Grouping By Similarity (using pg_trgm)?

[pg version 9.3 or 9.4]

Suppose I have a simple table:

create table data (
my_value TEXT NOT NULL
);
CREATE INDEX idx_my_value ON data USING gin(my_value gin_trgm_ops);

Now I would like to essentially do group by to get a count of all the
values that are sufficiently similar. I can do it using something like a
CROSS JOIN to join the table on itself, but then I still am getting all the
rows with duplicate counts.

Is there a way to do a group by query and only return a single "my_value"
column and a count of the number of times other values are similar while
also not returning the included similar values in the output, too?