LinkedIn doesn't directly allow you to post videos to your LinkedIn portfolio but it does support an application called "Creative Portfolio Display". You can use that application in conjunction with a free Behance account to include a video personal commercial as part of your LinkedIn profile.

Behance portfolios can include an embedded YouTube video. Each portfolio must have an image as a "cover page" to the portfolio but after that cover the next step in the portfolio could be to play the YouTube video of your personal commercial.

This video provides an example of how to link a Behance portfolio to your LinkedIn profile. While the context of the video is discussing an image portfolio, your portfolio could be simply a cover page and your video personal commercial: