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Audio Signal Classification Rough-Sets based Approach

Audio Signal Classification Rough-Sets based Approach. Outline. Introduction - the research goals Musical instrument acoustics Parameters of sounds and their separability Preprocessing for rough set tools: discretization (quantization) of parameters

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Audio Signal Classification Rough-Sets based Approach

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  1. Audio Signal ClassificationRough-Sets based Approach

  2. Outline • Introduction - the research goals • Musical instrument acoustics • Parameters of sounds and their separability • Preprocessing for rough set tools: discretization (quantization) of parameters • Automatic classification and results • Summary

  3. The Research Goals • Motivation – to deal with the problem of the automatic classification of musical data: • database searching: there is no possibility to find fragments performed by selected instruments inside files, unless such information is attached to the file • Aim – to check if it is possible to recognize sounds on the basis of a limited number of parameters, and reveal these parameters ?

  4. Problems • Amount of data in sound files 1 s, Fs=44.1kHz, 16 bits stereo, 176.4 kB • Musical instrument sound data are unrepeatable and inconsistent: • the sound depends on the articulation, the instrument itself, arrangement of microphones, reverberation, etc. • sounds of different instruments can be similar, whereas sounds of one instrument may change significantly within the scale of the instrument

  5. Musical Instrument Acoustics

  6. Bowed String Instruments • articulation: • bowed vibrato, muted/not muted, • pizzicato (string plucked), • sound: • body resonances • inharmonic partials: where f1- fundamental (pitch) • pizzicato: transients only

  7. Woodwind Instruments • articulation - vibrato/non vibrato • the length of the horn resonator is reduced by holes between the mouthpiece and the end • reed instruments – excited by vibrating reeds : • single reed: clarinet, saxophone • double reed: oboe, English horn, bassoon • flute: • blowing a stream of air across a hole in the body

  8. Brass Instruments • articulation: vibrato, muted/not muted • lip-driven • mouthpieces only help with tone production • long narrow body and extended flaring end - upper modes available • mechanical valves

  9. Processed Data • consequent sounds in the musical scale of instruments • source - CD: McGill University Master Samples • stereo, sampling frequency 44.1 kHz, 16 bits

  10. Parameterization – Frequency Domain • Fourier analysis: • example: oboe, 440 Hz A partials (harmonics) f

  11. Calculation Points for Parameters • The spectrum changes with time evolution t - starting transient qs - quasi-steady state time envelope of an exemplary sound

  12. Parameters of Sound • fdm– mean frequency deviation for low partials • hfd_max=1..5 – a partial with the greatest frequency deviation • A1-2 [dB] – amplitude difference between 1st and 2nd partial, • h1, h3,4,h5,6,7, h8,9,10, hrest – • energy of the selected partials • Od, Ev – contents of odd/even partials in the spectrum • Br– brightness of the sound:

  13. Other Parameters • f 1 [Hz] – fundamental • |f1max– f1min| – vibrato, • dfr – fractal dimension of the spectrum envelope: • where N(r) - minimal number of squares r covering the envelope, • f1/2 – energy of subharmonic partials in the spectrum • qs,te– proportional participation of the quasi-steady state and the ending transient in the total sound time • rl – release velocity [dB/s]

  14. Separability of Parameters • criterion: Di,j – measure of distances between classesi, j • Hausdorff metrics • max/min/mean distance between objects • from different classes – measure of dispersion in classi di • mean/max distance between class objects or • from the gravity center of the class • set of parameters is satisfying if Q>1

  15. Metrics • definition: • Euclidean • “city” • central

  16. Separability as a Function of Metrics d1/d2 - mean/max distance between class objects d3/d4 - mean/max distance from the gravity center D1 - Hausdorff metric D2/D3/D4 - max/min/mean distance between objects from different classes

  17. Quantization of Parameters • inductive learning methods require a small number of attribute values • global methods: simultaneously convert all continuous attributes – large tables • Boolean approach (Skowron, Nguyen) • cluster analysis (Chmielewski, Grzymala-Busse) • local methods: restricted to simple attributes • methods usually do not discern between points representing different classes

  18. Exemplary Local Methods • equal interval width method (EIWM) • maximum distance method (MDM) • statistical clusterization

  19. Separability vs. Quantization Method

  20. Foundations of Rough Set (RS) Based Systems - 1 Let – a decision table U - a universe - nonempty, finite set of objects A - a nonempty, finite set of attributes , the decision attribute implies indiscernibility relation IND(B) reduct - aminimal subset B such that IND(A)=IND(B)

  21. Foundations of RS Based Systems – 2 – lower approximation of X in A – upper approximation of X in A rough set in A - the family of all subsets of U having the same lower and upper approximations in A

  22. Foundations of RS Based Systems - 3 - B positive region of A - the generalized decision inA B - relative reduct iff B is a minimal subset of A such that The relative reduct is such minimal subset of A which preserves the positive region

  23. Rough Set Based Systems • generated rules where n - length of the rule • a rough measure m of the rule describing concept X Y – set of all examples described by the rule

  24. Exemplary RS Based Systems • LERS • allows unknown attribute values • possibility of removing inconsistent examples (i.e. of identical attribute values, but with different decisions) • priority of attributes is controlled • DataLogic • calculates attribute and rule strength • quantization of data is available

  25. A Proposed System • implemented in Mathematica • allows data quantization with number of methods, both local and global • ten-fold test included • priority of attributes is controlled • unnecessary attributes found by reducts and relative calculation • the use of produced rules available for whole data sets, not only for singular objects

  26. Exemplary Reducts reduct relative reduct 1 relative reduct 2 • up to 70% correct recognition obtained in RS tests • parameters 60,61,62 and 41,44,30,55 are the most significant

  27. Exemplary rules

  28. Summary (1) • the huge amount of data contained in digital sound representation requires parametrization as preprocessing • a great number of parameters is a consequence of the variety of musical instruments and differences in their sounds • inconsistency of the data implies soft computing techniques for automatic classification • quantization is necessary as preprocessing for RS algorithms

  29. Summary (2) • an appropriate choice of the quantization requires many experiments • rough set algorithms allow the evaluation of the significance of parameters • composition of parameters in RS reducts confirms that the evolution of the sound must be taken into account during parametrization • the use of learning algorithms allows finding rules for managing classification

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