Unpacking Songlevel features and support vector machines for music classification by Mandel and Elli

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Unpacking Song-level features and support vector
machines for music classification by Mandel and
Ellis

• Presented by Rebecca Fiebrink
• IFT6080
• 13 March 2006

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Basic idea

• Classify artists using MFCCs
• Compare song-level and artist-level features
• Compare kNN and SVM
• Compare Mahalanobis and KL-divergence as distance
  metrics
• Compare single Gaussians and GMMs, using
  appropriate computations for KL-divergence
• Look for album effect

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Mahalanobis distance

• Distance based on correlations between variables
• Useful for determining similarity of an unknown
  sample set to a known one
• Also useful for defining the dissimilarity
  between two random vectors of the same
  distribution
• Differs from Euclidean takes into account the
  correlations of the dataset, and its
  scale-invariant

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Mahalanobis distance defined

• Equation for two vectors
• Or, for a sample set to a known set
• Assumes u and v are random vectors from the same
  distribution, with covariance matrix ?
• Can approximate ? as a diagonal matrix of
  individual variances, and use equation

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Kullback Leibler divergence

• Also called Kullback Leibler distance,
  information divergence, information gain, and
  relative entropy
• Represents the distance between a true
  probability distribution P to an arbitrary
  probability distribution Q
• Always nonnegative only zero if P and Q are
  equal
• Asymmetric, so not a true distance metric
• Several alternative symmetric versions exist
• Choosing the artist model with the smallest KL
  divergence w.r.t. a songs representation is
  equivalent to choosing the artist model under
  which the songs frames have the maximum
  likelihood.

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KL divergence defined

• Equation
• Single Gaussian case
• Mixture of Gaussians Must approximate using
  Monte Carlo

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SVMs in Mandel Ellis

• Uses DAG-SVM for multi-class classification
• DAG contains one node for each pair of classes
• N(N-1)/2 nodes for N classes
• Each node may have one associated classifier
• Algorithm efficiently places 1-vs-1 SVMs into DAG
• Can do VC-style bound of generalization error
  (unlike max-wins)
• Generalization performance is about as accurate
  as max-wins and 1-vs-rest, but training and
  evaluation are faster

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Kernels in Mandel Ellis

• SVMs all use standard radial basis function (RBF)
  kernel, with tunable ? gt 0
• Distance D defined using DM(u,v) or DKL
  (Xi,Xj)DKL(XiXj) DKL(XjXi)
• Implementation pre-compute the Gram matrix
  (matrix of all possible inner products between
  vectors in a set), using K

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Song-level vs. artist-level

• Song-level features collect bag of all MFCCs
  for a song (ignore temporal organization)
• Represent each song as a point in feature space
• Artist-level features MFCCs are not grouped by
  song

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Song-level representations

• Single Gaussian, described by mean and covariance
  of each of the MFCCs over the duration of a song
• use closed-form KL-divergence for distance
• Vector representation of the means and
  covariances for MFCCs (same information as above)
• use Mahalanobis distance
• Mixture of Gaussians, fit using EM algorithm
• use Monte Carlo to estimate KL-divergence for
  distance
• kNN and SVM can use all three of these

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Example of song-level classification
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Artist-level representations

• Single GMM representing all of an artists songs
• 50 Gaussians used
• Classify a new song as the artist model with the
  maximum likelihood of generating its frames
• Or, use each MFCC vector individually
• Each MFCC vector is a training instance for SVM
• Classify all MFCCs from a song individually, and
  assign most frequently predicted class to be song
  label
• Computation-intensive!!

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Example of artist-level classification
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Experiments
Classification
Max likelihood
SVM
kNN
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Artist-level
Representation
Song-level
Album-conscious Training, Testing, Validation
sets
Album-blind 3-fold CV
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Results Feature set

• Conclusion Song-level features are better
• Extraction time is higher, but training time is
  much lower for song-level features

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Results Representation/Distance measure

• Mahalanobis and KL for single Gaussian are
  comparable
• However, KL is better when not controlling for
  album effect
• KL for GMMs (500-sample Monte Carlo) is worse
  than single Gaussian KL (computed directly)

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Uninvited commentary, part 1

• Mandel and Ellis squeeze a lot of information
  into a short paper.
• My experiments comparing Mahalanobis and simple
  min-max normalized Euclidean distance for kNN
  show that these are pretty comparable for MFCCs
  in terms of accuracy
• However, Mahalanobis distance is a bad choice for
  other features

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Uninvited commentary, Part 2

• My biggest criticism is this papers use of
  statistical significance
• Significant at what level? Not defined.
• Cant simply compare differences between best of
  all configurations from each category,
  especially when you use different numbers of
  configurations from each category
• See Jensen and Cohen 2000.
• My next-biggest criticism is the smallness of the
  dataset
• Only 18 artists
• Cant really generalize about practical
  applications

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References

• Duda, R., P. Hart, and D. Stork. 2001. Pattern
  classification. New York John Wiley Sons. (2nd
  ed.)
• Hsu, C., and C. Lin. 2002. A comparison of
  methods for multiclass support vector machines.
  IEEE transactions on neural networks 13(2)
  415-25.
• Jensen, D., and P. Cohen. 2000. Multiple
  comparisons in induction algorithms. Machine
  learning 38 309-338.
• Mandel, M., and D. Ellis. 2005. Song-level
  features and support vector machines for music
  classification. Proceedings of the International
  Conference on Music Information Retrieval
  (ISMIR). 594-599.
• Wikipedia. www.wikipedia.org. See esp. pages on
  Kullback Leibler divergence, Mahalanobis
  distance.