CN103530505A - Human brain language cognition modeling method - Google Patents

Abstract

The invention discloses a human brain language cognition modeling method. The human brain language cognition modeling method comprises the following steps of initialization of a cognitive state example, mapping of probability distribution between activation characteristics and observation data, definition of a brain tacit cognition model and parameter analysis of the tacit cognition model. In the cognition modeling process, input stimulation, the observation result and the tacit cognition state are defined as triple time sequences related to a dynamic event, namely a cognition stimulation task time sequence, an observation characteristic time sequence and a tacit cognition state time sequence, the triple time sequences are related to one another through a set of probability distribution, and not all collected brain data are treated as static information for statistics. Therefore, the human brain language cognition modeling method does not need to meet the basic assumption based on statistics, is established under a small sample data condition, and guarantees the correctness of the cognition analysis result, thereby achieving cognition modeling under the small sample data condition. The human brain language cognition modeling method improves the accuracy of cognition modeling, and provides an effective approach for complex cognition analysis.

Description

A kind of human brain language cognition modeling method

Technical field

The present invention relates to a kind of human brain language cognition technology, especially a kind of human brain language cognition modeling method.

Background technique

Cognition most direct reflection in human brain is that brain area activates or inhibits degree, from the angle of nuroinformatics, key to language acknowledging research is to study the process of human brain language cognition process Midbrain Area state and these state transitions, its most important means first is that according to nuroinformatics requirement contrived experiment, stimulate the cognitive function of subject (the mostly volunteer of special group), and functional acquisition data are carried out to it, then these data are analyzed using certain modeling technique.The brain imaging technique (positron emission computerized tomography, function nuclear magnetic resonance) to grow up in recent years is directly observed and is analyzed human brain function activity for people and provides means.The Brian Imaging analytical technology that present cognitive research institute relies on mainly generates corresponding t inspection mind map based on statistical modeling tool by statistical parameter drawing system, functional neurosurgery Image analysis system etc. to find which brain area controls a certain cognitive function.These by count based on cognitive modeling method be based on a basic assumption it is for statistical analysis to sample data, this hypothesiss is thought: give certain cognitive stimulation, human brain recognize in the cognitive state of the stimulation must occur.And in fact, the cognitive activation feature observed has event correlation, and cognitive state has the characteristics that additivity and data sample are lesser, do not have stringent statistical significance, also it is unsatisfactory for the premise of statistics cognitive modeling method, thus is easy to cause the cognition result of mistake.

Summary of the invention

To solve the above problems existing in the prior art, the present invention to design it is a kind of suitable for small sample, with the human brain language cognition modeling method of dynamic time feature.

To achieve the goals above, technical scheme is as follows: a kind of human brain language cognition modeling method, comprising the following steps:

A, cognitive state example initializes

With the cognitive state in h mark human brain, since h can not be directly observed with instrument and equipment, but Germicidal efficacy value is corresponding on probability, h is thus known as recessive cognitive state, recessive cognitive state h is expressed as four-tuple<W, d, Θ, Ω>, in which: d indicates the lasting scalar of h in time；W is the reflection square that Spatial dimensionality is d × V, and wherein V is the brain area dimension that h is related to；Θ is the parameter space of h, and Ω is the codomain of parameter space.It recognizes in observation process, according to input stimulus Δ, the activation of brain cognitive state can have certain time lag.To the cognitive state for being in activated state, it is cognitive state example, is marked with ξ, consider the time factor of recessive cognitive state h, cognitive state example is a triple<h, λ, o>, wherein: h is corresponding recessive cognitive state, λ is the input time point of experiment stimulation, and o is the time migration of cognitive state, and the initial time of cognitive state example ξ is λ+o, its duration d is identical as corresponding recessive cognitive state h duration, is all indicated with d (h).

B, the probability distribution between mapping activation feature and observation data

It is assumed that the t period activates feature b by the brain that imaging device observes subject in cognition experimentation_tIt is coefficient as a result, using ξ by L cognitive state example₁,ξ₂,…,ξ_LThis L cognitive state example is indicated, then note b_t={ξ₁,ξ₂,…,ξ_L}；b_tWith the component s of period t, Spatial Dimension v in observation time sequence S_tvNormal Distribution, it may be assumed that

s_tv~N (μ_tv(b_t),σ_v)  (1)

Wherein σ_vIt is standard variance, it reflects noise profile relevant to observation time sequence, has time independence；μ_tv(b_t) the corresponding period all related cognitive states of reflection Overlay, that is, meet following formula:

${\mathrm{\&mu;}}_{\mathrm{tv}}\left(b_t\right)=\underset{\mathrm{\&xi;}\&Element;a_t}{\mathrm{\&Sigma;}}\stackrel{d\left(h\left(\mathrm{\&xi;}\right)\right)}{\mathrm{\&Sigma;}}\mathrm{\&delta;}(\mathrm{\&lambda;}\left(\mathrm{\&xi;}\right)+o\left(\mathrm{\&xi;}\right)=t-\mathrm{\&tau;})w_{\mathrm{\&tau;v}}\left(h\left(\mathrm{\&xi;}\right)\right)---\left(2\right)$

Wherein δ () is indicator function, if independent variable is that very, otherwise it is 0 which, which is 1,；H (ξ) identifies the corresponding recessive cognitive state of cognitive state example ξ；w_τv(h (ξ)) is then the v component of recessive cognitive state reflection square W (h (ξ)) on the τ time step for identify period t.

C, brain low-profile cognitive model is defined

Definition brain low-profile cognitive model be a five-tuple<H, Φ, I, S, Ξ, Γ>, marked with HCM, in which: H is recessive cognitive state set；Φ is the parameter vector of low-profile cognitive model, they rely on experimental design parameters, it may be assumed that the time point of the type of stimulation, input stimulus；S is observation time sequence；The stimulus sequence that Ξ is made of input stimulus Δ；I is the time series of cognitive state example, since the activationary time point of cognitive state example is corresponding with observation time sequence, thus by the element b in I_tIt is abbreviated as b；Γ is < σ₁,σ₂,…,σ_v> variance collection, wherein σ_vIt is the standard variance in formula (1), the noise profile of reflecting time sequence；HCM defines I and S, Ξ constitute triple time serieses of probability correlation,

For stochastic variable defined in I, then the brain observed activates the probability distribution between feature and recessive cognitive state are as follows:

$P\left(S\right|\mathrm{HCM},\mathrm{\&Delta;})=\underset{c\&Element;C}{\mathrm{\&Sigma;}}P\left(S\right|\mathrm{HCM},\hat{I}=b)P(\hat{I}=b|\mathrm{HCM},\mathrm{\&Delta;})---\left(3\right)$

Wherein,

$P(\hat{I}=b|\mathrm{HCM},\mathrm{\&Delta;})=\frac{\underset{\mathrm{\&xi;}\&Element;b}{\mathrm{\&Pi;}}P\left(h\left(\mathrm{\&xi;}\right)\right|\mathrm{HCM},\mathrm{\&Delta;})P\left(o\left(\mathrm{\&pi;}\right)\right|h\left(\mathrm{\&xi;}\right),\mathrm{HCM},\mathrm{\&Delta;})}{\underset{b^{\&prime;}\&Element;I}{\mathrm{\&Sigma;}}\underset{{\mathrm{\&xi;}}^{\&prime;}\&Element;b^{\&prime;}}{\mathrm{\&Pi;}}P\left(h\left({\mathrm{\&xi;}}^{\&prime;}\right)\right|\mathrm{HCM},\mathrm{\&Delta;})P\left(o\left({\mathrm{\&xi;}}^{\&prime;}\right)\right|h\left({\mathrm{\&xi;}}^{\&prime;}\right),\mathrm{HCM},\mathrm{\&Delta;})}---\left(4\right)$

In formula, P (h (ξ) | HCM, Δ) it is the conditional probability that the stimulation of Chinese Cognition experimentation conditional is Δ activation recessiveness cognitive state h and corresponding cognitive state example ξ, P (o (ξ) | h (ξ), HCM, Δ) it is corresponding time lag conditional probability；The modeling process of low-profile cognitive model needs to determine its conditional probability for specific cognitive process, while the parameter vector of low-profile cognitive model is also predefined, and carries out maximal possibility estimation to HCM parameters；For HCM, had according to Bayes' theorem:

$P(\hat{I}=b|S,\mathrm{HCM},\mathrm{\&Delta;})=\frac{P\left(S\right|\hat{I}=b,\mathrm{HCM})P(\hat{I}=b|\mathrm{HCM},\mathrm{\&Delta;})}{\underset{b^{\&prime;}\&Element;I}{\mathrm{\&Sigma;}}P\left(S\right|\hat{I}=b^{\&prime;},\mathrm{HCM})P(\hat{I}=b^{\&prime;}|\mathrm{HCM},\mathrm{\&Delta;})}---\left(5\right)$

D, low-profile cognitive model Parameter analysis of electrochemical

Low-profile cognitive model determines the low-profile cognitive state probability to match with observation time sequence and its parameter by learning training, that is, minimizes objective function:

$f\left(\mathrm{\&Phi;}\right)=\underset{v=1}{\overset{V}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}\underset{b\&Element;I}{\mathrm{\&Sigma;}}\frac{P(\hat{I}=b|S,\mathrm{\&Phi;})}{{2\mathrm{\&sigma;}}_v^2}{(s_{\mathrm{tv}}-{\mathrm{\&mu;}}_{\mathrm{tv}}\left(b\right))}^2---\left(6\right)$

In formula, Φ indicates the mapping probabilities parameter between cognitive stimulation task time sequence in low-profile cognitive model, observational characteristic time series, the triple time serieses of recessive cognitive state time series, and T is the total time of low-profile cognitive model.

D1, initialization search group:

Population is formed by using n Search of Individual and carries out parallel search in the space determined by Φ, enables the maximum speed v of Search of Individual_max=r；When time step t=0, to the carry out random initializtion of n Search of Individual, i.e., the position p of the jth dimension of i-th Search of Individual_ijThe speed v of the jth of=Rand (- r, r) and i-th of Search of Individual dimension_ij=Rand(-v_max,v_max)；R is domain, and t is time step；

If D2, meeting predetermined maximum number of iterations or 10 iteration results without improvement, exports result p* and f (p*) and terminate to calculate；Otherwise, D3 is gone to step；

In formula, p* is individual state best in group composed by Search of Individual, and f (p*) is adaptive value determined by individual state best in group composed by Search of Individual.

D3, the adaptive value for calculating Search of Individual

The adaptive value of Search of Individual is calculated according to formula (6)；

D4, optimal save strategy

T=t+1 is enabled, optimum maintaining strategy is implemented, it may be assumed that

$p_i^{\#}\left(t\right)=\arg \underset{1\&le;i\&le;n}{\min }(f\left(p_i^{\#}(t-1)\right),f\left(p_i\left(t\right)\right))$

$p^{*}\left(t\right)=\arg \underset{1\&le;i\&le;n}{\min }(f\left(p^{*}(t-1)\right),f\left(p_1\left(t\right)\right),\&CenterDot;\&CenterDot;\&CenterDot;,f\left(p_n\left(t\right)\right))$

In formula, p* is individual state best in group composed by Search of Individual, p_i ^#It is that i-th of Search of Individual iterates to current best state since t=0, f (p*) is adaptive value determined by individual state best in group composed by Search of Individual.

D5, state shift joint operation

It introduces community superiority composed by Search of Individual dynamically to search for, executes state transfer joint operation according to formula (7) and (8) for every dimension of each Search of Individual:

$v_{\mathrm{ij}}\left(t\right)=w{v}_{\mathrm{ij}}(t-1)+c_1{r}_1(p_{\mathrm{ij}}^{\#}(t-1)-p_{\mathrm{ij}}(t-1))+c_2{r}_2(p_j^{*}(t-1)-p_{\mathrm{ij}}(t-1))---\left(7\right)$

x_ij(t)=v_ij(t)+x_ij(t-1)  (8)

Go to step D2.

Compared with prior art, the invention has the following advantages:

1, the present invention is during cognitive modeling, by input stimulus, observed result, low-profile cognitive state is defined as the relevant triple time serieses of dynamic event, that is: cognitive stimulation task time sequence, observational characteristic time series, recessive cognitive state time series, and this triple time series is associated by one group of probability distribution, it is not that brain data collected are considered as static information to count, thus cognitive modeling method of the invention is without meeting the basic assumption based on statistics, it is still set up under the conditions of Small Sample Database, it ensure that the correctness of cognitive analysis result, thus solves the problems, such as the cognitive modeling under Small Sample Database.

2, the time series brain activation data being observed in cognition experiment are corresponded to the reflection square set of Chinese Cognition stateful example by the present invention, wherein each stateful example works in some time interval according to probability, and the activation feature observed when data acquisition is affected in period each stateful example of its effect.If multiple stateful examples almost work simultaneously, the activation so observed is characterized in the effect superposition that all correlated condition examples generate, it provides the foundation for cognitive state subdivision, and then improves the precision of cognitive modeling, also provide effective way for complicated cognitive analysis.

3, brain low-profile cognitive model proposed by the invention introduces model cognitive state totality T, model cognitive state observation period t and its time step τ, test the input time point λ of stimulation, the time migration o time quantum of cognitive state, to make the model that there is cognitive state time effect, it is to recognize and test stimulation series as a kind of relevant time series dynamic observation method of event of foundation, the cognitive activation characteristic sequence that will be observed that during cognition detection is mapped to one or more low-profiles and recognizes the influence activated in the same period to brain, and observation sequence and recessive cognitive state sequence are not to correspond, but it is related to stimulation and different recessive cognitive states is activated according to certain probability, it provides the foundation for cognition dynamic analysis.

Detailed description of the invention

The present invention shares attached drawing 2 and opens, in which:

Fig. 1 is flow chart of the invention.

Fig. 2 is triple time series map example figures of the invention.

Specific embodiment

The present invention is further described through with reference to the accompanying drawing.As shown in Figs. 1-2, model method of the invention includes triple time serieses, that is: upper layer stimulation time sequence Ξ, middle layer low-profile cognition time sequence I, observation time sequence S, there are low-profile cognitions to be superimposed in observation sequence, there are multiple arrows to be directed toward identical map section when i.e. middle layer low-profile cognition sequence I is mapped to observation sequence S, but there are basic mapping relations for this triple time serieses, and this relationship is determined by probability parameter Φ, parses probability mapping relations determined by its probability parameter according to formula (6) by step D1~D5.Provide a simple examples: input stimulus time series Ξ is { Δ₁,Δ₂, Δ₃};Observation time sequence S is { s₁,s₂,s₃};It is { b that low-profile, which recognizes example time sequence I,₁,b₂,b₃, wherein b₁={ξ₁ ⁽¹⁾,ξ₂ ⁽¹⁾,ξ_L3 ⁽¹⁾},b₂={ξ₁ ⁽²⁾,ξ₂ ⁽²⁾,ξ₃ ⁽²⁾,ξ₄ ⁽²⁾},b₃={ξ₁ ⁽³⁾,ξ₂ ⁽³⁾,ξ₃ ⁽³⁾, the parenthesized digital subscript of ξ identifies it and belongs to corresponding cognition example;The corresponding low-profile cognitive state set H of I is { h₁,h₂,h₃,h₄}.Probability parameter Φ, main result are determined according to formula (6) by step D1~D5 are as follows: ξ₁ ⁽¹⁾→s₁(0.82),ξ₂ ⁽¹⁾→s₁(0.91),ξ₃ ⁽¹⁾→s₂(0.86);

ξ₁ ⁽²⁾→s₂(0.90),ξ₂ ⁽²⁾→s₂(0.76),ξ₃ ⁽²⁾→s₃(0.84),ξ₄ ⁽²⁾→s₃(0.69);

ξ₁ ⁽³⁾→s₃(0.78),ξ₂ ⁽³⁾→s₃(0.85),ξ₃ ⁽³⁾→s₃(0.80);

ξ₁ ⁽¹⁾→h₁(0.90),ξ₂ ⁽¹⁾→h₂(0.74),ξ₃ ⁽¹⁾→h₃(0.92);

ξ₁ ⁽²⁾→h₁(0.97),ξ₂ ⁽²⁾→h₂(0.88),ξ₃ ⁽²⁾→h₃(0.79),ξ₄ ⁽²⁾→h₄(0.85);

ξ₁ ⁽³⁾→h₁(0.93),ξ₂ ⁽³⁾→h₃(0.87),ξ₃ ⁽³⁾→h₄(0.91)。

In formula: " → " indicates the corresponding mapping probabilities of digital representation there are mapping relations, in bracket.

Claims (1)

1. a kind of human brain language cognition modeling method, it is characterised in that: the following steps are included:

A, cognitive state example initializes

With the cognitive state in h mark human brain, since h can not be directly observed with instrument and equipment, but Germicidal efficacy value is corresponding on probability, h is thus known as recessive cognitive state, recessive cognitive state h is expressed as four-tuple<W, d, Θ, Ω>, in which: d indicates the lasting scalar of h in time；W is the reflection square that Spatial dimensionality is d × V, and wherein V is the brain area dimension that h is related to；Θ is the parameter space of h, and Ω is the codomain of parameter space.It recognizes in observation process, according to input stimulus Δ, the activation of brain cognitive state can have certain time lag.To the cognitive state for being in activated state, it is cognitive state example, is marked with ξ, consider the time factor of recessive cognitive state h, cognitive state example is a triple<h, λ, o>, wherein: h is corresponding recessive cognitive state, λ is the input time point of experiment stimulation, and o is the time migration of cognitive state, and the initial time of cognitive state example ξ is λ+o, its duration d is identical as corresponding recessive cognitive state h duration, is all indicated with d (h)；

B, the probability distribution between mapping activation feature and observation data

It is assumed that the t period activates feature b by the brain that imaging device observes subject in cognition experimentation_tIt is coefficient as a result, using ξ by L cognitive state example₁,ξ₂,…,ξ_LThis L cognitive state example is indicated, then note b_t={ξ₁,ξ₂,…,ξ_L}；b_tWith the component s of period t, Spatial Dimension v in observation time sequence S_tvNormal Distribution, it may be assumed that

s_tv~N (μ_tv(b_t),σ_v)  (1)

Wherein σ_vIt is standard variance, it reflects noise profile relevant to observation time sequence, has time independence；μ_tv(b_t) the corresponding period all related cognitive states of reflection Overlay, that is, meet following formula:

${\mathrm{\&mu;}}_{\mathrm{tv}}\left(b_t\right)=\underset{\mathrm{\&xi;}\&Element;a_t}{\mathrm{\&Sigma;}}\stackrel{d\left(h\left(\mathrm{\&xi;}\right)\right)}{\mathrm{\&Sigma;}}\mathrm{\&delta;}(\mathrm{\&lambda;}\left(\mathrm{\&xi;}\right)+o\left(\mathrm{\&xi;}\right)=t-\mathrm{\&tau;})w_{\mathrm{\&tau;v}}\left(h\left(\mathrm{\&xi;}\right)\right)---\left(2\right)$

Wherein δ () is indicator function, if independent variable is that very, otherwise it is 0 which, which is 1,；H (ξ) identifies the corresponding recessive cognitive state of cognitive state example ξ；w_τv(h (ξ)) is then the v component of recessive cognitive state reflection square W (h (ξ)) on the τ time step for identify period t；

C, brain low-profile cognitive model is defined

Definition brain low-profile cognitive model be a five-tuple<H, Φ, I, S, Ξ, Γ>, marked with HCM, in which: H is recessive cognitive state set；Φ is the parameter vector of low-profile cognitive model, they rely on experimental design parameters, it may be assumed that the time point of the type of stimulation, input stimulus；S is observation time sequence；The stimulus sequence that Ξ is made of input stimulus Δ；I is the time series of cognitive state example, since the activationary time point of cognitive state example is corresponding with observation time sequence, thus by the element b in I_tIt is abbreviated as b；Γ is < σ₁,σ₂,…,σ_v> variance collection, wherein σ_vIt is the standard variance in formula (1), the noise profile of reflecting time sequence；HCM defines I and S, Ξ constitute triple time serieses of probability correlation,

For stochastic variable defined in I, then the brain observed activates the probability distribution between feature and recessive cognitive state are as follows:

$P\left(S\right|\mathrm{HCM},\mathrm{\&Delta;})=\underset{c\&Element;C}{\mathrm{\&Sigma;}}P\left(S\right|\mathrm{HCM},\hat{I}=b)P(\hat{I}=b|\mathrm{HCM},\mathrm{\&Delta;})---\left(3\right)$

Wherein,

$P(\hat{I}=b|\mathrm{HCM},\mathrm{\&Delta;})=\frac{\underset{\mathrm{\&xi;}\&Element;b}{\mathrm{\&Pi;}}P\left(h\left(\mathrm{\&xi;}\right)\right|\mathrm{HCM},\mathrm{\&Delta;})P\left(o\left(\mathrm{\&pi;}\right)\right|h\left(\mathrm{\&xi;}\right),\mathrm{HCM},\mathrm{\&Delta;})}{\underset{b^{\&prime;}\&Element;I}{\mathrm{\&Sigma;}}\underset{{\mathrm{\&xi;}}^{\&prime;}\&Element;b^{\&prime;}}{\mathrm{\&Pi;}}P\left(h\left({\mathrm{\&xi;}}^{\&prime;}\right)\right|\mathrm{HCM},\mathrm{\&Delta;})P\left(o\left({\mathrm{\&xi;}}^{\&prime;}\right)\right|h\left({\mathrm{\&xi;}}^{\&prime;}\right),\mathrm{HCM},\mathrm{\&Delta;})}---\left(4\right)$

In formula, P (h (ξ) | HCM, Δ) it is the conditional probability that the stimulation of Chinese Cognition experimentation conditional is Δ activation recessiveness cognitive state h and corresponding cognitive state example ξ, P (o (ξ) | h (ξ), HCM, Δ) it is corresponding time lag conditional probability；The modeling process of low-profile cognitive model needs to determine its conditional probability for specific cognitive process, while the parameter vector of low-profile cognitive model is also predefined, and carries out maximal possibility estimation to HCM parameters；For HCM, had according to Bayes' theorem:

$P(\hat{I}=b|S,\mathrm{HCM},\mathrm{\&Delta;})=\frac{P\left(S\right|\hat{I}=b,\mathrm{HCM})P(\hat{I}=b|\mathrm{HCM},\mathrm{\&Delta;})}{\underset{b^{\&prime;}\&Element;I}{\mathrm{\&Sigma;}}P\left(S\right|\hat{I}=b^{\&prime;},\mathrm{HCM})P(\hat{I}=b^{\&prime;}|\mathrm{HCM},\mathrm{\&Delta;})}---\left(5\right)$

D, low-profile cognitive model Parameter analysis of electrochemical

Low-profile cognitive model determines the low-profile cognitive state probability to match with observation time sequence and its parameter by learning training, that is, minimizes objective function:

$f\left(\mathrm{\&Phi;}\right)=\underset{v=1}{\overset{V}{\mathrm{\&Sigma;}}}\underset{t=1}{\overset{T}{\mathrm{\&Sigma;}}}\underset{b\&Element;I}{\mathrm{\&Sigma;}}\frac{P(\hat{I}=b|S,\mathrm{\&Phi;})}{{2\mathrm{\&sigma;}}_v^2}{(s_{\mathrm{tv}}-{\mathrm{\&mu;}}_{\mathrm{tv}}\left(b\right))}^2---\left(6\right)$

In formula, Φ indicates the mapping probabilities parameter between cognitive stimulation task time sequence in low-profile cognitive model, observational characteristic time series, the triple time serieses of recessive cognitive state time series, and T is the total time of low-profile cognitive model；

D1, initialization search group:

Population is formed by using n Search of Individual and carries out parallel search in the space determined by Φ, enables the maximum speed v of Search of Individual_max=r；When time step t=0, to the carry out random initializtion of n Search of Individual, i.e., the position p of the jth dimension of i-th Search of Individual_ijThe speed v of the jth of=Rand (- r, r) and i-th of Search of Individual dimension_ij=Rand(-v_max,v_max)；R is domain, and t is time step；

If D2, meeting predetermined maximum number of iterations or 10 iteration results without improvement, exports result p* and f (p*) and terminate to calculate；Otherwise, D3 is gone to step；

In formula, p* is individual state best in group composed by Search of Individual, and f (p*) is adaptive value determined by individual state best in group composed by Search of Individual；

D3, the adaptive value for calculating Search of Individual

The adaptive value of Search of Individual is calculated according to formula (6)；

D4, optimal save strategy

T=t+1 is enabled, optimum maintaining strategy is implemented, it may be assumed that

$p_i^{\#}\left(t\right)=\arg \underset{1\&le;i\&le;n}{\min }(f\left(p_i^{\#}(t-1)\right),f\left(p_i\left(t\right)\right))$

$p^{*}\left(t\right)=\arg \underset{1\&le;i\&le;n}{\min }(f\left(p^{*}(t-1)\right),f\left(p_1\left(t\right)\right),\&CenterDot;\&CenterDot;\&CenterDot;,f\left(p_n\left(t\right)\right))$

In formula, p* is individual state best in group composed by Search of Individual, p_i ^#It is that i-th of Search of Individual iterates to current best state since t=0, f (p*) is adaptive value determined by individual state best in group composed by Search of Individual；

D5, state shift joint operation

It introduces community superiority composed by Search of Individual dynamically to search for, executes state transfer joint operation according to formula (7) and (8) for every dimension of each Search of Individual:

$v_{\mathrm{ij}}\left(t\right)=w{v}_{\mathrm{ij}}(t-1)+c_1{r}_1(p_{\mathrm{ij}}^{\#}(t-1)-p_{\mathrm{ij}}(t-1))+c_2{r}_2(p_j^{*}(t-1)-p_{\mathrm{ij}}(t-1))---\left(7\right)$

x_ij(t)=v_ij(t)+x_ij(t-1)  (8)

Go to step D2.

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