It is not completely clear to me which algorithm typesetting package are you using, since you did not include the document preamble, and your code is a strange jumble of several different syntaxes, mostly looking like the old algorithms package syntax, but not quite. Your tags seem to indicate that you are using the algorithmicx bundle, so I assume that you use the algpseudocode package. You need to correct some syntax, for example algpseudocode does noy capitalize command, only first letter, so you should have \If ... \Else ... \EndIf etc.
Also, command \For and \If take an argument, so you need
\If{something something}
The \If does not use \Then, you should leave that out.
Every line must have a command, so you should either define your own commands for things like "Given:", or just use \State.
The following will hopefully do what you expect it to do:
\documentclass{article}
\usepackage{algpseudocode}
\usepackage{algorithm}
\begin{document}
\begin{algorithm}
\caption{Blah blah}
\begin{algorithmic}[1]
\State Given: User-Noun Matrix $X$
\For{$i = 1 \to n$}
\State Let $S_i$ = {$s{i,j}$ | $0\le j \le l_i$} be set of nodes which have links to $i$;
\If{$\left(l_i=0 \hbox{OR} l_i=1 \right)$}
\State $b_i=0$;
\Else
\State Compute the similarity score vectors $r_{s,1},r_{s,2},...,r_{s,l_i}$ for each $S_i=s_1,s_2,...s_{l_i}$; \\
\State Construct $l_i \times l_i$ matrix $R_i= \left[r_{s,1},r_{s,2},...,r_{s,l_i}\right]$;
\State Take the average of all non-diagonal elements in $R_i$ to obtain $\hat{r_s}$;
\State $b_i= 1/\hat{r_s}$;
\EndIf
\EndFor
\State \Return vector $b$ of bridging scores;
\end{algorithmic}
\end{algorithm}
\end{document}
The algorithmicx bundle have pretty good documentation with a number of examples, I suggest you take a look at it.
Here's an option that provides feasible output. I've removed the physical numbering in the caption:
\documentclass[10pt,twocolumn]{article}
\usepackage{algorithm,algpseudocode}% http://ctan.org/pkg/{algorithms,algorithmx}
\algnewcommand{\Inputs}[1]{%
\State \textbf{Inputs:}
\Statex \hspace*{\algorithmicindent}\parbox[t]{.8\linewidth}{\raggedright #1}
}
\algnewcommand{\Initialize}[1]{%
\State \textbf{Initialize:}
\Statex \hspace*{\algorithmicindent}\parbox[t]{.8\linewidth}{\raggedright #1}
}
\begin{document}
\begin{algorithm}
\caption{Boosted $K$ Nearest Neighbour}
\begin{algorithmic}[1]
\Inputs{$S={s_i}=\left(x_i,y_i\right)$}
\Initialize{\strut$w_i^0 \gets 0$, $i=1,\ldots,n$ \\ $S_0 \gets S$}
\For{t = 1 to T}
\State $S_t \gets S_{t-1}$
\For{$s_q \in S_t$}
\State $N_q \gets$ k nearest neighbors
\State of $s_q$ using $D(s_q,s_i)$
\State label($s_q$)$=argmax\sum_{s_i \in N_q}D(s_q,s_i)$;
\If{label($s_q$)$\ne y_q$}
\For{$s_i \in N_i$}
\If{$y_i \ne y_q$}
\State $w_{i}^{t} \gets w_{i}^{t} - \lambda/d(x_q,x_i)$;
\Else
\State $w_{i}^{t} \gets w_{i}^{t} + \lambda/d(x_q,x_i)$;
\EndIf
\EndFor
\EndIf
\EndFor
\If{label($s_q$)$=y_q \forall_{s_q}$}
\State break
\EndIf
\EndFor
\end{algorithmic}
\end{algorithm}
\end{document}
A newly-defined \Inputs and (equivalent) \Initialize takes one argument that sets its contents in a \Statex with an indent of \algorithmicindent - the default - to align with the other algorithm elements. The contents is stored in a top-aligned \parbox that fits across 80% of the line. I'm sure you won't need more, but in case you do, that can also be fixed to not cause overfull boxes.
Best Answer
You can use TikZ and
\tikzmarkfor this: first, using\tikzmarkyou place a mark right after\INPUTand another one right where your inputs end, and then use the\DrawBoxcommand with those two marks to draw the frame; the optional argument allows you to control some attributes (color, line width) of the frame:The code needs three runs to stabilize.
In a comment it has been requested to have a background color for the frame; this can be easily achieved using the
tikzmarklibrary (the library provides a sophisticated version of\tikzmark):Some remarks:
The library provides a sophisticated version of
\tikzmark, so there's no need to define it once the library has been loaded.The
\DrawBoxcommand must be used before the algorithm to which it will be applied; otherwise, the background will overwrite the contents of the input.Two or three runs are necessary for the code to stabilize.