How to get similar objects based on tags using Doctrine

I have a table with articles. Articles can have one or more tags. I'd like to retrieve simular articles based on their tags.

My table structure is very simple. It basically just a many to many relation between Articles and Tags

abstract class BaseArticle extends Doctrine_Record
{
    public function setTableDefinition()
    {
        $this->setTableName('article');
        $this->hasColumn('id', 'integer', 8, array(
             'type' => 'integer',
             'length' => 8,
             'primary' => true,
             'autoincrement' => true,
             ));
        $this->hasColumn('title', 'string', null, array(
             'type' => 'string'
             ));
    }

    public function setUp()
    {

        $this->hasMany('Articletag', array(
             'local' => 'id',
             'foreign' => 'article_id',
             'cascade'=>array('delete')));

        $this->hasMany('Dbtag as Dbtags', array('refClass'=&g开发者_开发知识库t;'Articletag',
                'local' => 'article_id',
                'foreign'=>'tag_id'
                )
        );

    }
}


abstract class BaseDbtag extends Doctrine_Record
{
    public function setTableDefinition()
    {
        $this->setTableName('dbtag');
        $this->hasColumn('id', 'integer', 4, array(
             'type' => 'integer',
             'length' => 4,
             'fixed' => false,
             'unsigned' => false,
             'primary' => true,
             'autoincrement' => true,
             ));
        $this->hasColumn('name', 'string', 255, array(
             'type' => 'string',
             'length' => 255,
             'fixed' => false,
             'unsigned' => false,
             'primary' => false,
             'notnull' => false,
             'autoincrement' => false,
             ));
    }

    public function setUp()
    {
        parent::setUp();
        $this->hasMany('Articletag', array(
             'local' => 'id',
             'foreign' => 'tag_id'));

    }
}

abstract class BaseArticletag extends Doctrine_Record
{
    public function setTableDefinition()
    {
        $this->setTableName('articletag');
        $this->hasColumn('article_id', 'integer', 8, array(
             'type' => 'integer',
             'length' => 8,
             'fixed' => false,
             'unsigned' => false,
             'primary' => true,
             'autoincrement' => false,
             ));
        $this->hasColumn('tag_id', 'integer', 4, array(
             'type' => 'integer',
             'length' => 4,
             'fixed' => false,
             'unsigned' => false,
             'primary' => true,
             'autoincrement' => false,
             ));
    }

    public function setUp()
    {
        parent::setUp();
        $this->hasOne('Article', array(
             'local' => 'article_id',
             'foreign' => 'id'));

        $this->hasOne('Dbtag', array(
             'local' => 'tag_id',
             'foreign' => 'id'));
    }
}

What i need is to retrieve similar articles based on tag set. I want to get say 10 articles sorted by count of matched tags.

A similar problem (with movies instead of articles) is solved in native SQL here.

What is the best way to do this in Doctrine using Doctrine_Query without using native SQL?