Computational Models of Music Similarity and their ... - OFAI

28 2 Audio-based Similarity Measures
on the expectations. The expectation step is:
P (m|x n , Θ) = p(x n|m, Θ)P m
p(x n )
=
N (x n |µ m , Σ m )P m
∑ M
m ′ =1 N (x . (2.14)
n|µ m ′, Σ m ′)P m ′
The maximization step is:
∑
µ ∗ m = ∑ n P (m|x n, Θ)x n
n
P (m|x ′ n ′, Θ)
∑n
Σ ∗ m =
P (m|x n, Θ)(x n − µ m )(x n − µ m )
∑
T
n
P (m|x ′ n ′, Θ)
Pm ∗ = 1 ∑
P (m|x n , Θ).
N
n
(2.15)
Cluster Model Similarity
To compute the similarity of pieces A and B a sample from each GMM
is drawn, X A and X B respectively. (It is not feasible to store and use the
original MFCC frames instead, due to memory constraints when dealing with
large collections.) In the remainder of this section a sample size of 2000 is
used. The log-likelihood L(X|Θ) that a sample X was generated by the
model Θ is computed for each piece/sample combination (Equation 2.13).
Aucouturier and Pachet [AP02a] suggest computing the distance as:
d AB = L(X A |Θ A ) + L(X B |Θ B ) − L(X A |Θ B ) − L(X B |Θ A ). (2.16)
Note that L(X A |Θ B ) and L(X B |Θ A ) are generally different values. However,
a symmetric similarity measure (d AB = d BA ) is very desirable for most
applications. Thus, both are used for d AB . The self-similarity is added
to normalize the results. In most cases the following statements are true:
L(X A |Θ A ) > L(X A |Θ B ) and L(X A |Θ A ) > L(X B |Θ A ).
The distance is (slightly) different every time it is computed due to the
randomness of the sampling. Furthermore, if some randomness is used to
initialize the GMM, different models will be produced every time and will
also lead to different distance values.
ISMIR 2004 Genre Classification Contest
An implementation of G30 using a nearest neighbor classifier with the following
parameters won the ISMIR 2004 genre classification contest. Three
minutes from the center of each piece (22kHz, mono) were used for analysis.
The MFCCs were computed using 19 coefficients (the first is ignored). The