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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

Audio Signal ClassificationRough-Sets based Approach


Outline
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


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

?


Problems
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



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

A

partials (harmonics)

f


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:

    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


    Metrics
    Metrics

    • 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



    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

    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



    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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