ANALYSIS METHOD FOR CAUSAL INFERENCE OF PHYSIOLOGICAL NETWORK IN MULTISCALE TIME SERIES SIGNALS

Abstract

An analysis method for the causal inference of human physiological network in multiscale time series signals includes the following steps: S1: decomposing physiological signals u.sub.1, u.sub.2, . . . , u.sub.m to be analyzed by using a noise-assisted multivariate empirical mode decomposition (NA-MEND) algorithm; S2: carrying out a causal analysis between two different physiological signals u.sub.i, u.sub.j, where i=1, 2, . . . , m, j=1, 2, . . . , m, and i≠j, to obtain a causality between the two signals; and S3: repeating step S2 for any two signals in u.sub.1, u.sub.2, . . . , u.sub.m until a causality between each two signals in u.sub.1, u.sub.2, . . . , u.sub.m is obtained to form the causal network. The present invention can effectively analyze the causal network of the physiological signals, thereby facilitating the application of the physiological signals.

Claims

1. An analysis method for a causal inference of a physiological network in multiscale time series signals, comprising the following steps: S1: inputting physiological signals to be analyzed:
u.sub.1={u.sub.1,1,u.sub.1,2, . . . ,u.sub.1,t}
u.sub.2={u.sub.2,1,u.sub.2,2, . . . ,u.sub.2,t}
. . .
u.sub.m={u.sub.m,1,u.sub.m,2, . . . ,u.sub.m,t}; decomposing the physiological signals u.sub.1, u.sub.2, . . . , u.sub.m to be analyzed by using a noise-assisted multivariate empirical mode decomposition (NA-MEMD) algorithm:
u.sub.1.Math.{IMF.sub.1,1,IMF.sub.1,2, . . . ,IMF.sub.1,n}
u.sub.2.Math.{IMF.sub.2,1,IMF.sub.2,2, . . . ,IMF.sub.2,n}
. . .
u.sub.m.Math.{IMF.sub.m,1,IMF.sub.m,2, . . . ,IMF.sub.m,n}
g.sub.1.Math.{IMF.sub.g.sub.1.sub.,1,IMF.sub.g.sub.1.sub.,2, . . . ,IMF.sub.g.sub.1.sub.,n}
g.sub.2.Math.{IMF.sub.g.sub.2.sub.,1,IMF.sub.g.sub.2.sub.,2, . . . ,IMF.sub.g.sub.2.sub.,n}
. . .
g.sub.{tilde over (m)}.Math.{IMF.sub.g.sub.{tilde over (m)}.sub.,1,IMF.sub.g.sub.{tilde over (m)}.sub.,2, . . . ,IMF.sub.g.sub.{tilde over (m)}.sub.,n}; wherein, “.Math.” represents a decomposition of a signal by the NA-MEMD algorithm; m represents a number of the physiological signals, m≥2, t∈N.sup.+, wherein N.sup.+ represents a positive integer; g.sub.1, g.sub.2, . . . , g.sub.{tilde over (m)} represent assistant noises selected by the NA-MEMD algorithm, and g.sub.1, g.sub.2, . . . , g.sub.{tilde over (m)} are uncorrelated random Gaussian noises; {tilde over (m)} represents a number of the assistant noises selected; n represents a number of intrinsic mode functions (IMFs) obtained after a decomposition of each of the physiological signals; S2: carrying out a causal analysis between a physiological signal u.sub.i and a physiological signal u.sub.j, where i=1, 2, . . . , m, j=1, 2, . . . , m, and i≠j: S201: pairing IMFs {IMF.sub.i,1, IMF.sub.i,2, . . . , IMF.sub.i,n} obtained by decomposing the physiological signal u.sub.i with the IMFs {IMF.sub.j,1, IMF.sub.j,2, . . . , IMF.sub.j,n} obtained by decomposing the physiological signal u.sub.j to obtain n IMF pairs: (IMF.sub.i,1,IMF.sub.j,1), (IMF.sub.i,2,IMF.sub.j,2), . . . , (IMF.sub.i,n,IMF.sub.j,n); where, the two IMFs in each IMF pair of the n IMF pairs have the same length of time; S202: calculating a mean instantaneous phase difference of the each IMF pair, comparing the mean instantaneous phase difference with a preset threshold to select IMF pairs each with a mean instantaneous phase difference less than the preset threshold, to generate intrinsic causal component (ICC) sets: {(IMF.sub.i,k.sub.1,IMF.sub.j,k.sub.1), (IMF.sub.i,k.sub.2,IMF.sub.j,k.sub.2), . . . , (IMF.sub.i,.sub.n,IMF.sub.j,.sub.n)}; where, k.sub.1 in IMF.sub.i,k.sub.1 represents that IMF.sub.i,k.sub.1 is a k.sub.1-th IMF in {IMF.sub.i,1, IMF.sub.i,2, . . . , IMF.sub.i,n}, and k.sub.1 in IMF.sub.j,k.sub.1 represents that IMF.sub.j,k.sub.1 is a k.sub.1-th IMF in {IMF.sub.j,1, IMF.sub.j,2, . . . , IMF.sub.j,n}; k.sub.2 in IMF.sub.i,k.sub.2 represents that IMF.sub.i,k.sub.2 is a k.sub.2-th IMF in {IMF.sub.i,1, IMF.sub.i,2, . . . , IMF.sub.i,n}, and k.sub.2 in IMF.sub.j,k.sub.2 represents that IMF.sub.j,k.sub.2 is a k.sub.2-th IMF in {IMF.sub.j,1, IMF.sub.j,2, . . . , IMF.sub.j,n}; similarly, k.sub.ñ in IMF.sub.i,k.sub.ñ represents that IMF.sub.i,k.sub.ñ is a k.sub.ñ-th IMF in {IMF.sub.i,1, IMF.sub.i,2, . . . , IMF.sub.i,n}, and k.sub.ñ in IMF.sub.j,k.sub.ñ represents that IMF.sub.j,k.sub.ñ is a k.sub.ñ-th IMF in {IMF.sub.j,1, IMF.sub.j,2, . . . , IMF.sub.j,n}; ñ represents the number of the IMF pairs in the ICC sets; S203: calculating a phase coherence of each of the IMF pairs in the ICC sets respectively: $\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}.fwdarw.{\mathrm{IMF}}_{j,k}\right)=\frac{1}{T}.Math.{\int }_0^T{e}^{i\left[{\varphi }_{i,k}\left(t\right)-{\varphi }_{j,k}\left(t\right)\right]}\mathrm{dt}.Math.;$ where, k=k.sub.1, k.sub.2, . . . , k.sub.ñ; T represents the length of time of IMF.sub.i,k and IMF.sub.j,k; ϕ.sub.i,k(t) represents an instantaneous phase of IMF.sub.i,k at a time t, and ϕ.sub.j,k(t) represents an instantaneous phase of IMF.sub.j,k at the time t; S204: signal re-decomposition: selecting an IMF pair with a highest frequency from the IMF pairs corresponding to serial numbers in the ICC sets, where since the frequencies of the IMFs decomposed by the NA-MEND algorithm are arranged in descending order, the IMF pair with the highest frequency is (IMF.sub.i,k.sub.1,IMF.sub.j,k.sub.1); subtracting IMF.sub.j,k.sub.1 from the physiological signal u.sub.j to obtain u.sub.j′, replacing u.sub.j in an input signal set u.sub.1, u.sub.2, . . . , u.sub.m with u.sub.j′ to obtain a first replaced input signal set, and carrying out a first NA-MEMD decomposition on the first replaced input signal set; obtaining decomposed IMFs {IMF.sub.j,1′, IMF.sub.j,2′, . . . , IMF.sub.j,n′} corresponding to u.sub.j′ after the first NA-MEMD decomposition; subtracting IMF.sub.i,k.sub.1 from the physiological signal u.sub.i to obtain u.sub.i′, replacing u.sub.i in an input signal set u.sub.1, u.sub.2, . . . , u.sub.m with u.sub.i′ to obtain a second replaced input signal set, and carrying out a second NA-MEMD decomposition on the second replaced input signal set; obtaining decomposed IMFs {IMF.sub.i,1′, IMF.sub.i,2′, . . . , IMF.sub.i,n′} corresponding to u.sub.i′ after the second NA-MEMD decomposition; S205: calculating a causality D(IMF.sub.i,k.sub.1.fwdarw.IMF.sub.j,k.sub.1) of u.sub.i to u.sub.j and a causality D(IMF.sub.j,k.sub.1.fwdarw.IMF.sub.i,k.sub.1) of u.sub.j to u.sub.i: $\{\begin{array}{c}D\left({\mathrm{IMF}}_{i,k_1}.fwdarw.{\mathrm{IMF}}_{j,k_1}\right)={\left\{\underset{k=k_1}{\overset{k_{\tilde{n}}}{.Math.}}{W_k\left[\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}.fwdarw.{\mathrm{IMF}}_{j,k}\right)-\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}.fwdarw.{\mathrm{IMF}}_{j,k}^{\prime }\right)\right]}^2\right\}}^{\frac{1}{2}}\\ D\left({\mathrm{IMF}}_{j,k_1}.fwdarw.{\mathrm{IMF}}_{i,k_1}\right)={\left\{\underset{k=k_1}{\overset{k_{\tilde{n}}}{.Math.}}{W_k\left[\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}.fwdarw.{\mathrm{IMF}}_{j,k}\right)-\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}^{\prime }.fwdarw.{\mathrm{IMF}}_{j,k}\right)\right]}^2\right\}}^{\frac{1}{2}}\\ W_k=\left({\sigma }_{i,k}^2\times {\sigma }_{j,k}^2\right)/\underset{k=k_1}{\overset{k_{\tilde{n}}}{.Math.}}\left({\sigma }_{i,k}^2\times {\sigma }_{j,k}^2\right)\end{array};$ wherein, σ.sub.i,k.sup.2 is a variance of a k-th IMF obtained by decomposing u.sub.i, and σ.sub.j,k.sup.2 is a variance of a k-th IMF obtained by decomposing u.sub.j; w.sub.k is an intermediate variable; obtaining an absolute causal strength (ACS):
ACS={D(IMF.sub.i,k.sub.1.fwdarw.IMF.sub.j,k.sub.1),D(IMF.sub.j,k.sub.1.fwdarw.IMF.sub.i,k.sub.1)}; S206: based on the ACS, calculating a ratio: $\frac{D\left({\mathrm{IMF}}_{i,k_1}.fwdarw.{\mathrm{IMF}}_{j,k_1}\right)}{D\left({\mathrm{IMF}}_{j,k_1}.fwdarw.{\mathrm{IMF}}_{i,k_1}\right)};$ wherein, if the ratio is greater than 1, then u.sub.i is a cause and u.sub.j is an effect; if the ratio is less than 1, then u.sub.i is the effect and u.sub.j is the cause; if the ratio is equal to 1, then u.sub.i and u.sub.j are reciprocal causation or are not causation; in this way, causal analysis results of u.sub.i and u.sub.j are obtained; and S3: repeating step S2 for any two signals in u.sub.1, u.sub.2, . . . , u.sub.m until a causality between each two signals in u.sub.1, u.sub.2, . . . , u.sub.m is obtained to form the causal network.

2. The analysis method for the causal inference of the physiological network in the multiscale time series signals according to claim 1, wherein step S202 comprises the following steps: S2021: setting mean instantaneous phase difference thresholds δ.sub.1, δ.sub.2, . . . , δ.sub.n for the n IMF pairs; S2022: calculating a mean instantaneous phase difference of an h-th IMF pair (IMF.sub.i,h,IMF.sub.j,h); letting mean(ϕ.sub.i,h) be a mean instantaneous phase of IMF.sub.i,h in the length of time, and letting mean(ϕ.sub.j,h) be a mean instantaneous phase of IMF.sub.j,h in the length of time; then obtaining the mean instantaneous phase difference of the h-th IMF pair (IMF.sub.i,h,IMF.sub.j,h) as:
|mean(ϕ.sub.i,h)−mean(ϕ.sub.j,h)|; comparing |mean(ϕ.sub.i,h)−mean(ϕ.sub.j,h)| with a corresponding threshold δ.sub.h, and determining whether the following condition is satisfied:
|mean(ϕ.sub.i,h)−mean(ϕ.sub.j,h)|<δ.sub.h; if the condition is satisfied, then adding the h-th IMF pair (IMF.sub.i,h,IMF.sub.j,h) into the ICC sets; if the condition is not satisfied, then discarding (IMF.sub.i,h,IMF.sub.j,h); and S2023: repeating step S2022 when h=1, 2, . . . n respectively to finally obtain the ICC sets as: {(IMF.sub.i,k.sub.1,IMF.sub.j,k.sub.1), (IMF.sub.i,k.sub.2,IMF.sub.j,k.sub.2), . . . , (IMF.sub.i,.sub.n,IMF.sub.j,.sub.n)}.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0051] FIGURE is a flowchart of the method according to the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] The technical solutions of the present invention are described in further detail below with reference to the drawings, but the scope of protection of the present invention is not limited thereto.

[0053] As shown in FIGURE, an analysis method for the causal inference of human physiological network in multiscale time series signals includes the following steps:

[0054] S1: physiological signals to be analyzed are input:

u.sub.1={u.sub.1,1,u.sub.1,2, . . . ,u.sub.1,t}

u.sub.2={u.sub.2,1,u.sub.2,2, . . . ,u.sub.2,t}

. . .

u.sub.m={u.sub.m,1,u.sub.m,2, . . . ,u.sub.m,t};

[0055] the physiological signals u.sub.1, u.sub.2, . . . , u.sub.m to be analyzed are decomposed by using a noise-assisted multivariate empirical mode decomposition (NA-MEMD) algorithm:

u.sub.1.Math.{IMF.sub.1,1,IMF.sub.1,2, . . . ,IMF.sub.1,n}

u.sub.2.Math.{IMF.sub.2,1,IMF.sub.2,2, . . . ,IMF.sub.2,n}

. . .

u.sub.m.Math.{IMF.sub.m,1,IMF.sub.m,2, . . . ,IMF.sub.m,n}

g.sub.1.Math.{IMF.sub.g.sub.1.sub.,1,IMF.sub.g.sub.1.sub.,2, . . . ,IMF.sub.g.sub.1.sub.,n}

g.sub.2.Math.{IMF.sub.g.sub.2.sub.,1,IMF.sub.g.sub.2.sub.,2, . . . ,IMF.sub.g.sub.2.sub.,n}

. . .

g.sub.{tilde over (m)}.Math.{IMF.sub.g.sub.{tilde over (m)}.sub.,1,IMF.sub.g.sub.{tilde over (m)}.sub.,2, . . . ,IMF.sub.g.sub.{tilde over (m)}.sub.,n};

[0056] where, “.Math.” represents the decomposition of the signal by the NA-MEMD algorithm; m represents the number of the physiological signals, m≥2, t∈N.sup.+, where N.sup.+ represents a positive integer; g.sub.1, g.sub.2, . . . , g.sub.{tilde over (m)} represent assistant noises selected by the NA-MEMD algorithm, and g.sub.1, g.sub.2, . . . , g.sub.{tilde over (m)} are uncorrelated random Gaussian noises; {tilde over (m)} represents the number of the assistant noises selected; n represents the number of intrinsic mode functions (IMFs) obtained after the decomposition of each of the physiological signals.

[0057] S2: a causal analysis is carried out between a physiological signal u.sub.i and a physiological signal u.sub.j, where i=1, 2, . . . , m, j=1, 2, . . . , m, and i≠j:

[0058] S201: the IMFs {IMF.sub.i,1, IMF.sub.i,2, . . . , IMF.sub.i,n} obtained by decomposing the physiological signal u.sub.i is paired with the IMFs {IMF.sub.j,1, IMF.sub.j,2, . . . , IMF.sub.j,n} obtained by decomposing the physiological signal u.sub.j to obtain n IMF pairs: [0059] (IMF.sub.i,1,IMF.sub.j,1), (IMF.sub.i,2,IMF.sub.j,2), . . . , (IMF.sub.i,n,IMF.sub.j,n);

[0060] where, the two IMFs in each IMF pair of the n IMF pairs have the same length of time.

[0061] S202: a mean instantaneous phase difference of the each IMF pair is calculated, the mean instantaneous phase difference is compared with a preset threshold to select IMF pairs each with a mean instantaneous phase difference less than the preset threshold, to generate intrinsic causal component (ICC) sets: [0062] {(IMF.sub.i,k.sub.1,IMF.sub.j,k.sub.1), (IMF.sub.i,k.sub.2,IMF.sub.j,k.sub.2), . . . , (IMF.sub.i,.sub.n,IMF.sub.j,.sub.n)};

[0063] where, k.sub.1 in IMF.sub.i,k.sub.1 represents that IMF.sub.i,k.sub.1 is a k.sub.1-th IMF in {IMF.sub.i,1, IMF.sub.i,2, . . . , IMF.sub.i,n}, and k.sub.1 in IMF.sub.j,k.sub.1 represents that IMF.sub.j,k.sub.1 is a k.sub.1-th IMF in {IMF.sub.j,1, IMF.sub.j,2, . . . , IMF.sub.j,n};

[0064] k.sub.2 in IMF.sub.i,k.sub.2 represents that IMF.sub.i,k.sub.2 is a k.sub.2-th IMF in {IMF.sub.i,1, IMF.sub.i,2, . . . , IMF.sub.i,n}, and k.sub.2 in IMF.sub.j,k.sub.2 represents that IMF.sub.j,k.sub.2 is a k.sub.2-th IMF in {IMF.sub.j,1, IMF.sub.j,2, . . . , IMF.sub.j,n};

[0065] similarly, k.sub.ñ in IMF.sub.i,k.sub.ñ represents that IMF.sub.i,k.sub.ñ is a k.sub.ñ-th IMF in {IMF.sub.i,1, IMF.sub.i,2, . . . , IMF.sub.i,n}, and k.sub.ñ in IMF.sub.j,k.sub.ñ represents that IMF.sub.j,k.sub.ñ is a k.sub.ñ-th IMF in {IMF.sub.j,1, IMF.sub.j,2, . . . , IMF.sub.j,n}; and

[0066] ñ represents the number of the IMF pairs in the ICC sets.

[0067] S203: a phase coherence of each of the IMF pairs in the ICC sets is calculated respectively:

[00004]$\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}.fwdarw.{\mathrm{IMF}}_{j,k}\right)=\frac{1}{T}.Math.{\int }_0^T{e}^{i\left[{\varphi }_{i,k}\left(t\right)-{\varphi }_{j,k}\left(t\right)\right]}\mathrm{dt}.Math.;$

[0068] where, k=k.sub.1, k.sub.2, . . . , k.sub.ñ; T represents the length of time of IMF.sub.i,k and IMF.sub.j,k; ϕ.sub.i,k(t) represents an instantaneous phase of IMF.sub.i,k at a time t, and ϕ.sub.j,k(t) represents an instantaneous phase of IMF.sub.j,k at the time t.

[0069] S204: signal re-decomposition:

[0070] an IMF pair with a highest frequency is selected from the IMF pairs corresponding to serial numbers in the ICC sets, where since the frequencies of the IMFs decomposed by the NA-MEND algorithm are arranged in descending order, the IMF pair with the highest frequency is (IMF.sub.i,k.sub.1,IMF.sub.j,k.sub.1);

[0071] IMF.sub.j,k.sub.1 is subtracted from the physiological signal u.sub.j to obtain u.sub.j′, u.sub.j in an input signal set u.sub.1, u.sub.2, . . . , u.sub.m is replaced with u.sub.j′ to obtain a first replaced input signal set, and a first NA-MEMD decomposition is carried out on the first replaced input signal set;

[0072] decomposed IMFs {IMF.sub.j,1′, IMF.sub.j,2′, . . . , IMF.sub.j,n′} corresponding to u.sub.j′ are obtained after the first NA-MEMD decomposition;

[0073] IMF.sub.i,k.sub.1 is subtracted from the physiological signal u.sub.i to obtain u.sub.i′, u.sub.i in an input signal set u.sub.1, u.sub.2, . . . , u.sub.m is replaced with u.sub.i′ to obtain a second replaced input signal set, and a second NA-MEMD decomposition is carried out on the second replaced input signal set;

[0074] decomposed IMFs {IMF.sub.i,1′, IMF.sub.i,2′, . . . , IMF.sub.i,n′} corresponding to u.sub.i′ are obtained after the second NA-MEMD decomposition;

[0075] S205: a causality D(IMF.sub.i,k.sub.1.fwdarw.IMF.sub.j,k.sub.1) of u.sub.i to u.sub.j and a causality D(IMF.sub.j,k.sub.1.fwdarw.IMF.sub.i,k.sub.1) of u.sub.j to u.sub.i are calculated:

[00005]$\{\begin{array}{c}D\left({\mathrm{IMF}}_{i,k_1}.fwdarw.{\mathrm{IMF}}_{j,k_1}\right)={\left\{\underset{k=k_1}{\overset{k_{\tilde{n}}}{.Math.}}{W_k\left[\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}.fwdarw.{\mathrm{IMF}}_{j,k}\right)-\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}.fwdarw.{\mathrm{IMF}}_{j,k}^{\prime }\right)\right]}^2\right\}}^{\frac{1}{2}}\\ D\left({\mathrm{IMF}}_{j,k_1}.fwdarw.{\mathrm{IMF}}_{i,k_1}\right)={\left\{\underset{k=k_1}{\overset{k_{\tilde{n}}}{.Math.}}{W_k\left[\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}.fwdarw.{\mathrm{IMF}}_{j,k}\right)-\mathrm{Coh}\left({\mathrm{IMF}}_{i,k}^{\prime }.fwdarw.{\mathrm{IMF}}_{j,k}\right)\right]}^2\right\}}^{\frac{1}{2}}\\ W_k=\left({\sigma }_{i,k}^2\times {\sigma }_{j,k}^2\right)/\underset{k=k_1}{\overset{k_{\tilde{n}}}{.Math.}}\left({\sigma }_{i,k}^2\times {\sigma }_{j,k}^2\right)\end{array};$

[0076] where, σ.sub.i,k.sup.2 is a variance of a k-th IMF obtained by decomposing u.sub.i, and σ.sub.j,k.sup.2 is a variance of a k-th IMF obtained by decomposing u.sub.j; w.sub.k is an intermediate variable; and

[0077] an absolute causal strength (ACS) is obtained:

ACS={D(IMF.sub.i,k.sub.1.fwdarw.IMF.sub.j,k.sub.1),D(IMF.sub.j,k.sub.1.fwdarw.IMF.sub.i,k.sub.1)}.

[0078] S206: based on the ACS, a ratio is calculated:

[00006]$\frac{D\left({\mathrm{IMF}}_{i,k_1}.fwdarw.{\mathrm{IMF}}_{j,k_1}\right)}{D\left({\mathrm{IMF}}_{j,k_1}.fwdarw.{\mathrm{IMF}}_{i,k_1}\right)};$

[0079] where, if the ratio is greater than 1, then u.sub.i is a cause and u.sub.j is an effect;

[0080] if the ratio is less than 1, then u.sub.i is the effect and u.sub.j is the cause;

[0081] if the ratio is equal to 1, then u.sub.i and u.sub.j are reciprocal causation or are not causation; and

[0082] in this way, causal analysis results of u.sub.i and u.sub.j are obtained.

[0083] S3: step S2 is repeated for any two signals in u.sub.1, u.sub.2, . . . , u.sub.m until a causality between each two signals in u.sub.1, u.sub.2, . . . , u.sub.m is obtained to form the causal network.

[0084] Step S202 includes:

[0085] S2021: mean instantaneous phase difference thresholds δ.sub.1, δ.sub.2, . . . , δ.sub.n for the n IMF pairs are set.

[0086] S2022: a mean instantaneous phase difference of an h-th IMF pair (IMF.sub.i,h,IMF.sub.j,h) is calculated as follows:

[0087] let mean(ϕ.sub.i,h) be a mean instantaneous phase of IMF.sub.i,h in the length of time, and let mean(ϕ.sub.j,h) be a mean instantaneous phase of IMF.sub.j,h in the length of time;

[0088] then the mean instantaneous phase difference of the h-th IMF pair (IMF.sub.i,h,IMF.sub.j,h) is obtained as:

|mean(ϕ.sub.i,h)−mean(ϕ.sub.j,h)|;

[0089] |mean(ϕ.sub.i,h)−mean(ϕ.sub.j,h)| is compared with the corresponding threshold δ.sub.h, and it is determined whether the following condition is satisfied:

|mean(ϕ.sub.i,h)−mean(ϕ.sub.j,h)|<δ.sub.h;

[0090] if the condition is satisfied, then the h-th IMF pair (IMF.sub.i,h,IMF.sub.j,h) is added into the ICC sets; and

[0091] if the condition is not satisfied, then (IMF.sub.i,h,IMF.sub.j,h) is discarded.

[0092] S2023: step S2022 is repeated when h=1, 2, . . . n respectively to finally obtain the ICC sets as: [0093] {(IMF.sub.i,k.sub.1,IMF.sub.j,k.sub.1), (IMF.sub.i,k.sub.2,IMF.sub.j,k.sub.2), . . . , (IMF.sub.i,.sub.n,IMF.sub.j,.sub.n)}.

[0094] In the embodiment of the present invention, the causality between two physiological signals A and B can be defined as follows: if the decomposed IMFs in both A and B are at a certain similar time scale and the IMF in B is removed from B itself, variable A causes variable B if the instantaneous phase dependency between the IMFs in A and B is eliminated, but not vice versa, namely variable A does not cause variable B if the instantaneous phase dependency between the IMFs in A and B is not eliminated.

[0095] The causality needs to satisfy the following conditions:

[0096] (1) any causality is based on the instantaneous phase coherence of the ICCs across multiple time series; and

[0097] (2) the phase behaviors in an effect are separable from the effect itself.

[0098] The specific implementations of the present invention are described above, but those skilled in the art should understand that they are only illustrative, and various changes or modifications may be made to these implementations without departing from the principle and implementation of the present invention. Therefore, the scope of protection of the present invention is defined by the appended claims.