If we have questions about Semantic code Semantic code Factor analysis and Factor analysis and More generally about multivariate statistics More generally.

If we have questions aboutIf we have questions about

Semantic codeSemantic code Factor analysis andFactor analysis and More generally about multivariate More generally about multivariate

statisticsstatistics Using Methods of Nonlinear Dynamic Using Methods of Nonlinear Dynamic

System Theory System Theory

And time to answer itsAnd time to answer its

Semantic Semantic Code Code

Low integrative modelLow integrative model

nn++–– number of subjects who scaled the concept as positive number of subjects who scaled the concept as positive

nn-- –– number of subjects who scaled the concept as number of subjects who scaled the concept as negativenegative

N N – – total number of subjectstotal number of subjects: N= n: N= n++ + + n-n-

1122 – – chi-square distribution with 1 degree of freedomchi-square distribution with 1 degree of freedom

If If SC SC > > 1122 then this scale is significant then this scale is significant

positive (ifpositive (if n n+ + > > n- n- ) or ) or

negative (ifnegative (if n n+ + < < n- n- ) )

for this concept.for this concept.

2

1

2

?)(

Nnn

SC

Factor analysis is the most frequently Factor analysis is the most frequently used method of multivariate statistics used method of multivariate statistics

Reconstruction of geometrical model of Reconstruction of geometrical model of Semantic spaceSemantic space– Scales form factors (according their factor loadings)Scales form factors (according their factor loadings)– Factor scores are used as coordinates of concepts Factor scores are used as coordinates of concepts

in geometrical space of factorsin geometrical space of factors Measurement of cognitive complexity (number Measurement of cognitive complexity (number

and significance of extracted factors)and significance of extracted factors) Classification of additional concepts not Classification of additional concepts not

included in factor analysis (according their included in factor analysis (according their factor scores)factor scores)

Comparing FA with other multivariate Comparing FA with other multivariate methods frequently used in methods frequently used in

Psychosemantics Psychosemantics

Cluster analysis gives classification Cluster analysis gives classification based on the ONE integrated featurebased on the ONE integrated feature

Multidimensional scaling provides Multidimensional scaling provides less objective interpretation of the less objective interpretation of the factors – there are no scales just factors – there are no scales just concepts.concepts.

Clusters:

Boris Eltsin

Victor Chernomyrdin

Anatoly Chubais

BorisBerezovsky

EgorGaidar

MichailGorbachev Unpopular Unpopular

LeadersLeaders

GovernmentGovernment

Ex-GovernmentEx-Government

VladimirZhirinovsky

GennadyZuganov

Old Old orthodox orthodox oppositiooppositionn

Boris Nemtsov

Grigory Yavlinsky

Yurij Luzhkov

AlexanderLebed

Popular LeadersPopular Leaders

Ivan Rybkin

Egor Stroev

StanislavGovorukhin

Aman Tuleev

AlexanderRutskoy

GenadijSeleznev

Free market’s ideas, but

opposition to government

way

Neo-Neo-CommunistiCommunisti

c and c and Socialistic Socialistic

ideasideas

Neo-Neo-National-National-Patriotic Patriotic

ideasideas

Semantic space of images of Russian political parties in social consciousness before Parliament’s election

(December 1995)F2+ Social-oriented economy

F2- Criminal economy

F1- West-oriented F1+ Totalitarian isolationism

The cloud of distribution of Kazakh subjects in the political semantic space (1991)

F1- Support the Separated national Republic

F1+ Support the Union of the Republics of the

Former USRR

Zone of possible electorate

The cloud of distribution of Russian subjects in the political semantic space (1991)

F1- Support the Separated national Republic

F1+ Support the Union of the Republics of the

Former USRR

Compare different Compare different forms of geometrical forms of geometrical

representationsrepresentationsPsychosemantic space of geopolitical Psychosemantic space of geopolitical

representations (1999).representations (1999).

From: Petrenko, Mitina, Bertnikov 2003From: Petrenko, Mitina, Bertnikov 2003

Traditional way using factor space

Semantic space of images Europe countries

By factor: Friendliness to Russia

Determinacy analysis (DA)Determinacy analysis (DA)

As usual mostly methods of data As usual mostly methods of data analysis in Humanitarian and Social analysis in Humanitarian and Social sciences got birth in North America sciences got birth in North America and West Europe. DA is an exclusion. and West Europe. DA is an exclusion. The author of this method is Russian The author of this method is Russian mathematician S.Chesnokov.mathematician S.Chesnokov.

DA algorithms to the maximum extent approach the DA algorithms to the maximum extent approach the principles of logical reasoning in natural language.principles of logical reasoning in natural language.

The basic concept of DA is “determination” which The basic concept of DA is “determination” which establishes correspondence between two establishes correspondence between two statements, objects, events, etc. according to the statements, objects, events, etc. according to the rule “if rule “if aa, then , then bb”. ”. aa and and b b are fixed answers to are fixed answers to different questions of the survey or any other different questions of the survey or any other features, properties of the investigated objects. features, properties of the investigated objects.

Here Here bb is the object’s property the appearing of is the object’s property the appearing of which is being explained, and which is being explained, and aa is the property of is the property of the object by the influence of which the object by the influence of which bb is is explained. explained.

For the analysis of the determinations the For the analysis of the determinations the conditional frequencies conditional frequencies P(b/a), P(a/b) P(b/a), P(a/b) of the of the appearance of appearance of aa and and b b features are used. features are used.

To analyze determination following To analyze determination following indices are used: exactness (I), indices are used: exactness (I),

completeness (C) and essentiality (E).completeness (C) and essentiality (E).

I characterizes the degree of correctness of the I characterizes the degree of correctness of the choice of the explanative feature. choice of the explanative feature.

C is used in order to determine how often the C is used in order to determine how often the explanative feature explanative feature aa chosen induces the chosen induces the presence of the feature presence of the feature bb which is being which is being explained.explained.

E shows in what degree the portion of objects E shows in what degree the portion of objects possessing both possessing both aa and and b b features among objects features among objects with the featurewith the feature a a is less or greater than the is less or greater than the portion of objects with the featureportion of objects with the feature b in the whole b in the whole sample. sample.

The advantage of DA is its orientation towards The advantage of DA is its orientation towards the work with nominative, non-parametric data.the work with nominative, non-parametric data.

From Pictures to From Pictures to MoviesMovies

How to use semantic spaces How to use semantic spaces to build Dynamical Cognitive to build Dynamical Cognitive

ModelsModels

Model build-upModel build-up The model offered here involves the The model offered here involves the

construction of trajectories in phase space. construction of trajectories in phase space. In phase space time is represented in the In phase space time is represented in the

trajectories rather than with its own axis.trajectories rather than with its own axis. The phase space allows to present graphically The phase space allows to present graphically

the evolution of system’s condition in time, the evolution of system’s condition in time, i.e. consecutive evolution of its state, with the i.e. consecutive evolution of its state, with the help of curves (trajectories)–a geometrical set help of curves (trajectories)–a geometrical set of points appropriate to the system’s of points appropriate to the system’s changing position in the phase space, which changing position in the phase space, which this system occupied at the consecutive this system occupied at the consecutive moments of time.moments of time.

These trajectories allow to see all set of These trajectories allow to see all set of movements that can appear at every possible movements that can appear at every possible initial conditions.initial conditions.

For building the phase For building the phase trajectories usetrajectories use

Differential equationsDifferential equations (used when we (used when we speak about the systems who's variables speak about the systems who's variables can be considered continuous)can be considered continuous)

Difference equationsDifference equations (used when we (used when we speak about the systems who's variables speak about the systems who's variables can be considered discrete)can be considered discrete)

These equations allow to describe the These equations allow to describe the dynamics of a process as functional dynamics of a process as functional dependence of different initial states of dependence of different initial states of the system.the system.

The solution of a difference The solution of a difference equationequation can be obtained can be obtained

With the help of calculus of finite With the help of calculus of finite differences. differences.

Analytically with the help of the Analytically with the help of the transition to the limit to the transition to the limit to the continuous differential equation, if continuous differential equation, if there is an algorithm of direct there is an algorithm of direct analytical integration of this analytical integration of this differential equation.differential equation.

The basic idea of the methodology of difference The basic idea of the methodology of difference equations equations

If the law of evolution on an interval between two moments of If the law of evolution on an interval between two moments of time is known, it is possible to connect the points on a time is known, it is possible to connect the points on a trajectory at the moment of time trajectory at the moment of time TTnn and and TTn+1n+1 with the help of with the help of

functional dependence. functional dependence. The mathematical model of a dynamic system The mathematical model of a dynamic system SS, set up with , set up with

the help of a difference equation, is based on the condition of the help of a difference equation, is based on the condition of the system the system SSnn, which is understood as the description of this , which is understood as the description of this

system at the moment of time system at the moment of time TTnn, and on the operator , and on the operator FF, ,

determining the transformation of system S in time. The determining the transformation of system S in time. The operator operator FF describes an iterative process: describes an iterative process: F[S], F[F[S]] . . .F[S], F[F[S]] . . . and and also specifies transformation of the dynamical system also specifies transformation of the dynamical system SSnn at the at the

moment of time moment of time TTnn to its condition to its condition SSn+1n+1 at the moment of time at the moment of time

TTn+1n+1::

SSn+1n+1=F [S=F [Snn] ] (1)(1)

The set of all possible states of a system S forms a phase The set of all possible states of a system S forms a phase space of states space of states ФФ(S).(S). This space together with the operator This space together with the operator F, F, form the mathematical model of the dynamical system form the mathematical model of the dynamical system defined by the difference equation (1).defined by the difference equation (1).

Stationary stateStationary state The fulfillment of the condition The fulfillment of the condition

SSnn=F[S=F[Snn]] (2)(2)means, that the system is in such condition means, that the system is in such condition that all its objects in each moment of time that all its objects in each moment of time following following TTnn move into themselves, i.e. move into themselves, i.e. remain in the same place (are motionless). remain in the same place (are motionless). Thus, the state of the system Thus, the state of the system SSnn, satisfying , satisfying the condition (2) is the condition (2) is stationary at a fixed stationary at a fixed point attractorpoint attractor. .

There are There are stable and unstablestable and unstable stationary stationary states.states.

The hypothesis about the ergodicity of dissipative systems The hypothesis about the ergodicity of dissipative systems allows:allows:

In case of absence of large sequence of data on the state of In case of absence of large sequence of data on the state of process at each moment of time process at each moment of time SS11, S, S22, S, S3, 3, . . . S. . . Sn n . . ., where n is . . ., where n is a large enough number from the point of view of statistical and a large enough number from the point of view of statistical and computing procedures, there is no opportunity to write and computing procedures, there is no opportunity to write and solve a difference equation. solve a difference equation.

It is possible to build a pseudo-phase space and extrapolate the It is possible to build a pseudo-phase space and extrapolate the function function SSn+1n+1=F(S=F(Snn)) on a multiple set of values on a multiple set of values {S{Stt, S, St+Tt+T},}, obtained as a result of observation and measurement of values obtained as a result of observation and measurement of values of the whole ensemble of points, representing the process at of the whole ensemble of points, representing the process at two different moments of time two different moments of time t t and and t+Tt+T. .

The synergetic approach allocating general laws of functioning The synergetic approach allocating general laws of functioning of natural and social systems proves the acceptance of the of natural and social systems proves the acceptance of the ergodicity in our case. However, the strict proof of the ergodicity in our case. However, the strict proof of the ergodicity hypothesis is very difficult and more often still ergodicity hypothesis is very difficult and more often still remains an unsolved task. remains an unsolved task.

It allows avoiding difficulties arising at "development in time" of It allows avoiding difficulties arising at "development in time" of this or that process, and to replace it by "development in this or that process, and to replace it by "development in space", i.e. with the data on a large number of objects in the space", i.e. with the data on a large number of objects in the system from information received at any moment of time. Using system from information received at any moment of time. Using this method it is possible to predict the behavior of the system this method it is possible to predict the behavior of the system at other stages of its development, even in the area of human at other stages of its development, even in the area of human sciences, when carrying out a number of measurements in sciences, when carrying out a number of measurements in longitudinal research frequently appears inconvenient.longitudinal research frequently appears inconvenient.

The system The system SS is defined by the position of is defined by the position of the included concepts. the included concepts.

The location of concepts is defined by a set The location of concepts is defined by a set of its’ coordinates in the semantic space.of its’ coordinates in the semantic space.

Each concept Each concept OO with coordinates with coordinates OOijij, where , where

ii=1 if we are speaking about the coordinates =1 if we are speaking about the coordinates of concept of concept OO, when the system is in a , when the system is in a condition condition SS11, and , and ii=2, if we are speaking =2, if we are speaking

about the coordinates of concept about the coordinates of concept OO, when , when the system is in a condition the system is in a condition SS22, and , and jj changes changes

from 1 up to from 1 up to NN. . SS11 and and SS22 are the two states of the same are the two states of the same

system.system.

LetLet A A be the regression operator constructed on the basis of be the regression operator constructed on the basis of

the statistical analysis of empirical values, specifying the the statistical analysis of empirical values, specifying the

coordinates of each of concepts for condition coordinates of each of concepts for condition SS11 and and SS22 in a in a

space of dimension space of dimension NN, so that from the point of view of , so that from the point of view of

statistical criteria statistical criteria SS22==AA((SS11) is the best theoretical ) is the best theoretical

approximation of the experimental data. Then it is possible approximation of the experimental data. Then it is possible

to write down the following simultaneous equations with the to write down the following simultaneous equations with the

help of the regression operator:help of the regression operator:

OO22jj=A(O=A(O1j1j), j=1... N), j=1... N

The choice of a type of the regression operator The choice of a type of the regression operator AA is probably is probably

one of the most difficult methodical questions and should be one of the most difficult methodical questions and should be

resolved on the basis of additional reasons concerning the resolved on the basis of additional reasons concerning the

laws and properties of the dependence under study.laws and properties of the dependence under study.

In our work we restricted ourselves to a linear operator, In our work we restricted ourselves to a linear operator, proceeding from the assumption that the majority of the proceeding from the assumption that the majority of the nonlinear operators in the limited vicinity can be nonlinear operators in the limited vicinity can be approximated by linear operators.approximated by linear operators.

The following model regression formulas were used:The following model regression formulas were used:

XXn+1n+1=a=a00+a+a11 X Xnn+a+a22 Y Ynn

YYn+1n+1=b=b00+b+b11 X Xnn+b+b22 Y Ynn

These equations can be transformed in the following way: These equations can be transformed in the following way:

XXn+1 n+1 –– XXnn= a= a00+(a+(a11–1) X–1) Xnn +a +a22 Y Ynn

YYn+1 n+1 – Y– Ynn= b= b00+b+b11 X Xnn+(b+(b22–1) Y–1) Ynn

The latter are replaced by the following simultaneous The latter are replaced by the following simultaneous linear differential equations:linear differential equations:

dx/dt= adx/dt= a00+(a+(a11–1) x+ a–1) x+ a22 y y

dy/dt= bdy/dt= b00+b+b11 x+(b x+(b22–1) y–1) y

Results of application Results of application the model to the data the model to the data

getting from getting from psychosemantic psychosemantic

researchresearch

Dynamical Cognitive Models of Dynamical Cognitive Models of Political-Social Issues in Russia Political-Social Issues in Russia

(1994-1998)(1994-1998)(Mitina, Petrenko 2001)(Mitina, Petrenko 2001)

List of the conceptsList of the concepts1 Privatization2 Private property on land3 Free exchange and sale of foreign currency4 Turning the enterprises into joint-stock companies by labor collectives5 Privatization of the enterprises on a competitive basis6 Planned economy7 Foreign investments8 The disintegration of the USSR9 The formation of the CIS 10 Conversion of the defense industry 11 Creation of commercial banks12 Introduction of paid education and paid public health services13. Introduction of system of bankruptcy for the unprofitable enterprises14 State monopoly on the foreign trade15 State subvention for agriculture 16 Social aid programs

17 Integration into the world global economy18 Mortgages19 The Government20 The President (as a social institute)21 The State Duma 22 The Army23 The International Monetary Fund24 The Church25 The Democrats26 The National Patriots27. The Communists28 Yeltsin29 Chernomyrdin30 Gaidar31 Luzhkov32 Zhirinovsky33 Chubais34 Rutskoi 35 Yavlinsky

Neural networks are considering Neural networks are considering as algorithms of data analysis, as algorithms of data analysis, not as models for constructions not as models for constructions

and functioning the Image of the and functioning the Image of the world.world.

The possible domains of applications:The possible domains of applications:– ClassificationClassification– Patterns recognitionPatterns recognition