How to avoid the number line for comments under algorithm2e

Here are no less than four ways to do it, maybe the second is preferable.

1. Use separate \KwData lines.
2. A new command \KwDataXX is defined that leaves space as if Data: is written, but without actually writing it.
3. Using an aligned environment; here, only one comment can be left to the right of the aligned block
4. using an align* environment with comments in the math block itself

Code:

\documentclass{article}
\usepackage[ruled,vlined]{algorithm2e}
\usepackage{amsmath,amssymb}
\usepackage{cprotect}%% only needed to have \verb work in \caption

\makeatletter
\algocf@newcommand{KwDataXX}[1]{%
  \sbox\algocf@inputbox{\hbox{\KwSty{Data}\algocf@typo: }}%
  \ifthenelse{\boolean{algocf@inoutnumbered}}{\relax}{\everypar={\relax}}%
  {\let\\\algocf@newinput\hspace{\wd\algocf@inputbox}\hangindent=\wd\algocf@inputbox\hangafter=\wd\algocf@inputbox#1\par}%
  \algocf@linesnumbered% reset the numbering of the lines
}
\makeatother

\begin{document}
\begin{algorithm}[!ht]
\LinesNumbered
\KwData{$\mathbf{X}\in \mathbb{R}^{i\times j}$            \tcp*{comment}}
\KwData{$p_x,p_y,p_z \in \mathbb{N}$                      \tcp*{comment}}
\KwData{$\alpha \in \mathbb{R}$                           \tcp*{comment}}
\KwResult{$\mathcal{X}\in \mathbb{R}^{i\times j\times k}$ \tcp*{comment}}
\cprotect\caption{algo -- separate \verb!\KwData! lines}
\label{alg:name}
\end{algorithm}

\begin{algorithm}[!ht]
\LinesNumbered
\KwData  {$\mathbf{X}\in \mathbb{R}^{i\times j}$          \tcp*{comment}}
\KwDataXX{$p_x,p_y,p_z \in \mathbb{N}$                    \tcp*{comment}}
\KwDataXX{$\alpha \in \mathbb{R}$                         \tcp*{comment}}
\KwResult{$\mathcal{X}\in \mathbb{R}^{i\times j\times k}$ \tcp*{comment}}
\cprotect\caption{algo2 -- using the new \verb!\KwDataXX! command}
\label{alg:name2}
\end{algorithm}

\begin{algorithm}[!ht]
\LinesNumbered
\DontPrintSemicolon
\KwData{%
  $\begin{aligned}
    \mathbf{X}  & \in \mathbb{R}^{i\times j}\\
    p_x,p_y,p_z & \in \mathbb{N}\\
    \alpha      & \in \mathbb{R}
  \end{aligned}$\tcp*{comment}
}
\KwResult{$\mathcal{X}\in \mathbb{R}^{i\times j\times k}$}
\cprotect\caption{algo3 -- using an \verb!aligned! environment, only one comment possible}
\label{alg:name3}
\end{algorithm}

\begin{algorithm}[!ht]
\LinesNumbered
\KwData{%
  \begin{align*}
    \mathbf{X}  & \in \mathbb{R}^{i\times j} && \text{comment}\\
    p_x,p_y,p_z & \in \mathbb{N} && \text{comment} \\
    \alpha      & \in \mathbb{R} && \text{comment}
  \end{align*}%
}
\KwResult{$\mathcal{X}\in \mathbb{R}^{i\times j\times k}$}
\cprotect\caption{algo4 -- using \verb!align*! with in-math comments}
\label{alg:name4}
\end{algorithm}
\end{document}

I usually use \LinesNumberedHidden before \begin{algorithm} and then use \ShowLn on each line that I want to have numbered.

For example:

\LinesNumberedHidden
\begin{algorithm}[H]
  \dontprintsemicolon
  \KwData{$\mathbf{X}\in \mathbb{R}^{i\times j}$\tcp*{comment}\;
  $\qquad\quad\:p_x,p_y,p_z \in \mathbb{N}$\tcp*{comment}\;
  $\qquad\quad\:\alpha \in \mathbb{R}$\tcp*{comment}\;}
  \KwResult{$\mathcal{X}\in \mathbb{R}^{i\times j\times k}$\tcp*{comment}\;}
 \ShowLn Line 2
 \ShowLn Line 3 etc...
\end{algorithm}

Although I know the previous answer is practically the general and efficient way to do this, I think this is the easiest. I know you would technically have to use the \ShowLn command on every line for this algorithm, but at least you don't have to define a new command.

The \LinesNumberedHidden command only applies for the next algorithm environment, but not for the rest of the algorithms in your document. So, this is another reason why I find it convenient.