Spectral Features for Automatic Text-Independent Speaker Recognition

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Spectral Features for Automatic Text-Independent
Speaker Recognition
Tomi Kinnunen Research seminar,
27.2.2004 Department of Computer
Science University of Joensuu
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Based on a True Story

• T. Kinnunen Spectral Features for Automatic
  Text-Independent Speaker Recognition, Ph.Lic.
  thesis, 144 pages, Department of Computer
  Science, University of Joensuu, 2004.
• Downloadable in PDF from
• http//cs.joensuu.fi/pages/tkinnu/research/index.h
  tml

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Introduction
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Why Study Feature Extraction ?

• As the first component in the recognition chain,
  the accuracy of classification is strongly
  determined by its selection

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Why Study Feature Extraction ? (cont.)

• Typical feature extraction methods are directly
  loaned from the speech recognition task
• ? Quite contradictory, considering the
  opposite nature of the two tasks
• In general, it seems that currently we are at
  the best guessing what might be invidual in our
  speech !
• Because it is interesting challenging!

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Principle of Feature Extraction
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Studied Features

• 1. FFT-implemented filterbanks (subband
  processing)
• 2. FFT-cepstrum
• 3. LPC-derived features
• 4. Dynamic spectral features (delta features)

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Speech Material Evaluation Protocol

• Each test file is splitted into segments of
  T350 vectors (about 3.5 seconds of speech)
• Each segment is classified by vector
  quantization
• Speaker models are constructed from the training
  data by RLS clustering algorithm
• Performance measure classification error rate
  ()

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1. Subband Features
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Computation of Subband Features
Windowed speech frame
Magnitude spectrum by FFT
Smoothing by a filterbank
Nonlinear mapping of the filter outputs

• Parameters of the filterbank
• Number of subbands
• Filter shapes bandwidths
• Type of frequency warping
• Filter output nonlinearity

Compressed filter ouputs
f (f1,f2, , fM)T
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Frequency Warping Whats That?!

• Real frequency axis (Hz) is stretched and
  compressed locally according to a (bijective)
  warping function

A 24-channel bark-warped filterbank
Bark scale
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Discrimination of Individual Subbands (F-ratio)
(Fixed parameters 30 linearly spaced triangular
filters)
Low-end (0-200 Hz) and mid/high frequencies ( 2
- 4 kHz) are important, region 200-2000 Hz less
important. (However, not consistently!)
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Subband Features The Effect of the Filter
Output Nonlinearity
Consistent ordering (!) cubic lt log lt linear
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Subband Features The Effect of the Filter Shape
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Subband Features The Number of Subbands (1)
Fixed parameters linearly spaced /
triangular-shaped filters, log-compression
Observation error rates decrease monotonically
with increasing number of subbands (in most
cases)
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Subband Features The Number of Subbands (2)
Fixed parameters linearly spaced /
triangular-shaped filters, log-compression
Helsinki (Almost) monotonous decrease in errors
with increasing number of subbands TIMIT Optimum
number of bands is in the range 50..100
Differences between corpora are (partly)
explained by the discrimination curves
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Discussion of the Subband Features

• (Typically used) log-compression should be
  replaced with cubic compression or some better
  nonlinearity
• Number of subbands should be relatively high (at
  least 50 based on these experiments)
• Shape of the filter does not seem to be important
• Discriminative information is not evenly spaced
  along the frequency axis
• The relative discriminatory powers of subbands
  depends on the selected speaker
  population/language/speech content

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2. FFT-Cepstral Features
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Computation of FFT-Cepstrum
Windowed speech frame
Magnitude spectrum by FFT
Smoothing by a filterbank
Common steps
Nonlinear mapping of the filter outputs
Decorrelation by DCT
Coefficient selection
Cepstrum vector
c (c1,,cM)T
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FFT-Cepstrum Type of Frequency Warping
Fixed parameters 30 triangular filters,
log-compression, DCT-transformed filter outputs,
15 lowest cepstral coefficients excluding c0
Helsinki Mel-frequency warped cepstrum gives the
best results on average TIMIT Linearly warped
cepstrum gives the best results on average Same
explanation as before discrimination curves
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FFT-Cepstrum Number of Cepstral Coefficients
( Fixed parameters mel-frequency warped
triangular filters, log-compression,
DCT-transformed filter outputs, 15 lowest
cepstral coefficients excluding c0, codebook
size 64)
Minimum number of coefficients around 10,
rather independent of the number of filters
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Discussion About the FFT-Cepstrum

• Same performance as with the subband features,
  but smaller number of features
• ? For computational and modeling reasons,
  cepstrum is the preferred method of these two in
  automatic recognition
• The commonly used mel-warped filterbank is not
  the best choice in general case !
• There is no reason to assume that it would be,
  since mel-cepstrum is based on modeling of human
  hearing and originally meant for speech
  recognition purposes
• I prefer / recommend to use linear frequency
  warping, since
• It is easier to control the amount resolution on
  desired subbands (e.g. by linear weighting). In
  nonlinear warping, the relationship between the
  real and warped frequency axes is more
  complicated

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3. LPC-Derived Features
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What Is Linear Predictive Coding (LPC) ?

• In time domain, current sample is approximated
  as a linear combination of the past p samples

• The objective is to determine the LPC
  coefficients ak k1,,p such that the squared
  prediction error is minimized

• In the frequency domain, LPCs define an
  all-pole IIR-filter whose poles correspond to
  local maximae of the magnitude spectrum

An LPC pole
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Computation of LPC and LPC-Based Features
Windowed speech frame
Autocorrelation computation
Solving of Yule-Walker AR equations
Levinson-Durbin algorithm
LPC coefficients (LPC)
Reflection coefficients (REFL)
LAR conversion
Complex polynomial expansion
LPC pole finding
Atals recursion
asin(.)
Arcus sine coefficients (ARCSIN)
Log area ratios (LAR)
Formants (FMT)
Linear Predictive Cepstral Coefficients (LPCC)
Root-finding algorithm
Line spectral frequencies (LSF)
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Linear Prediction (LPC) Number of LPC
coefficients

• Minimum number around 15 coefficients (not
  consistent, however)
• Error rates surprisingly small in general !
• LPC coefficients were used directly in
  Euclidean-distance -based classifier. In
  literature there is usually warning of the
  following form Do not ever use LPCs directly,
  at least with the Euclidean metric.

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Comparison of the LPC-Derived Features
Fixed parameters LPC predictor order p 15

• Overall performance is very good
• Raw LPC coefficients gives worst performance on
  average
• Differences between feature sets are rather
  small
• ? Other factors to be considered
• Computational complexity
• Ease of implementation

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LPC-Derived Formants
Fixed parameters Codebook size 64

• Formants give comparable, and surprisingly good
  results !

• Why surprisingly good ?
• 1. Analysis procedure was very simple (produces
  spurious formants)
• 2. Subband processing, LPC, cepstrum, etc
  describe the spectrum continuously - formants on
  the other hand pick only a discrete number of
  maximum peaks amplitudes from the spectrum (and
  a small number!)

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Discussion About the LPC-Derived Features

• In general, results are promising, even for the
  raw LPC coefficients
• The differences between feature sets were small
• From the implementation and efficiency viewpoint
  the following are the most attractive LPCC, LAR
  and ARCSIN
• Formants give (surprisingly) good results also,
  which indicates indirectly
• The regions of spectrum with high amplitude might
  be important for speaker recognition

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4. Dynamic Features
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Dynamic Spectral Features

• Dynamic feature an estimate of the time
  derivate of the feature
• Can be applied to any feature

• Two widely used estimatation methods are
  differentiator and linear regression method

• Typical phrase Dont use differentiator, it
  emphasizes noise

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Delta Features Comparison of the Two Estimation
Methods
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Delta Features Comparison with the Static
Features
Discussion About the Delta Features

• Optimum order is small (In most cases M1,2
  neighboring frames)
• The differentiator method is better in most
  cases (surprising result, again!)
• Delta features are worse than static features
  but might provide uncorrelated extra information
  (for multiparameter recognition)
• The commonly used delta-cepstrum gives quite
  poor results !

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Towards Concluding Remarks ...
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FFT-Cepstrum Revisited Question Is
Log-Compression / Mel-Cepstrum Best ?
Please note Now segment length is reduced down
to T100 vectors, thats why absolute recognition
rates are worse than before (ran out of time for
the thesis)
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FFT- vs. LPC-CepstrumQuestion Is it really
that FFT-cepstrum is more accurate ?
Helsinki
TIMIT
Answer NO ! (TIMIT shows this quite clearly)
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The Essential Difference Between the FFT- and
LPC-Cepstra ?

• FFT-cepstrum approximates the spectrum by linear
  combination of cosine functions (non-parametric
  model)
• LPC makes a least-squares fit of the all-pole
  filter to the spectrum (parametric model)
• FFT-cepstrum first smoothes the original
  spectrum by filterbank, whereas LPC filter is
  fitted directly to the original spectrum

However, one might argue that we could drop out
the filterbank from FFT-cepstrum ...
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General Summary and Discussion

• Number of subbands should be high (30-50 for
  these corpora)
• Number of cepstral coefficients (LPC/FFT-based)
  should high (? 15)
• In particular, number of subbands, coefficients,
  and LPC order are clearly higher than in speech
  recognition generally
• Formants give (surprisingly) good performance
• Number of formants should be high (? 8)
• In most cases, the differentiator method
  outperforms the regression method in
  delta-feature computation

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Philosophical Discussion

• The current knowledge of speaker individuality
  is far from perfect
• Engineers concentrete on tuning complex feature
  compensation methods but dont (necessarily)
  understand whats individual in speech
• Phoneticians try to find the individual code
  in the speech signal, but they dont
  (necessarily) know how to apply engineers
  methods
• Why do we believe that speech would be any less
  individual than e.g. fingerprints ?
• Compare the history fingerprint and
  voiceprint
• Fingerprints have been studied systematically
  since the 17th century (1684)
• Spectrograph wasnt invented until 1946 ! How
  could we possibly claim that we know what speech
  is with research of less than 60 years?
• Why do we believe that human beings are optimal
  speaker discriminators? Our ear can be fooled
  already (e.g. MP3 encoding).

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Thats All, Folks !