$1\mathrm{.}1(2$ points$)$ What is $($are$)$ the input parameter$($s$)$ needed to be specified by the user?

$1\mathrm{.}2(3$ points$)$ What is the dimension of $\backslash (\backslash$boldsymbol$\{\backslash$eta$\}\backslash )?$

$1\mathrm{.}3(5$ points$)$ What is the purpose of the second equation $($in terms of the connection to the third equation$)?$

$1.4(20$ points$)$ Suppose now we are allowed to set the values for only $4$ input parameters, which are $\backslash (\backslash$alpha$,\backslash$beta$,\backslash$gamma $\backslash ),$ and $\backslash (\backslash$eta $\backslash ).$ Adapt the above LDA and express your adapted LDA using algorithmic descriptions $($see page $23$ "Labeled LDA" in week $6$ as an example$).$