Audio signal classification rough sets based approach
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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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Audio signal classification rough sets based approach

Audio Signal ClassificationRough-Sets based Approach



  • 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

The research goals

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




  • 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

Musical instrument acoustics

Musical Instrument Acoustics

Bowed string instruments

Bowed String Instruments

  • articulation:

    • bowed vibrato, muted/not muted,

    • pizzicato (string plucked),

  • sound:

    • body resonances

    • inharmonic partials:

      where f1- fundamental (pitch)

    • pizzicato: transients only

Woodwind instruments

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

Brass instruments

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

Processed data

Processed Data

  • consequent sounds in the musical scale of instruments

  • source - CD: McGill University Master Samples

  • stereo, sampling frequency 44.1 kHz, 16 bits

Parameterization frequency domain

Parameterization – Frequency Domain

  • Fourier analysis:

  • example: oboe, 440 Hz


partials (harmonics)


Calculation points for parameters

Calculation Points for Parameters

  • The spectrum changes with time evolution

t - starting transient

qs - quasi-steady state

time envelope of an exemplary sound

Parameters of sound

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:

Other parameters

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]

  • Separability of parameters

    Separability of Parameters

    • criterion:


    – measure of distances between classesi, j

    • Hausdorff metrics

    • max/min/mean distance between objects

    • from different classes

    – measure of dispersion in classi


    • mean/max distance between class objects or

      • from the gravity center of the class

    • set of parameters is satisfying if Q>1



    • definition:

    • Euclidean

    • “city”

    • central

    Separability as a function of metrics

    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

    Quantization of parameters

    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

    Exemplary local methods

    Exemplary Local Methods

    • equal interval width method (EIWM)

    • maximum distance method (MDM)

    • statistical clusterization

    Separability vs quantization method

    Separability vs. Quantization Method

    Foundations of rough set rs based systems 1

    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)

    Foundations of rs based systems 2

    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

    Foundations of rs based systems 3

    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

    Rough set based systems

    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

    Exemplary rs based systems

    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

    A proposed system

    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

    Exemplary reducts

    Exemplary Reducts


    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

    Exemplary rules

    Exemplary rules

    Summary 1

    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

    Summary 2

    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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