Best Clustering Method for Dataset with Few Distinct Values

Question

I have a dataset that has the opinions of 30 different TV shows for 2000 high school students.

A student could have said they liked the show, did not have an opinion, or disliked the show. These values then translate to [1,0,-1] in my dataset.

I would now like to find approx 10-20 clusters of student types based on this dataset.

Because there are only 3 unique values in each field, it seems like this data should follow clustering rules for binary data (ex: avoid kmeans). I have been reading literature on that but am still struggling to determine what the best methods would be.

If anyone has any input on what would be best, I would really appreciate it!

Below is smaller example of the dataset:

Student	Friends	Seinfeld	HIMYM	Cheers
Student A	1	1	1	-1
Student B	1	0	0	-1
Student C	0	1	-1	-1

Answer 1

I don't think there is a "best" method in clustering. Here are some ideas (all use k-means in the end though):

1. Read this Netflix price paper and try to use matrix decomposition to assign each student a vector of small dimension, then cluster these vectors using k-means.

2. Choose a random matrix of dimensions d x 30, with row vectors standardized to length one, and d small. Multiply with your dataset. Try to cluster the resulting 2000 points of dimension d using k-means.

3. Or just use k-means because dimension 30 is not that large :).