{References}
 168
 169 \begin{frame}[plain]{References}
 170   \begin{center}
 171     \mbox{}\vspace{-\baselineskip}
 172     \printbibliography[heading=none]
 173   \end{center}
 174 \end{frame}
 175
 176 \end{document}