  Idea Density (ID) measures the rate at which ideas or elementary predications
are expressed in an utterance or in a text. Lower ID is found to be associated
with an increased risk of developing Alzheimer's disease (AD) (Snowdon et al.,
1996; Engelman et al., 2010). ID has been used in two different versions:
propositional idea density (PID) counts the expressed ideas and can be applied
to any text while semantic idea density (SID) counts pre-defined information
content units and is naturally more applicable to normative domains, such as
picture description tasks. In this paper, we develop DEPID, a novel
dependency-based method for computing PID, and its version DEPID-R that enables
to exclude repeating ideas---a feature characteristic to AD speech. We conduct
the first comparison of automatically extracted PID and SID in the diagnostic
classification task on two different AD datasets covering both closed-topic and
free-recall domains. While SID performs better on the normative dataset, adding
PID leads to a small but significant improvement (+1.7 F-score). On the
free-topic dataset, PID performs better than SID as expected (77.6 vs 72.3 in
F-score) but adding the features derived from the word embedding clustering
underlying the automatic SID increases the results considerably, leading to an
F-score of 84.8.
