2.6 Gaussian mixture model

Gaussian mixture model

A Gaussian Mixture Model (GMM) was used as our classification tool. As our work focused mainly on signalprocessing, we forgo a rigorous treatment of the mathematics behind the model in favor of a brief description of GMMs and itsapplication to our system.

GMMs belong to the class of pattern recognition systems. They model the probability density function ofobserved variables using a multivariate Gaussian mixture density. Given a series of inputs, it refines the weights of eachdistribution through expectation-maximization algorithms.

In this respect, GMMs are very similar to Support Vector Machines and Neural Networks , and all of these models have been used in instrument classification (1) . Reported success (2) with GMMs prompted us to use this model for our system.

Recognizing spectral patterns

We use 9 features in our recognition program and relied on the GMM to find patterns that would associate thesefeatures to the correct instrument. Some of our features consist of a vector (we used 12 MFCC, and tristimulus has 3 components), so weare actually working in 22 dimension space. For convenience, we focus here on recognizing a pattern between the instrument and twoof these dimensions, using the first two MFCC coefficients as an example.

Looking at the distribution of features for the three instruments in figure 1, we clearly see that there aresome feature differences based on instrument.

GMM detects the patterns in these features and gives us a nice decision rule, as pictured in figure 2. Based onthese two features alone, the GMM tells us which instrument most likely played the note, visually represented by the highest peak inthe three-dimensional representation.

Finally, we note that GMMs have been shown to be useful if features are particularly weak or missing (2) . This is of particular importance in polyphonic environments, as harmonicsmay overlap, thus causing some features to be unreliable measures of the instrument.

References

• A. Brenzikofer. “Instrument Recognition and Transcription in Polyphonic Music.” Term Project. Ecole Polytechnique Federale deLausanne, June 2004. URL: http://www.brenzi.ch/data/murec-report-web.pdf
• J. Eggink and G.J. Brown. “A Missing Feature Approach to Instrument Identification in Polyphonic Music,” in IEEEInternational Conference on Acoustics, Speech, and Signal Processing, Hong Kong, April 2003, 553-556.
• D. Ellis. Musical Content Analysis: A Practical Investigation of Singing Detection. URL:http://www.ee.columbia.edu/~dpwe/muscontent/practical/index.html