Application of parameters of voice singal autoregressive models to solve speaker recognition problems

sis of discriminant functions 
 Variables in the model: 6; group.: Speaker (10gr.) 
 N=500 Wilks’ lambda: .00004 abt. F (54.2477)=288.44 p <0.0000 
 Wilks’ Private F-expulsion P-level Tolerance 1- tolerance 
 lambda lambda (9.485) (R-sq.) 
 0.000159 0.252119 159.8553 0.000000 0.992158 0.007842 
 aˆ11
 0.000088 0.454148 64.7704 0.000000 0.995123 0.004877 
 aˆ9
 0.000436 0.091728 533.5973 0.000000 0.986232 0.013768 
 aˆ10
 0.000040 0.991295 0.4732 0.892698 0.000035 0.999965 
 aˆ7
 0.000041 0.984736 0.8353 0.583771 0.000026 0.999974 
 aˆ12
 0.000145 0.275083 142.0119 0.000000 0.987771 0.012230 
 aˆ8
 TABLE 4. AN EXAMPLE OF THE AC NON-REDUNDANT SET 
 CALCULATED BY THE SEGMENT MODEL OF THE SOUND IN THE WORD 
 Results of the analysis of discriminant functions 
 Variables in the model: 4; group.: Speaker (10gr.) 
 N=500 Wilks’ lambda: .00004 abt. F (36.1826)=701.20 p <0.0000 
 Wilks’ Private F-expulsion P-level Tolerance 1- tolerance 
 lambda lambda (9,487) (R-sq.) 
 0.000149 0.275758 142.1155 0.000000 0.992911 0.007089 
 0.000090 0.453074 65.3200 0.000000 0.995838 0.004162 
 0.000445 0.092043 533.7809 0.000000 0.990489 0.009511 
 0.000162 0.252499 160.1908 0.000000 0.994934 0.005066 
 Assessing the power of discrimination of non-
redundant ACs is based on a step-by-step The quality of the speakers classification can 
discriminant analysis with exceptions based on only be assessed as posteriori. For this purpose, at 
statistics of the following form [18]: the training stage, informative ACs are calculated 
 n g s 1  for each PW (password word) implementation for 
 F  , (14) all the speakers registered in the system. After 
 g 1 
 that, the average AC values for each j-th password 
where  W T , W and T – are the intra-group 
 word and k-th speaker aˆ jk . 
and inter-group correlation matrices of the AC, 
respectively, s – is the number of AC, n – is the At the classification stage, the AC values for 
number of VS realizations for all speakers. the target speaker aˆh , aˆh 1,..., aˆ p are calculated. 
 Then, when conditions of the following form The obtained values using the selected 
are satisfied: proximity measure must be compared with the 
 average AC values calculated at the training 
 F F ( , g 1, n g s) (15)
 expul 1 2 stage and, based on the results, decide on 
 discriminant power of the AC is significant. assigning the target speaker to a specific class. 
Otherwise, an insignificant AC must be excluded To assess the degree of proximity of AC values 
from the list of informative features. calculated for the target speaker to their 
 reference values obtained at the training stage, it 
 V. QUALITY ASSESSMENT OF SPEAKER is necessary to use some measure to find the 
 RECOGNITION distance between two points in the 
 Assessing the quality of speaker recognition multidimensional space of AC values. In the 
on the basis of the generated informative ACs general case, it is advisable to use the 
will be considered using the classification Mahalanobis distance, since, firstly, the 
problem as an example. standard deviations of the AC values may be 
 No 2.CS (10) 2019 31 
Journal of Science and Technology on Information Security 
unequal, and secondly, these values can be According to expression (16), the degree of 
correlated. To calculate the proximity degree of proximity of the target speaker to each speaker 
the target speaker to a particular class, an registered in the system is estimated, and the 
expression of the following form is used: target speaker is assigned to the class for which 
 p p the value of the proximity measure is minimal. 
 2 1
D A Ck (w )ij (aˆik aˆik )(aˆ jk aˆ jk ) ,(16) Then the indicator of the classification quality will 
 i h j h be the proportion of correctly assigned AC vectors 
where D2 A C – is the square of the distance to the corresponding class of speakers. It is clear 
 k that the closer its value is to 1, the more accurate 
from the AC values vector A of the target is the separation of speakers. 
speaker to the center of the class of vectors 
 1 To check the quality of speaker recognition 
characterizing the k-th speaker, (w )ij – is the based on the selected ACs, we analyzed the 
element of the matrix inverse to the intragroup classification matrix, which contains 
covariance AC matrix, aˆ – is the value of the i- information on the number and percentage of 
 ik correctly classified observations in each group. 
th AC in the class k, aˆik – is the average value of For example, Tables 5 and 6 show the results 
the i-th AC in class k. of applying the developed procedure for 
 comparing a set of coefficients aˆ7 aˆ12 , 
 In the particular case when the intragroup 
covariance matrix is single, the Mahalanobis calculated for the sound a in the word an and 
distance is the Euclidean distance. a set aˆ8 aˆ11 obtained after removing excess 
 ˆ ˆ
 coefficients a7 and a12 . 
 TABLE 5. SPEAKERS CLASSIFICATION RESULTS BY AC CALCULATED BY THE SEGMENT 
 MODEL OF THE SOUND a IN THE WORD an 
 Classification matrix 
 Line: observable classes 
 Columns: predicated classes 
 1 2 3 4 5 6 7 8 9
 Group 10
 rate
 accuracy
 speaker speaker speaker speaker speaker speaker speaker speaker speaker
 speaker
 speaker 1 96.08 49 1 0 0 0 1 0 0 0 0 
 speaker 2 87.75 0 43 0 0 4 0 2 0 0 0 
 speaker 3 84.00 0 0 42 2 0 0 0 5 1 0 
 speaker 4 88.00 0 4 2 44 0 0 0 2 2 0 
 speaker 5 88.00 2 2 0 0 44 0 0 0 0 0 
 speaker 6 98.00 1 0 0 0 0 49 0 0 0 0 
 speaker 7 98.00 0 1 0 0 0 0 49 0 0 0 
 speaker 8 88.00 0 0 6 0 0 0 0 44 0 0 
 speaker 9 98.00 0 0 0 1 0 0 0 0 49 0 
 speaker 10 100.00 0 0 0 0 0 0 0 0 0 50 
 Total 92.60 52 49 50 47 48 50 51 51 52 50 
32 No 2.CS (10) 2019 
 Nghiên cứu Khoa học và Công nghệ trong lĩnh vực An toàn thông tin 
 TABLE 6. SPEAKERS CLASSIFICATION RESULTS BY AC CALCULATED BY THE SEGMENT 
 MODEL OF THE SOUND ă IN THE WORD ăn 
 Classification matrix 
 Line: observable classes 
 Columns: predicated classes 
 1 2 3 4 5 6 7 8 9
 Group 10
 rate
 accuracy
 speaker speaker speaker speaker speaker speaker speaker speaker speaker
 speaker
 speaker 1 98.04 50 0 0 0 0 0 1 0 0 0 
 speaker 2 97.96 0 48 0 0 0 0 1 0 0 0 
 speaker 3 100.00 0 0 50 0 0 0 0 0 0 0 
 speaker 4 100.00 0 0 0 50 0 0 0 0 0 0 
 speaker 5 100.00 0 0 0 0 50 0 0 0 0 0 
 speaker 6 100.00 0 0 0 0 0 50 0 0 0 0 
 speaker 7 100.00 0 1 0 0 0 0 49 0 0 0 
 speaker 8 100.00 0 0 0 0 0 0 0 50 0 0 
 speaker 9 100.00 0 0 0 0 0 0 0 0 50 0 
 speaker 10 100.00 0 0 0 0 0 0 0 0 0 50 
 Total 99.40 50 49 50 50 50 50 51 50 50 50 
 It can be seen from the tables that the quality VI. CONCLUSION 
of the speakers classification using AC aˆ8 aˆ11 The article presents an approach to modeling 
(Tab. 6) significantly exceeds the quality of the VS to solve the speaker recognition problem. It 
speakers classification based on the initial set is shown that as informative features 
aˆ7 aˆ12 (Tab. 5). characterizing speakers one can use the 
 In case of significant errors in the speakers parameters of autoregressive time series models 
classification, it is advisable to analyze the sets of describing voice signals. 
autoregression coefficients in order to identify the An algorithm is proposed for VS automatic 
observations that caused these deviations. segmentation into quasistationary sections 
 If there are incorrect classifications, they based on interval estimation of speech samples 
must be excluded from the training set of VS standard deviation. At the same time, to solve 
implementations. The procedure of excluding the speaker recognition problem, segments are 
from training samples is that there is the AC set allocated to which the unchanged PTF and 
which should be excluded from the sample and maximum energy correspond, since they contain 
the number of its belonging to this group is the basic information about the features of the 
removed from the table of initial data, after speaker's features. 
which the process of assessing the quality of It is demonstrated that the segments formed 
speakers classification is repeated. When a on the basis of the developed algorithm are 
regular observation is deleted from the class, stationary time series, and it allows using 
new incorrectly assigned coefficient vectors autoregressive models of various orders to 
may appear, which were taken into account as describe them. In order to reduce the uncertainty 
correctly assigned before removal. The in the formation of the decisive rule for speaker 
procedure of excluding observations must be recognition, it is proposed to include only 
continued until the classification accuracy higher-order ACs in the model, since they are 
indicator reaches its maximum value. This the ones that characterize VS high-frequency 
approach allows, when forming informative variations and contain basic information about 
ACs, identifying and excluding VS the speaker's features. The possibility of using 
implementations for each speaker which for multivariate discriminant analysis to 
various reasons (illness, emotional state, etc.) substantiate an AC set of coefficients is shown. 
differ from the others in this class. 
 No 2.CS (10) 2019 33 
Journal of Science and Technology on Information Security 
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34 No 2.CS (10) 2019 
 Nghiên cứu Khoa học và Công nghệ trong lĩnh vực An toàn thông tin 
 ABOUT THE AUTHORS 
 PhD. Evgeny Novikov PhD. Vladimir Trubitsyn 
 Workplace: The Academy of Workplace: The Academy of 
 Federal Guard Service of the Federal Guard Service of the 
 Russian Federation. Russian Federation. 
 Email: nei05@rambler.ru Email: gremlin.kop@mail.ru 
 The education process: Received The education process: 
 his Ph.D. degree at the Research received his Ph.D. degree at 
 Institute of Radio-Electronic Belgorod technical University of the Russian 
Systems of the Russian Federation in Sep 2010. Federation in Dec 2014. 
Research today: modeling of random processes, Research today: modeling of random processes, 
statistical data processing and analysis, decision-making. information and coding theory, voice signal processing 
The education process: received his Ph.D. degree in and analysis. 
Engineering Sciences in Academy of Federal Guard 
Service of the Russian Federation in Dec 2013. 
Research today: information security, unauthorized 
access protection, mathematical cryptography, 
theoretical problems of computer science. 
 No 2.CS (10) 2019 35