Dimensionality Reduction of Speech Signals using Singular Value
Decomposition and Karhunen-Loeve
Domy Kristomo
1
and Yudhi Kusnanto
2
1
Department of Informatics Engineering, STMIK AKAKOM, Yogyakarta, Indonesia
2
Department of Computer Engineering, STMIK AKAKOM, Yogyakarta, Indonesia
Keywords:
Speech, singular value decomposition, wavelet, karhunen-loeve.
Abstract:
The design of speech recognition system requires the reliable feature in order to improve the performance of
speech recognition system. Thus it requires the efficient feature in order to minimizing computational time
and to obtaining the optimal classification result. This paper proposes the combined method of various time-
frequency feature extraction techniques with singular value decomposition (SVD) for extracting, selecting,
and classifying the Indonesian stop consonants in initial position of Consonant-Vowel (CV) syllables as well
as the word of stop consonant. The results of the study are divided into two parts, first: the implementation of
the extraction method and selection of features based on Singular Value Decomposition (SVD) on stop con-
sonant data, second: the implementation of the extraction method and selection of features based on Singular
Value Decomposition (SVD) on word sound data formed by stop consonants. The experimental result shows
that SVD gives improved the classification scores. The classification of stop consonants is more difficult than
classifying of word of stop consonants.
1 INTRODUCTION
Speech recognition technology is currently growing
rapidly. Speech recognition technology enables a
computer to recognize and understand language spo-
ken by humans (speakers). The technology is cur-
rently widely applied in various applications, such as
security systems, smart devices, smartphones, and so
on. Some researches related to speech recognition
have been carried out by previous researchers, how-
ever, research to recognize the sounds of stop con-
sonant words in Indonesian as well as to apply the
method of dimensionality reduction to the voice data
is still very limited and received less attention from
local researchers.
In research related to speech recognition systems,
the main stages commonly used by researchers are to
be able to classify or recognize sound cues, including:
preprocessing, segmentation, feature extraction, fea-
ture selection, and classification or recognition. Fea-
ture selection becomes an important stage in speech
signal recognition system, this is intended to deter-
mine the featuress that are efficient, relevant and ap-
propriate so that the optimal speech recognition or
classification results are obtained. Feature selection
is a process of selecting a subset of original features
so that the dimension / size of features is optimally
reduced according to evaluation criteria. Dimension
features that are too large will affect the performance
of classification and computational load, because the
number of features that many will make the number of
parameters in the classifier (for example the number
of synaptic weights in the Neural Network). There-
fore, the urgency of this research is to choose the
right traits through the Singular Value Decomposition
(SVD) and Karhunen-Loeve (KL) -based dimension-
ality reduction methods which have not been done by
previous (local) researchers. So that this research is
expected to be able to provide new references in re-
search in the field of Indonesian speech recognition
and also improve the performance of the Indonesian
speech recognition system through the dimensionality
reduction method.
Singular Value Decomposition (SVD) based,
Karhunen-Loeve (KL) or Principal Component Anal-
ysis (PCA) based methods, Correlation based Feature
Selection (CFS), and other feature selection meth-
ods have been used by previous researchers to re-
duce feature dimensions in data 1 dimension (1-D)
and 2-dimensional (2-D) data. In research (Hariharan
et al., 2009), SVD is used to reduce the features of
Mel Frequency Band Energy Coefficients (MFBECs).
78
Kristomo, D. and Kusnanto, Y.
Dimensionality Reduction of Speech Signals using Singular Value Decomposition and Karhunen-Loeve.
DOI: 10.5220/0009432200780084
In Proceedings of the International Conferences on Information System and Technology (CONRIST 2019), pages 78-84
ISBN: 978-989-758-453-4
Copyright
c
 2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

The experimental results show that SVD provides
improved performance in the pathology sound sig-
nal classification. In research (Lukasik, 2000), SVD
is used to reduce the entropy matrix of the Wavelet
Packet (WP) method for each class of plosive con-
sonant sounds /k/, /t/, /p/. In research (Chakroborty
and Saha, 2010), an alternative to feature selec-
tion using QR decomposition with column pivoting
(SVD-QRcp) is proposed. The experimental results
show that SVD-QRcp increases the ratio compared to
MFCC and LFCC. The KL or PCA method has also
been applied to medical cues such as heart sounds
(Sarac¸O
˘
gLu, 2012)(Yazdanpanah et al., 1999). The
study (Sarac¸O
˘
gLu, 2012) used the PCA method to
select the features of heart sounds for heart valve ab-
normality, then classified using the Hidden Markov
Model (HMM). The results showed that by selecting
/ reducing the dimensions of features using PCA can
improve the performance of the classification of heart
sound signals. Research (Yazdanpanah et al., 1999)
analyzes the performance of four different approaches
to feature selection using the Karhunen-Loeve Expan-
sion (KLE) method to select the most discriminant
feature set to classify the status of bioprostetic heart
valves. Previous researchers analyzed the characteris-
tic of SVD in a number of word similarity extraction
tasks (Gamallo and Bordag, 2011). The results lead
them to conclude that SVD makes the extraction less
computationally efficient and much less precise than
other more basic models for extracting word data.
On the side of speech recognition in Indone-
sian has also been done by previous researchers
(Yessivirna and Marji, 2013) (Nafisah et al.,
2016)(Fachrie and Harjoko, 2015). In research
(Yessivirna and Marji, 2013), spectral domain-based
spectral (Spectral Centroid and Spectral Flux) fea-
ture extraction methods using the K-Nearest Neigh-
bor (KNN) classification system to classify the sounds
of the word ”I” that are spoken normally by adults.
The results of this study indicate the accuracy of the
sound classification based on gender with the KNN
method is quite good. The lowest accuracy in the
trial with a frame width value of 1024, frame shift
31.25%, and an alpha value of 0.97 is 71.2% and the
highest accuracy is 77.1%. In research (Nafisah et al.,
2016), the MFCC-based feature extraction method
with a variety of window functions is used to clas-
sify word sound data from an isolated word database
in Indonesian (Database for Isolated Word) using the
Back Propagation Neural Network (BPNN) classifi-
cation system. The results showed that the MFCC
method and the rectangle window (rectwin) function
in the frame blocking process can improve the per-
formance of Automatic System Recognition (ASR).
In research (Fachrie and Harjoko, 2015), the MFCC
method combined with natural logarithm of Frame
Energy (lnFE) was used to extract features digit word
sounds in Indonesian by using Elman Recurrent Neu-
ral Network (ERNN) as the classification. In research
(Ferdiansyah and Purwarianti, 2011), the ASR sys-
tem was developed from an existing system model to
recognize words in Indonesian. However, there are
no studies that apply the SVD and Karhunen Loeve
feature selection method for Indonesian word sound
data.
This research is a development from previous re-
search that applies the SVD method to reduce the
dimension of Indonesian speech features (Kristomo
et al., 2018), which is still limited to the second re-
duction level and only to the stop consonant data.This
study aims to obtain efficient and effective traits in
Indonesian word sound cues by applying the Singu-
lar Value Decomposition (SVD) and Karhunen-Loeve
(KL) -based trait selection method. So that the trait
selection is expected to be able to improve the per-
formance of speech recognition systems. This re-
search will be divided into 4 main stages namely pre-
processing, feature extraction, feature dimensional-
ity reduction, and classification, which this research
will be more focused on the dimensionality reduction
stage.
2 MATERIAL AND METHODS
2.1 Database
The research was conducted by firstly collected the
speech database from several speakers that were used
for training and testing to the system. Stop consonant
sound data used in this study were 560 utterances and
for word data were 300 utterances. The stop conso-
nant data was segmented for 60 ms while for word
data was segmented for 480 ms. The set of word are
listed in Table 1.
Table 1: The List of Stop Consonants Words Data.
Words in Indonesian English Translation
Kakak Older sibling/cousin
Tutup Closed
Bibit Seed
Papan Board
Duduk Sit
Gigit Bite
Dimensionality Reduction of Speech Signals using Singular Value Decomposition and Karhunen-Loeve
79

2.2 Feature Extraction
2.2.1 Time-frequency Features
We used three main method namely Wavelet, Au-
toregressive Power Spectral Density (AR-PSD), and
Renyi Entropy. The wavelet transform (WT) has a
strength to localize the transient events emergence
(Boccaletti et al., 1997). It is considered to be the best
in describing the signal anomaly, pulses, and other
events which appear in the brief duration of the sig-
nal (Fugal, 2009), e.g. speech signal of the stop con-
sonants. In conducting this feature extraction pro-
cess, DWT was used at the decomposition level-7. In
addition, a lower frequency band or also referred to
as approximation was used in the process of DWT
decomposition. The decomposition which was con-
ducted as the 7th level gave the lowest frequency band
of 0–31.25 Hz. Therefore, since it results in a very
low frequency, there is no more decomposition was
conducted as such frequency would be insignificant
and would not have any discriminatory information.
After the decomposition of the the speech signal fre-
quency sampling of 8 kHz, the frequency bands ob-
tained were 2000-4000, 1000-2000, 500-1000, 250-
500, 125-250, 62.5-125, 31.25-62.5, and 0-31.25 Hz.
In this study, PSD using Yule-Walker AR algo-
rithm was performed. This algorithm is used for
transformation of the speech signal from time domain
to frequency domain. Whereas Renyi Entropy is used
to obtain the speech signal features in time domain
(Kristomo et al., 2016).
2.2.2 Wavelet
The sub-band tree structure of WPT feature extraction
method adopted in this work refers to the previous re-
search. The words data in this research have 8 kHz of
sampling frequency, giving 4 kHz bandwidth signal.
A frame size of 480 ms has been used to derive the
WPT. All these frequency bands were decomposed
using full 4-level WP to obtain sixteen sub-bands each
of 0.25 kHz. So the sixteen frequency bands obtained
after decomposition from the lower to the higher fre-
quency band were 0-0.25 kHz (f1), 0.25-0.5 kHz (f2),
0.5-0.75 kHz (f3), 0.75- 1 kHz (f4), 1-1.25 kHz (f5),
1.25-1.5 kHz (f6), 1.5- 1.75 kHz (f7), 1.75-2 kHz (f8),
2-2.25 kHz (f9), 2.25-2.5 kHz (f10), 2.5-2.75 kHz
(f11), 2.75-3 kHz (f12), 3-3.25 kHz (f13), 3.25-3.5
kHz (f14), 3.5-3.75 kHz (f15), and 3.75-4 kHz (f16)
respectively.
2.3 Dimensionality Reduction
This study uses the Singular Value Decomposition
(SVD) and Karhunen-Loeve (KL) method to select
the feature of Indonesian word sound signal.
2.3.1 Singular Value Decomposition
Singular Value Decomposition (SVD) is a matrix fac-
torization that can be used to for a real matrix and a
complex matrix. SVD is a classic and reliable method
in linear algebra that is used for dimension reduction
and ranking in pattern recognition. SVD allows fac-
torization of feature matrices into three matrices de-
noted as USVT. Where U represents N x N orthog-
onal matrix (N = amount of data), S represents N x
n diagonal matrix with singular values of the original
feature value matrix on the diagonal, and V shows the
orthogonal matrix n x n (n = number of features). VT
is the Hermitian transpose of V. Figure 1 shows the
interpretation of the matrix product related to SVD
(Theodoridis and Koutroumbas, 2009).
Figure 1: The factorization and reduction ilustration using
SVD in the estimation of X by X.
2.3.2 Karhunen Loeve
Karhunen-Loeve (KL) or Principal Component Anal-
ysis (PCA) is one of the most popular methods for
feature generation and dimension reduction in pattern
recognition.
The step in the selection of features using the KL
transformation is shown in equations 1 to 8. First of
all a data matrix in the form:
x
i
=


a
b
c


, x = [x
1
, x
2
, x
3
, ..., x
n
] (1)
Then the covariance (C
x
) of the data matrix is cal-
culated:
C
x
=
1
n
Σ
n
k=1
X
k
X
t
k
− (m
x
m
t
x
) (2)
Where m
x
is the average of the data matrix
CONRIST 2019 - International Conferences on Information System and Technology
80

m
x
=
1
n
Σ
n
k=1
X
k
(3)
After (C
x
) is obtained then the eigen value (λ) is
calculated
det|c
x
− λi| (4)
And also the eigen vector (e)
(c
x
− λi)v = 0 (5)
Then the eigen value (λ) is sorted from the largest
to the smallest
λ
1
> λ
2
(6)
Based on the order of the eigen value (λ) arrange
e
t
i
into a transformation matrix as follows
A =

e
t
1
e
t
2

(7)
Then transform the data matrix in a way
y1 = A(x
i
− m
x
) (8)
3 RESULTS AND DISCUSSION
The results of the study are divided into two parts The
first result is applying the SVD method to speech sig-
nal data with a reduction index variation from 1 to 30
for three types of feature sets namely WS, WPSDS,
and WRPSDS. In this experiment, we compare the
performance of the time-frequency features without
feature reduction using SVD and the time-frequency
features with feature reduction using SVD. The fea-
ture set without dimensionality reduction is denoted
as WS, WPSDS, and WRPSDS, whereas the fea-
ture set with dimensionality reduction is denoted as
WS+SVD2, WPSDS+SVD1, and WRPSDS+SVD10
as shown in Figure 2.
Figure 2: Classification Result of stop consonants using 10-
Fold Cross Validation.
From the result shown in Figure 2, it can be seen
that SVD gives improved the classification scores as
shown by accuracy of 72.23%, 66.1%, and 68.33%
for WPSDS+SVD1 /a, i/ and WRPSDS+SVD10 /u/,
respectively. However, some parts of stop consonant
syllables shows better result without feature selection
using SVD, such as /ki/ in WS, /ka, ku/ in WPSDS
and WRPSDS; /da/ in WPSDS; /pa, pu/ in WRPSDS;
and /tu/ in WPSDS.
Based on Figure 1 it can be seen that the optimal
classification results are achieved in the reduction in-
dices 2, 1, and 10 for the WS, WPSDS, and WRPSDS
feature sets respectively. The WS feature set starts to
decrease continuously at the 10th reduction index and
reaches the minimum classification results on the 27th
reduction index and so on. The results of WRPSDS
classification are better than WPSDS and WS but in
certain reduction indices the results of WS classifica-
tion are better than WRPSDS.
The second research result is applying the SVD
method to the word voice signal data with a reduc-
tion index variation from 1 to 25 with the Wavelet
Packet Transform (WPT) feature extraction method
in decomposition 4. The singular values and the ma-
trix reduction process are listed in descending order
as follow (Equation 8 to 10):
Figure 3: Classification results of stop consonants by using
three sets of features with SVD reduction index variations.
U
1
=



U
1,1
... U
1,299
0
... ... ... 0
... ... ... 0
U
30Q1
... U
30Q299
0



U
1
=



−0.03834 ... −0.0406 0
... ... ... 0
... ... ... 0
0.003032 ... −0.03778 0



U
2
=



−0.03834 ... 0 0
... ... 0 0
... ... 0 0
0.003032 ... 0 0



(9)
Dimensionality Reduction of Speech Signals using Singular Value Decomposition and Karhunen-Loeve
81

S
1
=





λ
1
0 0 ... 0
0 λ
2
0 ... 0
0 0 ... 0 0
... ... 0 λ
23
...
0 0 ... 0 0





S
1
=





2.296941 0 0 ... 0
0 1.657405 0 ... 0
0 0 ... 0 0
... ... 0 0.001605 ...
0 0 ... 0 0





S
2
=





2.296941 0 0 ... 0
0 1.657405 0 ... 0
0 0 ... 0 0
... ... 0 0 ...
0 0 ... 0 0





(10)
V
T 1
=



V
11
... ... V
125
... ... ... ...
V
241
... ... V
2425
0 0 0 0



V
1
=



−0.72144 ... ... −0.00165
... ... ... ...
0.000035 ... ... −0.03348
0 0 0 0



V
2
=



−0.72144 ... ... −0.00165
... ... ... ...
0 ... ... 0
0 0 0 0



(11)
Figure 4: Classification results of word by using WPT fea-
ture set with SVD reduction index variations
Table 2: Confusion Matrices of Each Reduction Index.
1- REDUCTION INDEX
A B C D E F
A 48 0 0 2 0 0
B 0 50 0 0 0 0
C 0 0 43 0 0 7
D 2 0 0 48 0 0
E 0 1 0 0 49 0
F 0 0 5 0 0 45
2- REDUCTION INDEX
A B C D E F
A 48 0 0 2 0 0
B 0 50 0 0 0 0
C 0 0 46 0 0 4
D 1 0 0 49 0 0
E 0 1 0 0 49 0
F 0 0 5 0 0 45
3- REDUCTION INDEX
A B C D E F
A 46 0 0 4 0 0
B 0 50 0 0 0 0
C 0 0 43 0 1 6
D 3 0 0 47 0 0
E 0 0 0 1 49 0
F 0 0 6 0 0 44
4- REDUCTION INDEX
A B C D E F
A 48 0 0 2 0 0
B 0 50 0 0 0 0
C 0 0 46 0 0 4
D 3 0 0 47 0 0
E 0 1 0 0 49 0
F 0 0 6 0 0 44
5- REDUCTION INDEX
A B C D E F
A 48 0 0 2 0 0
B 0 50 0 0 0 0
C 0 0 45 0 0 5
D 4 0 0 46 0 0
E 0 0 0 1 49 0
F 0 0 8 0 0 42
CONRIST 2019 - International Conferences on Information System and Technology
82

6- REDUCTION INDEX
A B C D E F
A 47 0 0 3 0 0
B 0 50 0 0 0 0
C 0 0 39 0 0 11
D 3 0 0 47 0 0
E 0 1 0 0 49 0
F 0 0 7 0 0 43
7- REDUCTION INDEX
A B C D E F
A 48 0 0 2 0 0
B 0 50 0 0 0 0
C 0 0 41 0 0 9
D 2 0 0 48 0 0
E 0 1 0 0 49 0
F 0 0 7 0 0 43
8- REDUCTION INDEX
A B C D E F
A 46 0 0 4 0 0
B 0 50 0 0 0 0
C 0 0 40 0 0 10
D 3 0 0 47 0 0
E 0 2 0 0 48 0
F 0 0 8 0 0 42
9- REDUCTION INDEX
A B C D E F
A 48 0 0 2 0 0
B 0 50 0 0 0 0
C 0 0 41 0 0 9
D 2 0 0 48 0 0
E 0 2 0 0 48 0
F 0 0 8 0 0 42
10- REDUCTION INDEX
A B C D E F
A 47 0 0 3 0 0
B 0 50 0 0 0 0
C 0 0 40 0 1 9
D 1 1 0 48 0 0
E 0 2 0 0 48 0
F 0 0 8 0 0 42
11- REDUCTION INDEX
A B C D E F
A 47 0 0 3 0 0
B 0 50 0 0 0 0
C 0 0 40 0 0 10
D 1 1 0 48 0 0
E 0 2 0 0 48 0
F 0 0 8 0 0 42
...25- REDUCTION INDEX
A B C D E F
A 10 5 10 10 15 0
B 10 5 10 10 15 0
C 10 5 10 10 15 0
D 10 5 10 10 15 0
E 10 5 10 10 15 0
F 10 5 10 10 15 0
Based on Figure 4, it appears that the best classi-
fication results are on the second SVD index that is
equal to 95.67%. The classification results begin to
decrease continuously at the 20th index, and achieve
the lowest classification results at the 25th index. This
indicates that the greater the reduction index at a cer-
tain threshold will reduce the accuracy of classifica-
tion, while for a reduction that is not too large can
allow an increase in the classification results, because
the new matrix with a reduction value that is not too
large can be more discriminatory. For the classifica-
tion results with the variation of the reduction index
in the form of a confusion matrix are shown in Table
2, where the class of data is as follows a = kakak, b
= tutup, c = bibit, d = papan, e = duduk, f = gigit.
Based on Table 2 it appears that the data class f or
sound ”gigit” is always the lowest accuracy in each
reduction index, this is likely due to the similarity of
the sound signal / characteristic between the sound
”gigit” with data c or ”bibit”. While the highest clas-
sification results are in the data class b or ”tutup” be-
cause it has the most discriminant characteristic of
other data classes. In the 2nd reduction index there
was an increase in data classes c (43− > 46) and d
(48− > 49), but again decreased in the 3rd reduction
index for data classes c (46− > 43) and d ( 49− >
47), and is still changing (up and down) fluctuatively
in the next reduction index.
Table 3 shows the results of word sound classi-
fication using WPT features before and after being
reduced by SVD and KL feature reduction methods.
Based on Table 3 it can be seen that the results of
word sound classification using WPT features without
reduction reached 95% whereas after reduction with
the SVD method the 2nd reduction index increased to
95.67%. The use of the KL method in the reduction
of feature dimensions reduces the classification accu-
Dimensionality Reduction of Speech Signals using Singular Value Decomposition and Karhunen-Loeve
83

racy level by 89%. However, the KL method is able
to reduce the features to 18 which indicates that the
KL method is more efficient.
Table 3: Word of stop consonants classification result.
Feature Acc. classification (%)
WPT (25 features) 95
WPT + SVD2 95,67
WPT + KL (18 features) 89
4 CONCLUSIONS
In this paper, a dimensionality reduction method
based on SVD combined with time-frequency fea-
tures was performed for classifying the Indonesian
stop consonants in the context of CV syllable as well
as the word of stop consonants. Based on the ex-
perimental result presented in this paper, it can be
concluded that the SVD gives improved the clas-
sification scores as shown by average classification
rate of 68.7%, and 67.58 for WPSDS+SVD1 and
WRPSDS+SVD10, respectively which are 3.34% and
3.69% increase than WPSDS and WRPSDS without
dimensionality reduction by using SVD. The appli-
cation of the SVD method in the dimension of word
sound features, at a certain level of the reduction in-
dex (index-2) can increase the classification results,
however an increase in the reduction index that is
too high tends to reduce the results of the classifica-
tion. Classification of stop consonants is more diffi-
cult when compared to words of stop consonant. The
highest classification result for the words is 95.67%.
ACKNOWLEDGEMENTS
This work has been supported by Directorate Gen-
eral of Research, Technology, and Higher Educa-
tion (RISTEKDIKTI) of Indonesia under “Peneli-
tian Dosen Pemula” scheme with contract number
B/1435.28/L5/RA.00/2019.
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