How to recommend the next achievement

Short version:

I have a similar setup to StackOverflow. Users get Achievements. I have many more achievements than SO, lets say on the order of 10k, and each user has in the 100s of achievements. Now, how would you recommend (to recommend) the next achievement for a user to try for?

Long version:

The objects are modeled like this in django (showing only important parts) :

class User(models.Model):
    alias = models.ForeignKey(Alias)

class Alias(models.Model):
    achievements = models.ManyToManyField('Achievement', through='Achiever')

class Achievement(models.Model):
    points = models.IntegerField()

class Achiever(models.Model):
    achievement = models.ForeignKey(Achievement)
    alias = models.ForeignKey(Alias)
    count = models.IntegerField(default=1)

and my algorithm is just to find every other user that has a shared achievement with the logged in user, and then go through all their achievements and sort by number of occurrences :

def recommended(request) :
    user = request.user.get_profile()

    // The final response
    r = {}

    // Get all the achievements the user's aliases have received 
    // in a set so they aren't double counted
    achievements = set()
    for alias in user.alias_set.select_related('achievements').all() :
        achievements.update(alias.achievements.all())

    // Find all other aliases that have gotten at least one of the same
    // same achievements as the user
    otherAliases = set()
    for ach in achievements :
        otherAliases.update(ach.alias_set.all())

    // Find other achievements the other users have gotten in addition to
    // the shared ones.
    // And count the number of times each achievement appears
    for otherAlias in otherAliases :
        for otherAch in otherAlias.achievements.all() :
            r[otherAch] = r.get(otherAch, 0) + 1

    // Remove all the achievements that the user has already gotten
    for ach in achievements :
        r.pop(ach)

    // Sort by number of times the achievements have been received
    r = sorted(r.items(), lambda x, y: cmp(x[1], y[1]), reverse=True)

    // Put in the template for showing on the screen
    template_values = {}
    template_values['achievements'] = r

But it takes FOREVER to run, and always returns the whole list, which is unneeded. A user would only need the top few achievements to go after.

So, I'm welcome to recommendations on other algorithms and/or code improvements. I'll give you an achievement in my system for coming up with the recommendation algorithm :)

Solution

One method you can recommend which achievements to go for is to see how many of your users already have those achievements and recommend those popular ones. When they have achieved those you go down the list and recommend slightly less popular ones. However, this has a naive assumption that everyone wants to go for popular achievements. It might cause popular achievements to be even more popular and less popular ones, well... A consolation is that this doesn't take up much resources and is likely to run very fast. (Just keep a list of achievements + number of times it's achieved)

Another method (which attempts to guess which achievements the user is likely to go after based on what achievements he already had) is to use some machine learning algorithms. I think the k-nearest neighbor algorithm will perform quite well here. Select a threshold and just output everything that is above this threshold. Now, I don't know if this will run faster than what you already have, but you should just run the recommendation engine once every time the user has made a new achievement, store the top (let's say) five, and just output it back to the user whenever a recommendation is needed.

I hope this helps. =)