Magento产品视图 - 显示产品的某些类别

Hello and thank you in advance for your future answers. My problem is as follows: I'm working on Magento with several store views. Each store have its own Category tree, like this:

Store 1

Kids

Ladies

Mens

Store 2

Kids

Ladies

Mens

Store 3

Kids

Ladies

Mens

Now... on the product page I thought it would be neat to display all the categories that products belongs to. The code I'm using is this:

                <?php $categories = $_product->getCategoryIds(); ?>
               <?php foreach($categories as $k => $_category_id): ?>
               <?php $_category = Mage::getModel('catalog/category')->load($_category_id) ?> 
                            <div class="attr-prod">
                              <a href="<?php echo $_category->getUrl() ?>"><?php echo $_category->getName() ?></a>
                            </div>
               <?php endforeach; ?>

which works, except the fact that it's bringing up ALL the categories from ALL the stores. Is there a way to pick just the categories within a certain root category, for instance "Store 2"?