improving music mood classification using lyrics, audio and social tags

Proof: Let p and
lyrics
paudio
denote the posterior probabilities of a data sample being estimated
as positive by the lyric-based and audio-based classifiers, and
p lyrics
and p
audio
denote the
probabilities of the sample being estimated as negative by the two classifiers respectively.
The multiplying rule says:
if
p × p > p × p
lyrics
audio
lyrics
audio
(2)
then the hybrid classifier would predict positive, otherwise, predict negative. In the case of
binary classification, (2) can be rewritten as:
p
lyrics
⇒ p
× p
lyrics
audio
+ p
> p
audio
lyrics
× p
audio
> 1 ⇒
= ( 1−
p
p
lyrics
+ p
2
lyrics
audio
)( 1−
p
> 0.5
audio
)
=
1−
p
lyrics
− p
audio
+ p
lyrics
× p
audio
This is, in fact, the rule of averaging.
Therefore, this research uses the weighted averaging as the rule of late fusion. For each
testing instance, the final estimation probability is calculated as:
p = α p + ( 1−
α)
p
(3)
hybrid
lyrics
audio
where α is the weight given to the posterior probability estimated by the lyric-based classifier. A
song is classified as positive when the hybrid posterior probability is larger or equal than 0.5. In
this experiment, the value of α was changed from 0.1 to 0.9 with an increment step of 0.1. The α
value resulting in the best performing system was used to build the late fusion system, which was
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