List<String> personAccountsIDs = getPersonAccountsIDs(accountList);

    List<Contact> contactList = [Select ID,Name
                                (Select Name,ID,Brand__c,Customer_Type__c from Profiles__r),
                                (Select ID,Brand__c from Purchases__r)
                                from Contact
                                where AccountID in : personAccountsIDs];

    for(Contact c : contactList){

            Set<String> brandPurchased = new Set<String>();
            for(Purchase__c p : c.Purchases__r){
                if(p.Brand__c !=null)
                    brandPurchased.add(p.Brand__c.toLowerCase());
            }
     ....
}