This feature already exists in jekyll, enabling this feature in octopress is a trival task.
See http://jcftang.github.com/ for an example of its use, click into some of the posts to see.
Firstly add this to your _config.yml file
lsi: true
The create a file such as source/_includes/custom/asides/related.html with the following content
<section>
<h1>Related Posts</h1>
<ul class="posts">
{% for post in site.related_posts limit:5 %}
<li class="related">
<a href="{{ root_url }}{{ post.url }}">{{ post.title }}</a>
</li>
{% endfor %}
</ul>
</section>
It is possible to style the list, but in the above I have chosen to keep the same style as the recent posts.
Finally, add the file to your default asides list in your _config.yml file
default_asides: [custom/asides/related.html, ...]
There are some issues with enabling LSI in jekyll/octopress, the primary issue will be performance. The default implementation will be slow if you have lots of posts to classify. It would be recommended that rb-gsl be installed to accelerate the classification process.
Building native extensions. This could take a while...
ERROR: Error installing gsl:
ERROR: Failed to build gem native extension.
...
The gsl gem requires gsl 1.14. Installing gsl using apt-get or brew will get you 1.15, which leads to another error when installing the rb-gsl gem.
$ curl -O http://mirror.aarnet.edu.au/pub/gnu/gsl/gsl-1.14.tar.gz
$ tar xfz gsl-1.14.tar.gz
$ cd gsl-1.14
$ ./configure
$ make clean
$ make # can take a while, be patient
$ sudo make install
$ gem install gsl
See http://bretthard.in/2012/03/getting-related_posts-lsi-and-gsl-to-work-in-jekyll/#.UEZRSLQgeoM