Causal analysis method based on compensation dispersion transfer entropy

Abstract

The invention relates to the technical field of image processing, in particular to a compensation dispersion transfer entropy-based causal analysis method, and aims to accurately capture an instantaneous causal relationship and improve the accuracy of a constructed brain network. The method comprises the following steps: acquiring an original time sequence, and normalizing the original time sequence by adopting a normal cumulative distribution function to obtain a normalized time sequence; and performing dispersion processing on the normalized time sequence, and endowing each normalized data point with an integer in a preset integer range through a linear algorithm to obtain a dispersion time sequence. And performing information transmission quantitative analysis on the dispersive time sequence based on the information entropy, and evaluating the uncertainty degree of information flow transmission from the source system to the target system and the uncertainty degree of information flow transmission from the source system to the target system under the constraint of a preset condition. And introducing a compensation mechanism to optimize the uncertainty evaluation result.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to a causal analysis method based on compensated dispersion transfer entropy. Background Technology

[0002] Epilepsy, a common neurological disorder, affects over ten million people in my country, with approximately 30% suffering from drug-resistant epilepsy. These patients experience frequent seizures, facing not only a high risk of accidental injury but also a heavy financial burden of medical expenses, resulting in a severely diminished quality of life. Clinical data shows that the recurrence rate after surgery for drug-resistant epilepsy is as high as 35%-40%, reflecting significant shortcomings in current diagnostic and treatment technologies regarding the understanding and prevention of epilepsy transmission mechanisms.

[0003] Epilepsy is essentially a disorder of brain network connectivity, and accurately characterizing the information transmission relationships between brain regions is crucial for revealing its propagation mechanism. Transfer entropy, a commonly used causal measure, can analyze the flow of information between variables and has been applied in neuroscience research. However, traditional transfer entropy methods have significant drawbacks in practical applications: firstly, they require a high signal-to-noise ratio, and their performance deteriorates significantly under noise interference; secondly, they cannot effectively handle instantaneous causal relationships, and when the signal temporal resolution is insufficient, spurious causal connections are easily generated, leading to reduced accuracy of the constructed brain network.

[0004] Therefore, there is an urgent need for an improved method that can adapt to low signal-to-noise ratio neural signals while accurately capturing transient causal relationships. This would enhance the accuracy and reliability of epilepsy transmission network construction, providing more reliable technical support for clinical lesion localization, surgical planning, and efficacy evaluation. This would not only help improve treatment outcomes for patients with drug-resistant epilepsy but also be of great significance for understanding the information transmission mechanisms of complex brain systems. Summary of the Invention

[0005] The purpose of this invention is to provide a causal analysis method based on compensated dispersion transfer entropy, which is designed to adapt to low signal-to-noise ratio neural signals and accurately capture instantaneous causal relationships, thereby improving the accuracy of the constructed brain network.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a causal analysis method based on compensated dispersion transfer entropy, comprising: S1: obtaining the original time series and normalizing it using a normal cumulative distribution function to obtain a normalized time series; S2: performing dispersion processing on the normalized time series, assigning each data point within a preset integer range to it using a linear algorithm to obtain a dispersion time series; S3: performing information transfer quantification analysis on the dispersion time series based on information entropy, evaluating the uncertainty of information flow from the source system to the target system, and the uncertainty of information flow from the source system to the target system under preset constraints; S4: introducing a compensation mechanism to optimize the uncertainty assessment results.

[0007] In step S1, the original time series is mapped to the range of [0,1] using the normal cumulative distribution function, so that the normalized time series data are within a uniform numerical range.

[0008] In step S3, the specific process of information transmission quantification analysis includes: using the calculation logic of information entropy to quantify the information interaction intensity between data points in the dispersive time series, and forming the information transmission quantification result.

[0009] In step S3, based on the information transmission quantification results, the uncertainty of the impact of the source system's time series on the target system's time series is analyzed, and the uncertainty assessment result under the single constraint condition is used as the uncertainty assessment result of the information flow transmitted from the source system to the target system.

[0010] Based on the uncertainty assessment results under single constraints, the time series influence of the conditional system is incorporated to analyze the uncertainty of information flow from the source system to the target system under multiple constraints. The resulting uncertainty assessment results under multiple constraints are used as the uncertainty assessment results of information flow from the source system to the target system under preset constraints.

[0011] In step S4, the zero-lag term is incorporated into the uncertainty assessment calculation process. If the instantaneous effect is determined to be a valid causal relationship, the zero-lag term corresponding to the source system is incorporated into the relevant calculation of the target system to achieve compensation for the instantaneous causal relationship.

[0012] Step S4 is followed by step S5: verifying the causal relationship identification results through multiple batches of simulated datasets, where the simulated datasets are pre-constructed test data sets with clear causal relationships.

[0013] The multi-batch simulation dataset includes the first batch of simulation datasets, which is used to evaluate the algorithm's noise resistance performance. By introducing different levels of interference noise into the data, the stability of the causal relationship identification results is verified.

[0014] The multi-batch simulation dataset also includes a second batch of simulation datasets; the second batch of simulation datasets is used to verify the algorithm's ability to capture instantaneous causal relationships, and the data contains explicit instantaneous causal relationships and lagged causal relationships.

[0015] The multi-batch simulation dataset also includes a third batch of simulation datasets; the third batch of simulation datasets consists of epileptic seizure-related data generated by the epilepsy dynamics model, used to verify the accuracy of the algorithm in constructing causal relationships for epilepsy.

[0016] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. The causal analysis method based on compensated dispersion transfer entropy provided by this invention first uses a normal cumulative distribution function to map the original time series to the [0,1] interval, realizing the normalization of the original data. This effectively eliminates the dimensional differences of physiological signals from different sources and of different magnitudes (such as EEG signals from different brain regions), ensuring that each data point is within a unified numerical range. This significantly improves the accuracy and comparability of subsequent dispersion processing and information transfer quantification, avoiding analytical bias caused by data magnitude imbalance. Dispersion processing assigns integers within a preset range to the normalized data using a linear algorithm, completing the coarse-grained transformation of the time series. This process can accurately filter out high-frequency noise in the original signal while completely preserving the core trend and key features of the signal, significantly improving the algorithm's anti-interference capability. For EEG signals, which are inherently susceptible to interference from environmental and physiological factors, this operation can ensure stable causal analysis even under low signal-to-noise ratio conditions, solving the core pain point of weak noise resistance in traditional transfer entropy algorithms.

[0017] 2. The causal analysis method based on compensated dispersive transfer entropy provided by this invention further quantifies the information interaction intensity of the dispersive time series through information entropy, and then evaluates the uncertainty of information flow from the source system to the target system at two levels: single constraint and multiple constraint. On the one hand, the calculation logic of information entropy can accurately characterize the information transfer intensity between brain regions, providing a quantitative basis for causal inference; on the other hand, the multi-constraint evaluation incorporates the influence of third-party conditional systems, which can restore the complex scenario of multi-brain region interaction in the brain network, avoiding the one-sidedness of causal relationship inference under a single constraint, and making the analysis of information flow between brain regions more in line with physiological reality. Step S4, by introducing a zero-lag term and integrating it into the target system calculation after effective instantaneous causal determination, realizes the compensation of instantaneous causal relationship. This mechanism can accurately capture the instantaneous interaction between brain regions within the same lag period, solving the defects of traditional transfer entropy algorithms that cannot identify instantaneous causality and are prone to misjudging false directed connections, allowing the causal relationship of the epilepsy transmission network to cover both lag transfer and instantaneous interaction dimensions, greatly improving the completeness and accuracy of causal network construction. Attached Figure Description

[0018] Figure 1This is a flowchart of a causal analysis method based on compensated dispersion transfer entropy provided in an embodiment of this application; Figure 2 This is a schematic diagram of experimental results for capturing causal relationships at different noise levels, provided in an embodiment of this application. Figure 3 This is a schematic diagram of experimental results showing the performance under different instantaneous causal conditions, as provided in an embodiment of this application. Figure 4 This is a schematic diagram of experimental results for constructing a causal relationship for epilepsy, provided in an embodiment of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0020] This application provides a causal analysis method based on Compensated Dispersion Transfer Entropy (CDTE), for example, such as... Figure 1 As shown. The method includes: S1: Obtain the original time series and normalize it using the normal cumulative distribution function to obtain the normalized time series.

[0021] In step S1, the original time series is processed using the Normal Cumulative Distribution Function (NCDF). Mapping to the range of values ​​in [0,1] yields... This ensures that the normalized time series data falls within a uniform numerical range.

[0022] Among them, the original time series is a data sequence that reflects the change of system state over time. As a possible implementation method, the original time series is obtained from the regular electrophysiological changes generated by different brain regions with physiological activities, that is, the electrophysiological signals of each brain region; the normal cumulative distribution function is a probability distribution function used to map data to a specific range of values.

[0023] For example, the normal cumulative distribution function As shown below: in, Let be the point whose probability is to be determined. This represents the mean. The standard deviation is denoted as ; under standard normal distribution .

[0024] S2: Dispersion processing is performed on the normalized time series. Each data point after normalization is assigned an integer within a preset integer range using a linear algorithm to obtain the dispersion time series.

[0025] Dispersion processing involves coarse-grained transformation of the normalized time series to filter out high-frequency noise. For example, a linear algorithm is used for each... Assign integers from 1 to c, and then transform the normalized time series into a dispersive time series using dispersive processing. .

[0026] For example, the linear algorithm is as follows: S3: Based on information entropy, perform quantitative analysis of information transmission in the dispersive time series, and evaluate the uncertainty of the information flow from source system X to target system Y, as well as the uncertainty of the information flow from source system X to target system Y under preset constraint Z.

[0027] For example, the TE algorithm is used to identify causal relationships and dynamic information flow between dispersive time series, and information entropy is used to measure the time series in system X. The information transfer between them is defined as follows: in The information entropy of system X is represented by... Representing data points The probability of occurrence in the time series of system X.

[0028] From a practical physiological perspective, source system X and target system Y directly correspond to two independent functional brain regions. Source system X is the region that generates specific physiological signals, neural instructions, or cognitive functions, equivalent to the source of information at the physiological level. Target system Y receives physiological signals and neural instructions from source system X, equivalent to the destination of information at the physiological level. For example, in constructing a causal network for epilepsy, X might be the core brain region where the epileptic focus is located, while Y might be the downstream brain region where the signal from the focus is transmitted. From the perspective of signal carriers, source system X is the signal analysis unit corresponding to the brain region that initiates the information flow, and target system Y is the signal analysis unit corresponding to the brain region that receives the information flow. This division serves to accurately infer the causal transmission relationship of neural signals between brain regions. Information entropy initially measures the time series within system X, and later evolves to measure the information transmission between two systems X and Y.

[0029] In step S3, the specific process of information transmission quantification analysis includes: using the calculation logic of information entropy to quantify the information interaction intensity between data points in the dispersive time series, and forming the information transmission quantification result.

[0030] In step S3, based on the information transmission quantification results, the uncertainty of the impact of the source system's time series on the target system's time series is analyzed, and the uncertainty assessment result under the single constraint condition is used as the uncertainty assessment result of the information flow transmitted from the source system to the target system.

[0031] For example, arrive The dispersion transfer entropy (DTE) is defined as: in, Representative source system To the target system The degree of uncertainty in transmitting information flow and For each system and The time series, where p represents probability. Representative System From time Time All state vector variables (assuming) The current time is set to [current time], and the origin of the time is [time point]. , Representation of process The complete historical sequence, Similarly).

[0032] Based on the uncertainty assessment results under single constraints, the time series influence of the conditional system is incorporated to analyze the uncertainty of information flow from the source system to the target system under multiple constraints. The resulting uncertainty assessment results under multiple constraints are used as the uncertainty assessment results of information flow from the source system to the target system under preset constraints.

[0033] For example, when multiple systems exist, let... , and To describe a stationary stochastic process in which the system state changes over time, the condition is... Down arrive The DTE is defined as: in, Representative conditions Down arrive Information transmission , and For a moment For random variables obtained by sampling from each process, p represents the probability.

[0034] S4: Introduce a compensation mechanism to optimize the uncertainty assessment results.

[0035] In step S4, the zero-hysteresis term is... In the calculation process of uncertainty assessment, if the instantaneous effect is determined to be a valid causal relationship, the zero-lag term corresponding to the source system is incorporated into the relevant calculation of the target system to achieve compensation for the instantaneous causal relationship.

[0036] Zero-latency synchronization corresponds to the instantaneous statistical correlation between two time processes, providing a direct explanation of the immediate interactions between brain regions. The compensatory mechanism defines the algorithm as an expression of conditional entropy difference, supporting the realization of zero-latency interaction through two substitution strategies. When the instantaneous effect is determined to have a meaningful causal relationship, the zero-latency term of the source process... It will be incorporated into the relevant calculations of the target system.

[0037] For example, the CDTE algorithm is as follows: in, Representative conditions Down arrive Information transmission , and For a moment For random variables obtained by sampling from each process, p represents the probability.

[0038] Step S4 is followed by step S5: verifying the causal relationship identification results through multiple batches of simulated datasets, where the simulated datasets are pre-constructed test data sets with clear causal relationships.

[0039] The multi-batch simulation dataset includes the first batch of simulation datasets, which is used to evaluate the algorithm's noise resistance performance. By introducing different levels of interference noise into the data, the stability of the causal relationship identification results is verified.

[0040] As one possible implementation, the first batch of simulation datasets corresponds to a multivariable nonlinear system, and the three time series can be generated by the following equation: It should be understood that the three time series generated here are used to validate the CDTE algorithm. Each time series contains 4000 time points. To reduce errors caused by random factors, each model is run 100 times to generate different simulated data, covering linear relationships ( ) and nonlinear causal relationships ( , The degree of nonlinearity is determined by the parameter. Regulation, , , This represents the noise term. The specific process for adding Gaussian white noise to this dataset is as follows: first, calculate the average standard deviation of all channels; then, select 10%, 30%, and 50% of this average as the noise standard deviation and add them to the dataset. By setting different proportions of noise intensity, the performance of the CDTE algorithm under different noise interference levels can be explored.

[0041] Experimental results of the causal relationship capture capabilities of TE, DTE, and CDTE algorithms under different noise levels are as follows: Figure 2 As shown, both the DTE and CDTE algorithms exhibit good performance under three noise conditions, accurately identifying... , , Information flow relationship between ( , , The results show that dispersion processing can effectively improve the noise resistance of the algorithm to a certain extent, and help the algorithm to more accurately identify the causal relationship between variables in noisy environments.

[0042] The multi-batch simulation dataset also includes a second batch of simulation datasets; the second batch of simulation datasets is used to verify the algorithm's ability to capture instantaneous causal relationships, and the data contains explicit instantaneous causal relationships and lagged causal relationships.

[0043] For example, construct a system containing M=3 linear stochastic processes. , and In the simulated scenario, the interaction of the three follows the equation: in, , and These are independent white noises, all with a mean of 0 and variances of [missing values]. , and . and Both are second-order autoregressive processes, characterized by two complex conjugate poles, with pole moduli of... Phase is Given pole modulus and center frequency: , , , Quantification and The parameter values ​​for its own historical dependency are: , , , ; Used to define causal relationships between time series. Different types of effects are applied: arrive This is an instantaneous lag effect. arrive It is a completely instantaneous effect. arrive This is a complete lag effect. Each time series consists of 4000 time points. To minimize the error caused by random factors, each model is repeated 100 times.

[0044] The experimental results of the performance of TE and Conditional Transfer Entropy (CTE) under different instantaneous causal conditions are shown in the figure below. Figure 3 As shown, for the conditions Down arrive For TE or CTE, the first process uses a vector. The second process involves retrieving data from the source time series in the second and third steps. Select several past vectors By introducing These past vectors allow for a more comprehensive consideration. right The effect of this, thus successfully capturing arrive The results demonstrate that the CTE algorithm is superior to the traditional TE algorithm in capturing causal information transmission that includes transient lag effects, exhibiting greater capability and accuracy compared to its performance under different transient causal conditions.

[0045] The multi-batch simulation dataset also includes a third batch of simulation datasets; the third batch of simulation datasets consists of epileptic seizure-related data generated by the epilepsy dynamics model, used to verify the accuracy of the algorithm in constructing causal relationships for epilepsy.

[0046] For example, the following equations are used to simulate epileptic seizure data with known propagation paths: in, Where τ0 = 2857, τ2 = 10, =3.1, =0.45, γ=0.01. The excitability of brain regions is determined by parameters. It indicates. In In cases >-2.1, isolated epileptic nodes can cause seizures. and Represents the rapid discharge phase; and This represents the slow peak and fluctuating oscillation phases. As a dielectric constant variable, it determines the transition of brain electrical activity from the relatively stable interictal period to the epileptic seizure state. and This represents a coupled differential equation. , , , , They represent , , , , The first derivative with respect to time. and These represent the external input currents during the rapid discharge phase and the slow spike phase, respectively. K is the brain region coupling strength coefficient.

[0047] The results of CDTE and TE algorithms in constructing causal relationships are as follows: Figure 4In the diagram, the black dots represent contacts that deviate from the simulated data in the third batch of simulated datasets. In simulated data E1, the TE algorithm incorrectly captured contacts GPH3 and GPH7; in simulated data E2, TE failed to capture contacts OP6 and OT1 and their connections. However, the CDTE algorithm not only more accurately identifies causal relationships consistent with the actual situation in the simulated data but also effectively reduces misjudgments and omissions. It demonstrates stronger adaptability and accuracy in both identifying diseased contacts and capturing corresponding causal connections, providing more reliable analytical results for causal relationship research.

[0048] In the description of this specification, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0049] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A causal analysis method based on compensated dispersion transfer entropy, comprising: S1: Obtain the original time series, and normalize the original time series using the normal cumulative distribution function to obtain the normalized time series; S2 S3: The normalized time series is subjected to dispersion processing. Each data point after normalization is assigned an integer within a preset integer range using a linear algorithm to obtain the dispersion time series; S4: The dispersion time series is subjected to information transmission quantification analysis based on information entropy. The uncertainty of the information flow transmitted from the source system to the target system and the uncertainty of the information flow transmitted from the source system to the target system under preset constraints are evaluated respectively. S4: Introduce a compensation mechanism to optimize the uncertainty assessment results.

2. A causal analysis method based on compensated dispersion transfer entropy according to claim 1, characterized in that, In step S1, the original time series is mapped to the range of [0,1] using the normal cumulative distribution function, so that the normalized time series data are within a uniform numerical range.

3. A causal analysis method based on compensated dispersion transfer entropy according to claim 1, characterized in that, In step S3, the specific process of the information transmission quantification analysis includes: using the calculation logic of information entropy to quantify the information interaction intensity between data points in the dispersive time series, and forming the information transmission quantification result.

4. A causal analysis method based on compensated dispersion transfer entropy according to claim 3, characterized in that, In step S3, based on the information transmission quantification results, the uncertainty of the influence of the source system's time series on the target system's time series is analyzed, and the uncertainty assessment result under the single constraint condition is used as the uncertainty assessment result of the information flow transmitted from the source system to the target system.

5. A causal analysis method based on compensated dispersion transfer entropy according to claim 4, characterized in that, Based on the uncertainty assessment results under the single constraint condition, the time series influence of the condition system is incorporated, and the uncertainty of the information flow from the source system to the target system under multiple constraints is analyzed. The resulting uncertainty assessment results under multiple constraints are used as the uncertainty assessment results of the information flow from the source system to the target system under the preset constraints.

6. A causal analysis method based on compensated dispersion transfer entropy according to claim 1, characterized in that, In step S4, the zero-lag term is incorporated into the uncertainty assessment calculation process. If the instantaneous effect is determined to be a valid causal relationship, the zero-lag term corresponding to the source system is incorporated into the relevant calculation of the target system to achieve compensation for the instantaneous causal relationship.

7. A causal analysis method based on compensated dispersion transfer entropy according to claim 1, characterized in that, Step S4 is followed by step S5: verifying the causal relationship identification results through multiple batches of simulated datasets, wherein the simulated datasets are pre-constructed test data sets with clear causal relationships.

8. A causal analysis method based on compensated dispersion transfer entropy according to claim 7, characterized in that, The multi-batch simulated dataset includes a first batch of simulated datasets, which is used to evaluate the noise resistance performance of the algorithm. By introducing different levels of interference noise into the data, the stability of the causal relationship identification results is verified.

9. A causal analysis method based on compensated dispersion transfer entropy according to claim 7, characterized in that, The multi-batch simulation dataset also includes a second batch of simulation datasets; the second batch of simulation datasets is used to verify the algorithm's ability to capture instantaneous causal relationships, and the data contains explicit instantaneous causal relationships and lagged causal relationships.

10. A causal analysis method based on compensated dispersion transfer entropy according to claim 1, characterized in that, The multi-batch simulation dataset also includes a third batch of simulation datasets; the third batch of simulation datasets consists of epileptic seizure-related data generated by the epilepsy dynamics model, used to verify the accuracy of the algorithm in constructing epilepsy causal relationships.

Images