=Paper=
{{Paper
|id=Vol-3318/short1
|storemode=property
|title=Extreme Learning Machines For Efficient Speech Emotion Estimation In Julia
|pdfUrl=https://ceur-ws.org/Vol-3318/short1.pdf
|volume=Vol-3318
|authors=Georgios Drakopoulos,Phivos Mylonas
|dblpUrl=https://dblp.org/rec/conf/cikm/DrakopoulosM22
}}
==Extreme Learning Machines For Efficient Speech Emotion Estimation In Julia==
https://ceur-ws.org/Vol-3318/short1.pdf
Extreme Learning Machines For Efficient Speech Emotion
Estimation In Julia
Georgios Drakopoulos∗ , Phivos Mylonas
Department of Informatics, Ionian University, Tsirigoti Sq. 7. Kerkyra 49100, Hellas
Abstract
Speech is a mainstay of communication across literally all human activities. Besides facts and statements speech carries
substantial information regarding experiences, thoughts, and emotions, therefore adding significant context. Moreover,
non-linguistic elements such as pauses add more to the message. The field of speech emotion recognition (SER) has been
developed precisely to develop algorithms and tools performing what humans learn to do from early on. One promising
line of research comes from applying deep learning techniques trained on numerous audio attributes to discern between
various emotions as dictated by a given model of fundamental human emotions. Extreme learning machines (ELMs) are
neural network architectures achieving efficiency through simplicity and can potentially operate akin to a sparse coder. When
trained by a plethora of audio attributes, such as cepstral coefficients, zero crossing rate, and autocorrelation, then it can
classify emotions in speech based on the established emotion wheel model. The evaluation, done with the Toronto emotional
speech set (TESS) on an ELM implemented in Julia, is quite encouraging.
Keywords
extreme learning machine, speech emotion recognition, emotion classification, Plutchik model, higher order patterns,
spectrogram, cepstral coefficients, zero crossing rate, TESS dataset, Julia
1. Introduction emotion classification as is the case here.
Among the various models proposed for the vari-
Language, whether oral or written, is among the major ous SER tasks, extreme learning machines (ELMs) have
sources of human emotion and perhaps a mainstay of shown considerable potential. The latter can be partially
civilization itself. The field of speech emotion recog- at least attributed to the ELM structure which has only a
nition (SER) almost since its formulation has been an single but very long hidden layer. In turn, this allows for
essentially demanding field systematically garnering in- straightforward and easy to interpret training schemes,
tense interdisciplinary interest since it aims to answer all of which eventually stem from a synaptic weight reg-
fundamental questions regarding human speech, which ularization property. This is aligned with the intuition
includes major elements such as intonation and pitch as that a certain optimality condition should hold in order
well as latent and non-linguistic elements such as pauses for the weights to be uniquely derived.
and the length of sentences. Because of the complexity The primary research contribution of this conference
and volatility of human speech, SER relies heavily on paper is the development of an ELM implemented in Julia
machine learning (ML) and recently on deep learning and operating like a sparse encoder for the emotion classi-
(DL) techniques for performing tasks. fication of sentences coming from the ubiquitous Toronto
Human emotion models such as the emotion wheel emotion speech set (TESS) collection, a benchmark for
by Plutchik [1] and the universal emotion models [2] training ML and DL models for SER tasks.
have been developed to explain not only which emotions The remainder of this work is structured as follows.
are fundamental, with interpretations ranging from so- The recent scientific literature regarding ELMs, SER, and
cial conditioning to brain functionality and evolutionary graph mining is briefly reviewed in section 2. In section
goals, but also how they are composed, which may well 3 the proposed methodology is described, whereas the
entail non-linear operations. In any case, such models results obtained using the TESS dataaset are analysed in
can serve well as training guides to ML models for speech section 4. Possible future research directions are given in
section 5. Bold capital letters denote matrices, bold small
CIKM’22: 31st ACM International Conference on Information and vectors, and small scalars. Acronyms are explained the
Knowledge Management (companion volume), October 17–21, 2022, first time they are encountered in the text. Finally, the
Atlanta, GA notation of this work is summarized in table 1.
∗
Corresponding author.
Envelope-Open c16drak@ionio.gr (G. Drakopoulos); fmylonas@ionio.gr
(P. Mylonas)
Orcid 0000-0002-0975-1877 (G. Drakopoulos); 0000-0002-6916-3129
2. Related Work
(P. Mylonas)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Because of its interdisciplinary nature SER has been at
Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org) the attention focus of a number of fields [3]. To address
1
Georgios Drakopoulos et al. CEUR Workshop Proceedings 1–7
Table 1 is given in [34], sequential graph collaborative filtering
Notation Summary is the topic of [35], mining hot sports in trajectories with
graph based methodologies is developed in [36], and fMRI
Symbol Meaning First in
image classification with tensor distance metrics is the
△
= Equality by definition Eq. (1) focus of [37].
‖⋅‖ Vector or matrix norm Eq. (6)
𝜑(⋅) Activation function Eq. (3)
tanh (⋅) Hyperbolic tangent function Eq. (3) 3. Methodology
tr (⋅) Matrix trace Eq. (7)
3.1. Attributes
Emotion models have been developed in order to explain
the inherent complexity of the SER tasks, ML approaches
how emotions work, their intensity and elicit conditions,
such as ensemble learning [4], deep convolutional neu-
how they may be composed in case of emotion levels,
ral networks [5], domain invariant feature learning [6],
and possibly their evolutionary purpose. In this set of
two-dimensional convolutional neural networks [7], and
models the one proposed by Plutchik has been among
multimodal deep learning [8] have been proposed in the
the earliest and one of the most commonly used in en-
scientific literature. Human emotion models such as the
gineering applications. Additionally, it has an easy to
emotion wheel by Plutchik [1] or the universal emotion
understand and intuitive-friendly visual interpretation,
theory by Ekman [2] typically describe a fundamental set
which is shown in figure 1. Notice that this figure depicts
of emotions [9, 10, 11] along with composition rules and
a two dimensional projection of a cone.
possible evolutionary explanations for them [12]. More
recently, personality taxonomies go beyond single emo-
tional reactions and treat personality as a whole such
as the Myers-Brigs type indicator (MBTI). A reasoning
based framework for emotion classification is [13].
ELMs have been used in ML because of the simplicity
of their architecture [14]. They have been used as part of
ML pipelines for wavelet transforms [15], in conjunction
with an autoencoder for predicting the concentration of
emitted greenhouse gases from boilers [16], and in opti-
mizing a Kalman filter for determining the aging factors
of supercapacitors [17]. Further applications include es-
timating soil thermal conductivity [18] and an evolving
kernel assisted ELM for medical diagnosis [19], whereas
an extensive list of applications is given in [20].
Graph mining is a field relying heavily on ML [21]
and graph signal processing techniques [22]. Regarding
the use of ML, self organizing maps (SOMs) for recom-
mending cultural content are presented in [23], exploiting
natural language attributes for finding linked require-
ments between software artefacts is the focus of [24],
decompressing a sequence of Twitter graphs compressed Figure 1: Plutchik model (From Wikipedia).
with the two-dimensional discrete cosine transform us-
ing a tensor stack network (TSN) is described in [25], According to this model each emotion corresponds to
combining graph mining with transformers is shown a location in a circle which is primarily a function of its
in [26], advanced graph clustering techniques for clas- valence as well as of its direction. The latter is related
sifying variation of cancer genomes [27], message pass- to the nature of the emotion under consideration, which
ing graph neural networks for fuzzy [28] and ordinary also determines at least in part its polarity. Specifically,
Twitter graphs [29] are described, a GPU-based system there are in total eight directions with three scales each.
for efficient graph mining is shown in [30], partitioning Moreover, there are some emotions which are combina-
the user base of a portal for cultural content recommen- tions of others from two directions. Moreover, the set of
dation is explained in [31], visualizing massive graphs emotions is categorized as basic, primary, secondary, and
for human feedback is described in [32], approximating tertiary. Primary emotions are archetypes the remain-
directed graphs with undirected ones under optimality ing ones are patterned after or are derived of. They are
conditions is shown in [33], classification of noisy graphs characterized by especially high survival value.
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Georgios Drakopoulos et al. CEUR Workshop Proceedings 1–7
Table 2 The individual output of the 𝑗-th neuron can be com-
Primary Emotions In Plutchik’s Model puted from the nonlinear combination of equation (2).
Therein 𝑞 is the number of input neurons which is much
Emotion Polarity Opposite
smaller than that of the hidden neurons 𝑝, namely 𝑞 ≪ 𝑝,
Neutral Neutral Neutral and equal to the dimensionality of each data point.
Surprise Positive or negative Anticipation
Anticipation Positive or negative Surprise 𝑞
△
Joy Positive Sadness ℎ𝑗 (x𝑖 ) = 𝜑𝑗 (∑ 𝑤𝑗,𝑘 x𝑖 [𝑘]) = 𝜑𝑗 (w𝑇𝑗 x𝑖 ) (2)
Trust Positive Disgust 𝑘=1
Anger Negative Fear
The nonlinear activation function 𝜑𝑘 (⋅) may take a
Sadness Negative Joy
Disgust Negative Trust number of forms such as the logistic function or poly-
Fear Negative Anger nomial kernels. In this case it is the hyperbolic tangent
function of (3). It has the advantage of being differen-
tiable and of being the Bayes estimator of a bipolar source
As stated earlier, each of the above emotions has an under additive white Gaussian (AWGN) noise.
associated emotional polarity. For most emotions this △
𝜑𝑘 (𝑥; 𝛽0 ) = tanh (𝑥; 𝛽0 ) (3)
polarity is clear, although is some cases such as surprise
this has to be determined by the context. The intensity The first derivative 𝜓 of 𝜑 can be expressed as a sec-
of each emotion essentially determines its location on a ond order polynomial of the latter as shown in (4). This
given affective axis. The higher the intensity, the more expression is that of Malthus population models.
emotional a person is at a given time.
The primary emotions in the model of Plutchik are △ 𝜕𝜑(𝑥; 𝛽0 )
𝜓(𝑥; 𝛽0 ) = = 𝛽0 (1 − 𝜑 2 (𝑥; 𝛽0 )) (4)
shown in table 2. Their location on the intensity scale 𝜕𝑥
and their relationship to other emotions are shown in fig-
ure 1. Moreover, the primary emotions come in four bipo- The column synaptic weight vector w𝑗 is formed by
lar opposite emotions in the sense that they accomplish stacking the 𝑞 weights w𝑗,𝑘 connecting the 𝑗-th hidden
opposite objectives and their physical manifestations are neuron with the 𝑘-input one. Moreover, this is also the
considerably different. Bipolarity does not necessarily 𝑗-th column of the synaptic weight matrix W. If the data
mean that in every pair there is one feeling with positive points are stacked on top of each other, then the input
polarity, though this may be the case as in the pair of matrix X is formed. Thus H of (1) can be rewritten as in
joy and sadness. Instead, both emotions in the anger (5), where the function of (3) is elementwise applied.
and fear pair are both perceived as negative, but they are △
H = 𝜑(WX𝑇 ) (5)
diametric opposites in the context of fight or flight.
In general ELMs, depending on their training formu-
3.2. Training lation, can perform regularized least squares fitting in
order to determine the optimal weights as in (6) where
ELM training has a simpler compared to other neural
𝜂0 is a hyperparameter. Therein the regularization term
network architectures since it has only one hidden layer
adds robustness to the algorithmic minimization process.
with a large number 𝑝 of processing neurons. With the
To this end, the nonlinear least squares problem of (6)
proper training, each neuron can be specialized in a par-
was formulated, where the Frobenius matrix norm is used
ticular subset of the training set, which comprises of 𝑛
since it is differentiable. Also Y is the ground truth ma-
data vectors. In this case the ELM output matrix H has
trix containing the one hot encoding of the eight primary
the elementwise structure of equation (1).
emotions and W∗ is the solution.
From its structure the 𝑖-th row of H contains the output
of each neuron for 𝑖-th data point 0 ≤ 𝑖 ≤ 𝑛 − 1, while the W∗ =△ argmin [𝐽] = argmin [𝜂 ‖W‖2 + ‖𝜑(WX𝑇 ) − Y‖2 ]
0 𝐹 𝐹
𝑗-th column consists of the output of the 𝑗-th neuron 0 ≤
(6)
𝑗 ≤ 𝑝 − 1 across all the available data points, preserving
Expanding (6) and taking into consideration the ex-
the order in which they were given to the ELM.
pansion of the Frobenius norm the objective function 𝐽
ℎ (x ) ℎ1 (x0 ) … ℎ𝑝−1 (x0 ) to be minimized can be recast as in (7). Because of the
⎡ 0 0 ⎤ form Frobenius norm and that of the nonlinear activation
ℎ0 (x1 ) ℎ𝑘 (x1 ) … ℎ𝑝−1 (x1 ) ⎥
H= ⎢
△
⎢ ⎥ ∈ ℝ𝑛×𝑝 function 𝐽 not only is differentiable but it also has a single
⎢ ⋮ ⋮ ⋱ ⋮ ⎥ global minimum. Additionally, the regularization term
⎣ℎ0 (x𝑛−1 ) ℎ1 (x𝑛−1 ) … ℎ𝑝−1 (x𝑛−1 )⎦ ensures that synaptic weight sparsity also taken into con-
(1)
sideration. Thus, minimizing 𝐽 translates into finding the
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Georgios Drakopoulos et al. CEUR Workshop Proceedings 1–7
weight set achieving a tradeoff between fitting the ELM its central frequency. This allows the details of a speech
response to the target response with the least possible signal to be more discernible.
energy. The latter can be considered as the explanation The spectrogram of a signal is a function of time and
closest to that dictated by Occam’s razor. frequency and shows how its frequency content evolves
in small time steps. Typically it can be obtained by the
𝑇
𝐽 = 𝜂0 tr (W𝑇 W) + tr ((𝜑(WX𝑇 ) − Y) (𝜑(WX𝑇 ) − Y)) wavelet transform, by the short time Fourier transform
(7) (STFT), or by a bank of bandpass filters such as Gabor
The minimization problem of (7) is a regularized non- and shifted Chebyshev filters. In any case, the resulting
linear least squares problem. The hyperparameter 𝜂0 heatmap has been transformed to a long column vec-
determines the relative weight of the synaptic weight tor, which incurs some information loss as the spatial
matrix sparsity compared to how well the ELM response structure is lost. This is attributed to the fact that the
matches the target response. The problem of (7) can be proposed ELM is trained with data points with are real
solved by a plethora of methodologies including iterative vectors. An architecture natively handling matrices may
ones such as fixed point methods. However, they should be more adept in this scenario.
take into consideration the nonlinear term introduced The 𝑘-th autocorrelation coefficient 𝑎 [𝑘] of any real-
by the activation function. This can be accomplished by valued stationary sequence 𝑠 [𝑖] is defined as the expected
utilizing methods such as the Gauss-Newton or a regu- value of the sequence multiplied by a shifted version of
larized version thereof. In this work the steepest descent itself by 𝑘 positions. In practice these stochastic coef-
iterative method was selected because of its simplicity ficients are often approximated by the sample mean of
and because of the single global minimum 𝐽 has, since equation (8) under the assumption of ergodicity. Autocor-
the latter is essentially a sum of squares. relation coefficients are a measure of the self-similarity
Furthermore, it can be argued that the proposed ELM, of the sequence under consideration and play a central
if properly trained, operates like a sparse coder with role in discovering higher order patterns through the
each activation neuron corresponding to a single emo- Wiener filter. It should be noted that the higher 𝑘 is, the
tion. This approach is clear it can be extended to an less reliable the estimation of 𝑎 [𝑘] becomes as fewer term
arbitrary number of emotions, provided of course that pairs are available. Therefore, 𝑘 in most engineering ap-
the appropriate attributes are available. However, the plications is small compared to the total length 𝑛 of the
ELM proposed here can in fact discover the emotional speech sample sequence. As a direct consequence of the
direction and not the valence itself. Cauchy-Schwarz inequality, the maximum autocorrela-
tion coefficient is the first one 𝑎 [0].
3.3. Attributes 1
𝑛−𝑘−1
𝑎 [𝑘] ≈ ∑ 𝑠 [𝑖] 𝑠 [𝑖 + 𝑘] , 0≤𝑘 ≤𝑛−1 (8)
In this subsection the various features used to train the 𝑛 − 𝑘 𝑖=0
ELM described here, their primary properties, and their
respective meaning are explained. Said attributes are also Finally, the zero crossing rate (ZCR) is an important
shown in table 3 along with a brief explanation. feature which assumes that the mean value of the speech
The cepstral coefficients 𝑐 [𝑘] express a modified short signals has been subtracted from it during a preprocess-
term power spectrum of a signal 𝑠 [𝑘] consisting of speech ing phase. ZCR is closely tied with the primary mode
samples. They are derived by an algorithmic process of the Hilbert-Huang spectrum (HHS), which is built on
which involves the following steps: fundamental signals inherent in the sequence. Thus, in-
tuitively speaking, the HHS is very similar to the Fourier
• The sequence is pre-emphasized such that higher spectrum but it is composed of basis signals progressively
frequencies receive an energy boost. extracted from the original signal itself and hence having
• The spectrum is smoothed with a window, usually irregular shapes instead of weighted complex exponen-
a Hamming window of odd length. tials. In this context ZCR plays a role analogous to that
• The power spectrum is translated in the nonlinear of the fundamental frequency in Fourier analysis.
Mel scale where resolution is not constant. The audio attributes used in this work are also shown
• The logarithm of said power spectrum, which is in table 3 along with their interpretation.
always real, is computed.
• The coefficients of the inverse Fourier spectrum 4. Results
are the cepstral coefficients.
The natural meaning of the cepstral coefficients is that 4.1. ELM Architecture
they represent a power spectrum where each frequency The architecture of the proposed ELM is shown in 2. No-
band has a resolution roughly inversely proportional to tice that all hidden neurons belong to the same ELM layer
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Georgios Drakopoulos et al. CEUR Workshop Proceedings 1–7
Table 3
Audio Attributes
Attribute Meaning
Cepstral coefficients Short term windowed power spectrum
Spectrogram Frequency content evolution over short time steps
Autocorrelation Self-similarity patterns in the speech sequence
Zero crossing rate Tied to primary mode of Hilbert-Huang spectrum
TESS
attributes
Ιnput layer
Hidden layer seg. 1 Hidden layer seg. 2 Hidden layer seg. 3 Hidden layer seg. 4 ... Hidden layer seg. n
Figure 2: Proposed architecture.
and they are conceptually but not physically segmented In figure 3 is shown the heatmap resulting from the
to show they are an integer multiple of the neurons of analysis of the ELM training. From it the following can
the input layer. Hence the hidden layer can be thought be immediately inferred:
of as comprising of segments, although in practice all
• The neutral emotional state is the only one which
hidden neurons are simultaneously trained.
can be accurately discovered in the context of
The implementation language of choice was Julia.
this work. This can be attributed to the fact that
It is a rapidly emerging multiparadigm high level lan-
compared to the other states there is no valence.
guage aiming at computation-heavy tasks such as those
In turn this allows its isolation from the rest of
frequently encountered in DL and ML scenarios, large
the states in the attribute space with a margin
database clustering, extensive and fine grained simula-
sufficient for the ELM to discern it.
tions, and graph signal processing.
• On the contrary anger is the most difficult to be
discovered. A possible explanation is that its bipo-
4.2. Emotion Recognition lar opposite emotion is also present in TESS and,
The TESS dataset contains 200 target words spoken in the thus, certain instances have been misattributed
context of a carrier phrase by two actresses, a younger to it. Moreover, anger is also confused with sur-
and an older one aged 26 and 64 respectively. Each record- prise and sadness. The former is possibly due to
ing contains 2000 data points, which are sufficient for valence, whereas the latter because of polarity.
processing, and they represent the neutral state plus six • Concerning the other bipolar pair of sadness and
of the primary emotions according to Plutchik’s model, happiness, they are clearly distinguished from
namely these of anger, disgust, fear, happiness, pleas- each other, but nevertheless there is a small prob-
ant surprise, and sadness. Therefore, from the emotions ability they will be misclassified respectively as
listed in table 2 anticipation and trust are absent. Conse- disgust and as pleasant surprise. This can be at-
quently, from the four pairs of primary bipolar emotions tributed to their valence as well as to the seman-
only two are fully present in TESS. tics of each emotion under consideration.
• The remaining emotions can be also be distin-
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Georgios Drakopoulos et al. CEUR Workshop Proceedings 1–7
guished relatively easy from the others in the tectures capable of natively handling two-dimensional
dataset. Still, the negative emotions tend to be attributes such as the class of graph neural networks.
classified with a lower level accuracy compared
to the positive ones, with the single exception of
sadness. This can be explained by their preva- Acknowledgments
lence in TESS.
This conference paper is part of Project 451, a long term
research initiative with a primary objective of develop-
ing novel, scalable, numerically stable, and interpretable
higher order analytics.
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