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%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
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% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
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% Document Info
\author{chakra}
\pdfinfo{
  /Title (introduction-to-data-science-ii.pdf)
  /Creator (Cheatography)
  /Author (chakra)
  /Subject (introduction\_to\_data\_science\_ii Cheat Sheet)
}

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% Commands
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% Header and Footer
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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{introduction\_to\_data\_science\_ii Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{chakra} via \textcolor{DarkBackground}{\uline{cheatography.com/147981/cs/32207/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}chakra \\
  \uline{cheatography.com/chakra} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 25th May, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{formulas}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{standard units: z = (original - mean) / standard deviation} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{β1 = cov(x,y) / var(x)} \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{cov(x,y) = (∑ (y\_i - ȳ)(x\_i - x̄)) / n} \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{corr(xy) = cov(x,y) / (s\_x * s\_y)} \tn 
% Row Count 5 (+ 1)
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{hierarchical clustering}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{find successive clusters using previously established clusters \{\{nl\}\} - common approach is bottom-up: start with each element in a  separate cluster} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{single linkage: use minimum distance \{\{nl\}\} complete linkage: use maximum distance \{\{nl\}\} average linkage: use average linkage} \tn 
% Row Count 6 (+ 3)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{"minimum distance between group 1 points and group 2 points is larger than the minimum within-group distance for the same points"} \tn 
% Row Count 9 (+ 3)
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\par\addvspace{1.3em}

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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{knn classification}}  \tn
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% Row Count 0 (+ 0)
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{k-means}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{k-means algorithm: 1. construct clusters by associating each point with the closest centroid, 2. calculate new centroids for each set; repeat both till convergence} \tn 
% Row Count 4 (+ 4)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{as k increases, average variance of clusters decreases} \tn 
% Row Count 6 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{8.4cm}}{use features (x\_n) to partition data into K clusters (represented by its {\bf{centroid}} -{}- center of points in the cluster)} \tn 
% Row Count 9 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{goal is to minimize intra-class centroid points distances and find cnk (0 - 1 cluster membership) and µk (centroids) that minimize} \tn 
% Row Count 12 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{artificial neural networks}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{activation functions: \{\{nl\}\} - sigmoid (0, 1) \{\{nl\}\} sigmoid(z) = (exp z) / (1+exp z) \{\{nl\}\} - hyperbolic tangent (-1, 1) \{\{nl\}\} tanh(z) = (exp (z) – exp(-z) ) / (exp(z) + exp(-z))} \tn 
% Row Count 4 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}