If your table looks something like this:
SELECT * from categories;
+---------+----------+
| page_id | category |
+---------+----------+
| 1 | a |
| 1 | b |
| 1 | a |
| 1 | c |
| 1 | a |
| 1 | b |
| 1 | a |
| 2 | d |
| 2 | d |
| 2 | c |
| 2 | d |
| 3 | a |
| 3 | b |
| 3 | c |
| 4 | c |
| 4 | d |
| 4 | c |
+---------+----------+
17 rows in set (0.00 sec)
Then you may want to try this query:
SELECT c1.page_id, MAX(freq.total),
(
SELECT c2.category
FROM categories c2
WHERE c2.page_id = c1.page_id
GROUP BY c2.category
HAVING COUNT(*) = MAX(freq.total)
LIMIT 1
) AS category
FROM categories c1
JOIN (
SELECT page_id, category, count(*) total
FROM categories
GROUP BY page_id, category
) freq ON (freq.page_id = c1.page_id)
GROUP BY c1.page_id;
Which returns this:
+---------+-----------------+----------+
| page_id | MAX(freq.total) | category |
+---------+-----------------+----------+
| 1 | 4 | a |
| 2 | 3 | d |
| 3 | 1 | a |
| 4 | 2 | c |
+---------+-----------------+----------+
4 rows in set (0.00 sec)
Compare the results with the actual frequency distribution:
SELECT page_id, category, COUNT(*) FROM categories GROUP BY page_id, category;
+---------+----------+----------+
| page_id | category | COUNT(*) |
+---------+----------+----------+
| 1 | a | 4 |
| 1 | b | 2 |
| 1 | c | 1 |
| 2 | c | 1 |
| 2 | d | 3 |
| 3 | a | 1 |
| 3 | b | 1 |
| 3 | c | 1 |
| 4 | c | 2 |
| 4 | d | 1 |
+---------+----------+----------+
10 rows in set (0.00 sec)
Note that for page_id = 3
, there is no leading frequency, in which case this query makes no guarantee on which category will be chosen in such a case.