Sign detection device, sign detection method, program, and recording medium

Abstract

A sign detection device 1 comprises: an acquisition unit 10 that acquires space-time data of a multidimensional variable indicating a state of a target; a prediction error analysis unit 20 that estimates a deviation between a prediction value and an actual measurement value of time data in the space-time data; a fluctuation analysis unit 30 that estimates fluctuation of the space-time data; and a sign detection unit 40. The prediction error analysis unit 20 calculates the prediction value by converting the space-time data of the multidimensional variable into time data of a target variable which is a variable to be predicted by the sign detection device 1, and estimates the deviation between the prediction value and the actual measurement value. The fluctuation analysis unit 30 calculates fluctuation of the state of the target by means of fluctuation analysis using the space-time data. When the deviation estimated by the prediction error analysis unit 20 exceeds a predetermined first threshold value and the fluctuation estimated by the fluctuation analysis unit exceeds a predetermined second threshold value, the sign detection unit 40 detects that there is a sign of a state transition in the target.

Description

Sign detection device, sign detection method, program, and recording medium

[0001] The present invention relates to a sign detection device, a sign detection method, a program, and a recording medium.

[0002] It is known that when a natural phenomenon (such as the occurrence of an earthquake or the onset of a disease) or a social phenomenon (such as a large fluctuation in stock prices) reaches a critical point (hereinafter also referred to as a "branch point" or "tipping point"), a sudden transition occurs from one stable state to another (see, for example, Non-Patent Documents 1 to 5). If a sign of a sudden state transition can be detected at this time, it is expected that it will be possible to respond to sudden changes in natural and social phenomena.

[0003] In particular, research into the dynamic mechanisms of complex diseases has been known to have modeled the progression process of disease worsening (e.g., asthma attacks, cancer onset and recurrence) as a time-dependent nonlinear dynamic system, and by analyzing this, has discovered a relationship between state transitions at branching points and sudden worsening of the disease (see, for example, non-patent document 6).

[0004] Against this background, a technology for detecting candidates for dynamic network biomarkers (hereinafter also referred to as "DNB"), which serve as indicators of biological symptoms, has been disclosed (see, for example, Patent Document 1). DNBs are based on measurement data of multiple factor items obtained by biological measurements. Furthermore, a technology has been disclosed in which, during a transition state from a healthy state to a diseased state, state changes of a target factor and connection factors that are dynamically directly connected to this factor are regarded as local network entropy, and a pre-disease state is detected based on this local network entropy (see, for example, Patent Document 2). Furthermore, a technology has been disclosed in which data obtained by collecting and analyzing biological materials from multiple healthy individuals is stored, and analysis data of biological materials collected only once from a subject is added to the data, and whether DNB has occurred is determined (see, for example, Patent Document 3).

[0005] JP 2014-64515 JP 2014-83194 WO 2018 / 207925

[0006] Venegas, J.G., Winkler, T., Musch, G., Melo, M.F.V., Layfield, D., Tgavalekos, N., Fischman, A.J., Callahan, R.J., Bellani, G., and Harris, R.S., “Self-organized patchiness in asthma as a prelude to catastrophic shifts” Nature 434, pp. 777-782 (2005)McSharry, P.E., Smith, L.A., and Tarassenko, L., “Prediction of epileptic seizures: are nonlinear methods relevant?” Nature Medicine 9, pp. 241-242 (2003)Barriuso, R.P., Guallar, E., and Coresh, J., “Transition models for change-point estimation in logistic regression” Statistics in Medicine 22(7), pp. 1141-1162 (2003)Paek, S.H., Chung, H.-T., Jeong, S.S., Park, C.-K., Kim, C.-Y, Kim, J.E., Kim D.G., and Jung, H.-W., “Hearing preservation after gamma knife stereotactic radiosurgery of vestibular schwannoma” Cancer 104, pp. 580-590 (2005)Liu, J.K., Rovit, R.L., and Couldwell, W.T., “Pituitary Apoplexy” Seminars in Neurosurgery 12, Thieme, pp. 315-320 (2001)Tanaka, G., Tsumoto, K., Tsuji, S., and Aihara, K., “Bifurcation analysis on a hybrid systems model of intermittent hormonal therapy for prostate cancer” Physica D: Nonlinear Phenomena Volume 237, pp. 2616-2627 (2008)Takens, F., “Dynamical Systems and Turbulence.”In: Rand, D. and Young, LS, Eds., Lecture Notes in Mathematics, Vol. 898, pp. 366-381, (1981)Sauer, T., Yorke, JA, and Casdagli, M., “Embedology” J. Stat. Phys. 65, pp. 579-615(1991)Liu, R., Chen, P., Aihara, K., and Chen, L., “Identifying Early-Warning Signals of Critical Transitions with Strong Noise by Dynamical Network Markers” Scientific Reports volume 5, Article number: 15736 (2015)Chen, L., Liu, R., Liu, Z.-P., Li, M., and Aihara K., “Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers” Scientific Reports volume 2, Article number: 342 (2012).

[0007] The techniques disclosed in Patent Documents 1 to 3 can realize noise resistance in sign detection and simplify the sampling required for sign detection, etc. However, there is still room for improvement in the exact timing and accuracy of sign determination.

[0008] The present invention has been made in view of the above circumstances, and its purpose is to accurately detect the timing of a sign that a target state will transition.

[0009] To solve the above-mentioned problems, one aspect of the present invention provides a sign detection device that detects signs of a state transition of an object, and includes an acquisition unit that acquires spatio-temporal data of multidimensional variables that indicate the state of the object, a prediction error analysis unit that estimates a discrepancy between a predicted value and an actual measured value of temporal data in the spatio-temporal data, a fluctuation analysis unit that estimates fluctuations in the spatio-temporal data, and a sign detection unit. The prediction error analysis unit calculates a predicted value by converting the spatio-temporal data of the multidimensional variables into temporal data of a target variable that is a variable of the object to be predicted by the sign detection device, and estimates a discrepancy between the predicted value and the actual measured value. The fluctuation analysis unit calculates fluctuations in the state of the object through fluctuation analysis using the spatio-temporal data. The sign detection unit detects that the object has a sign of a state transition when the discrepancy estimated by the prediction error analysis unit exceeds a predetermined first threshold and the fluctuation estimated by the fluctuation analysis unit exceeds a predetermined second threshold.

[0010] In an embodiment of the symptom detection device, the transformation from the spatiotemporal data to the temporal data of the target variable may be a transformation by embedding in a non-time-delayed coordinate space or by embedding in a time-delayed coordinate space.

[0011] In an embodiment of the symptom detection device, the conversion from spatiotemporal data to temporal data of the target variable may be calculated using machine learning.

[0012] In an embodiment of the symptom detection device, the fluctuation analysis unit may calculate fluctuations in the state of the target by converting the spatiotemporal data into time data of a virtual variable based on the spatiotemporal data.

[0013] In an embodiment of the symptom detection device, the virtual variables may be data representing the movement of the target state on a central manifold.

[0014] In an embodiment of the symptom detection device, the fluctuation analysis unit may estimate fluctuations in the spatiotemporal data using dynamic network markers.

[0015] In an embodiment of the symptom detection device, the fluctuation analysis unit may calculate the fluctuation when the deviation estimated by the prediction error analysis unit exceeds a predetermined first threshold value.

[0016] The state transition of interest may be the occurrence of an earthquake.

[0017] In an embodiment of the sign detection device, the sign of a transition in the subject's state may be the occurrence of a pre-disease state, which is a state in which a healthy state transitions to a diseased state.

[0018] In one embodiment of the precursor detection device, the transformation from the non-time-dilated coordinate space to the time-dilated coordinate space is Z ｔ is the vector at time t in the non-delay coordinate space, V ｔ is a vector at time t in the time delay coordinate space, Φ and Ψ are nonlinear transformations, and I is an identity transformation. ｔ ) = V ｔ , Z ｔ = Ψ(V ｔ ), which may be expressed as Φ·Ψ=I.

[0019] In the symptom detection device of one embodiment, the transformation from the non-time-delayed coordinate space to the time-delayed coordinate space is expressed as PF(Z ｔ ) = V ｔ , F(Z ｔ ) = QV ｔ , PQ=E.

[0020] Another aspect of the present invention is a system state transition sign detection method. This sign detection method detects a sign of a state transition of an object, and includes an acquisition step of acquiring spatio-temporal data of multidimensional variables indicating the state of the object, a prediction error analysis step of estimating a discrepancy between a predicted value and an actual measured value of time data in the spatio-temporal data, a fluctuation analysis step of estimating fluctuations in the spatio-temporal data, and a sign detection step. The prediction error analysis step calculates a predicted value by converting the spatio-temporal data of the multidimensional variables into time data of a target variable, which is a variable of the object to be predicted by the sign detection method, and estimates the discrepancy between the predicted value and the actual measured value. The fluctuation analysis step calculates fluctuations in the state of the object by fluctuation analysis using the spatio-temporal data. The sign detection step detects that the object has a sign of a state transition when the discrepancy estimated in the prediction error analysis step exceeds a predetermined first threshold and the fluctuation estimated in the fluctuation analysis step exceeds a predetermined second threshold.

[0021] Yet another aspect of the present invention is a program for causing a computer to execute a method for detecting a sign of a state transition of an object. The program includes an acquisition step of acquiring spatio-temporal data of multidimensional variables indicating the state of the object, a prediction error analysis step of estimating a discrepancy between a predicted value and an actual measured value of time data in the spatio-temporal data, a fluctuation analysis step of estimating fluctuations based on the spatio-temporal data, and a sign detection step. The prediction error analysis step calculates a predicted value by converting the spatio-temporal data of the multidimensional variables into time data of a target variable, which is a variable of the object to be predicted by the program, and estimates the discrepancy between the predicted value and the actual measured value. The fluctuation analysis step calculates fluctuations in the state of the object by fluctuation analysis using the spatio-temporal data. The sign detection step detects that the object has a sign of a state transition when the discrepancy estimated in the prediction error analysis step exceeds a predetermined first threshold and the fluctuation estimated in the fluctuation analysis step exceeds a predetermined second threshold.

[0022] Yet another aspect of the present invention is a recording medium having a program recorded thereon that causes a computer to execute a method for detecting a sign of a state transition of an object. The program recorded on the recording medium includes an acquisition step of acquiring spatio-temporal data of multidimensional variables indicating the state of the object, a prediction error analysis step of estimating a discrepancy between a predicted value and an actual measured value of time data in the spatio-temporal data, a fluctuation analysis step of estimating fluctuations based on the spatio-temporal data, and a sign detection step. The prediction error analysis step calculates a predicted value by converting the spatio-temporal data of the multidimensional variables into time data of a target variable, which is a variable of the object to be predicted by the program, and estimates the discrepancy between the predicted value and the actual measured value. The fluctuation analysis step calculates fluctuations in the state of the object by fluctuation analysis using the spatio-temporal data. The sign detection step detects that the object has a sign of a state transition when the discrepancy estimated in the prediction error analysis step exceeds a predetermined first threshold and the fluctuation estimated in the fluctuation analysis step exceeds a predetermined second threshold.

[0023] Any combination of the above components, and any transformation of the present invention into an apparatus, method, system, recording medium, computer program, etc., are also valid aspects of the present invention.

[0024] According to the present invention, it is possible to accurately detect the timing of a sign that a state of an object will transition.

[0025] FIG. 1 is a functional block diagram of a sign detection device according to a first embodiment. FIG. 2 is a graph showing the time evolution of predicted values ​​and actual measured values ​​of spatio-temporal data. FIG. 3 is a graph showing the time evolution of fluctuations in spatio-temporal data. FIG. 4 is a graph showing the detection of signs of an earthquake and the timing of the actual occurrence of an earthquake. FIG. 5 is a schematic diagram showing the embedding of time-delayed coordinates. FIG. 6 is a schematic diagram showing the embedding of non-time-delayed coordinates. FIG. 7 is a schematic diagram showing vectors of multidimensional spatio-temporal data and target variables. FIG. 8 is a schematic diagram showing an autoreservoir neural network. FIG. 9 is a flowchart showing the processing steps of a sign detection method according to a second embodiment. FIG. 10 is a schematic diagram explaining the definition of pre-illness. FIG. 11 is a schematic diagram showing the integration of DNB theory analysis and prediction theory analysis.

[0026] The present invention will be described below based on preferred embodiments with reference to the drawings. In the embodiments and modifications, identical or equivalent components and members are designated by the same reference numerals, and redundant description will be omitted where appropriate. The dimensions of the components in the drawings are enlarged or reduced as appropriate for ease of understanding. Some components that are not important for explaining the embodiments are omitted from the drawings. Terms including ordinal numbers such as "first" and "second" are used to describe various components, but these terms are used only to distinguish one component from another and do not limit the components.

[0027] 1 shows a functional block diagram of a sign detection device 1 according to a first embodiment. The sign detection device 1 is a device that detects signs of a transition in the state of an object. The sign detection device 1 includes an acquisition unit 10, a prediction error analysis unit 20, a fluctuation analysis unit 30, and a sign detection unit 40.

[0028] The acquisition unit 10 acquires spatiotemporal data of multidimensional variables indicating the state of the target. For example, if the target is a human, the spatiotemporal data is biological information data such as gene expression generated from a human biological sample. In this case, the precursor corresponds to a pre-disease state, which is a turning point when a person transitions from a healthy state to a diseased state. Alternatively, for example, if the target is the Earth, the spatiotemporal data is the movement of the Earth's surface over a wide area acquired by a Global Navigation Satellite System (GNSS). In this case, the precursor corresponds to the state immediately before transitioning from a normal state to an earthquake-occurring state.

[0029] The acquisition unit 10 transmits the acquired spatiotemporal data to the prediction error analysis unit 20 and the fluctuation analysis unit 30 .

[0030] The prediction error analysis unit 20 estimates the discrepancy between the predicted value and the actual measured value of the time data in the spatio-temporal data. Specifically, the prediction error analysis unit 20 calculates a predicted value by converting the spatio-temporal data of multidimensional variables into time data of a target variable, which is a variable to be predicted by the sign detection device 1, and estimates the discrepancy between this predicted value and the actual measured value.

[0031] When the predicted and measured values ​​of time data in spatio-temporal data are monitored for a certain period of time, the discrepancy between the two may suddenly increase. The moment when this discrepancy increases is considered to be one of the indicators representing the turning point of a state transition. Therefore, when this discrepancy exceeds a certain value (threshold), it is possible to determine the sign of a state transition. Note that further details of the method for estimating the discrepancy between the predicted and measured values ​​will be explained later.

[0032] The fluctuation analysis unit 30 estimates the fluctuation of the spatiotemporal data. Specifically, the fluctuation analysis unit 30 calculates the fluctuation of the state of the target by fluctuation analysis using the spatiotemporal data.

[0033] When spatiotemporal data is monitored for a certain period of time, sudden large fluctuations may occur in the data. The moment when such large fluctuations occur can also be considered as an indicator of a branching point in a state transition. Therefore, when the fluctuations in the spatiotemporal data exceed a certain value (threshold), it is possible to determine the signs of a state transition. Further details of the method for calculating the fluctuations of a target state through fluctuation analysis will be explained later.

[0034] The precursor detection unit 40 detects that the object has a precursor to a state transition when the deviation estimated by the prediction error analysis unit 20 exceeds a predetermined first threshold and the fluctuation estimated by the fluctuation analysis unit 30 exceeds a predetermined second threshold.

[0035] An embodiment of detecting a precursor to an earthquake will be described below, taking the occurrence of an earthquake as an example of a target state. In this case, the spatiotemporal data is the movement of the Earth's surface over a wide area obtained from crustal movement observation instruments using GNSS in various locations, seismometers in various locations, and the like.

[0036] FIG. 2 shows the time evolution of predicted and measured values ​​of spatiotemporal data. As shown in the figure, the magnitude of the difference between the predicted and measured values ​​increases at time t ＦＳ It increases rapidly just before time t ＦＳ At this time t ＦＳ is considered to be an important factor in predicting the occurrence of an earthquake.

[0037] 3 shows the time evolution of fluctuations in spatiotemporal data. As shown in the figure, the magnitude of fluctuations in spatiotemporal data increases at time t ＵＳ It increases rapidly just before time t ＵＳ At this time t ＵＳ is also considered to be an important factor in predicting the occurrence of an earthquake.

[0038] FIG. 4 shows the timing between the detection of an earthquake precursor and the actual occurrence of an earthquake. As shown in the figure, in this example, first, at time t ＦＳ The difference between the predicted value and the actual measured value exceeds the first threshold at time t ＵＳ The sign detection unit 40 of the sign detection device 1 determines that the deviation has exceeded the first threshold and the deviation has exceeded the second threshold at the later time t ＵＳ is detected as a sign of an earthquake. ＵＳ An actual earthquake occurs immediately after the earthquake, and it can be seen that the sign of an earthquake occurrence has been correctly detected. In this case, too, the sign detection unit 40 detects a sign of a transition in the state of the target when both of the two conditions, that the deviation exceeds the first threshold and the fluctuation exceeds the second threshold, are satisfied.

[0039] In the above example, first, time t ＦＳ The difference between the predicted value and the actual measured value exceeds the first threshold at time t ＵＳ However, depending on the type of object and the situation, the fluctuation may exceed the second threshold at time t ＵＳ The fluctuation exceeds the second threshold at time t ＦＳ In some cases, the difference between the predicted value and the actual measured value exceeds the first threshold value.

[0040] In this way, the technology disclosed herein integrates information obtained from prediction errors of spatiotemporal data with information obtained from fluctuations, and detects when both show significant signs (i.e., exceed a predetermined threshold), thereby realizing sign detection of state transitions. This type of sign detection method is extremely novel and has not been disclosed or suggested in prior art.

[0041] According to this embodiment, it is possible to realize a device that accurately detects the timing of a sign that a target state will transition.

[0042] Hereinafter, unless otherwise specified, vectors and matrices will be represented by uppercase letters (e.g., vector V, matrix A, etc.), and scalars will be represented by lowercase letters (e.g., value x, etc.).

[0043] The state of a k-dimensional dynamical system at a certain time can be expressed by k state variables. However, in actual experiments, it is not always possible to observe all k state variables, and it is often the case that the dimensions of the original dynamical system are unknown. Therefore, we consider reconstructing the attractor from the time series data of the target variable. For this purpose, we use a transformation to a time-delay coordinate system to reconstruct the attractor from the observed time series data of the target variable x ０ , x １ , …, x Ｎ－１ From the above, n state variables are extracted for each appropriate delay time τ, and an n-dimensional vector V(t) = (x ｔ , x ｔ＋τ , …, x ｔ＋（ｎ－１）τ ) is created (t = 0, 1, ..., N-1-(n-1)τ). However, for simplicity, we will assume that τ = 1 below. The time trajectory that V(t) traces in n-dimensional space becomes the reconstructed attractor. Figure 5 shows an attractor reconstructed in this way.

[0044] Alternatively, attractors can be created by non-delayed embedding. That is, the spatiotemporal data X of multidimensional variables including the time series of the target variable ｔ = (x ｔ １ , x ｔ ２ , …, x ｔ Ｄ )' is obtained (where D is the number of observation points, and t = 1, 2, ..., m. The symbol "'" represents the transpose of a vector (same below)), and some observation points are selected (for example, x ｔ i , x ｔ j , x ｔ s ), and the space vector Xｔ (i.e. (x ｔ i , x ｔ j , x ｔ s )) can be used as the reconstructed attractor. According to embedding theory, if D > 2d > 0 and L > 2d > 0, these attractors can reconstruct dynamics that are topologically equivalent to the original system (Turkens' embedding theorem and its extensions. See, for example, Non-Patent Documents 7 and 8). Here, d is the dimension of the original dynamical system or the box-count dimension of the attractor of the dynamical system.

[0045] [Conversion from spatiotemporal data to temporal data of target variables] Space vector X ｔ and the time-delay coordinate vector Y of the target variable ｔ The following relationship holds between these two: Hereinafter, the transformation expressed by this formula may also be referred to as "spatiotemporal information transformation." where Φ is a differentiable nonlinear transformation from a D-dimensional vector space to an L-dimensional vector space. L is the time delay coordinate vector Y ｔ dimensional. Also, Ψ is a differentiable nonlinear transformation from an L-dimensional vector space to a D-dimensional vector space. And Φ·Ψ=I (i.e., the composite transformation of Φ and Ψ is the identity transformation).

[0046] For a given number m, there are m states x ｔ (t=1, 2, ..., m) are observed, and at t=m, the target variable y has L-1 unknown future values ​​{y ｍ＋１ , y ｍ＋２ , ..., y ｍ＋Ｌ－１}. Figure 7 shows a schematic diagram of multidimensional spatiotemporal data and a vector of a target variable.

[0047] In practice, it is difficult to find such nonlinear transformations Φ and Ψ. Therefore, for example, the nonlinear transformations Φ and Ψ are linearized as follows (t=1, 2, ..., m): Here, AB = E. However, A is an LxD matrix, B is a DxL matrix, and E is an LxL identity matrix (D and L, which represent the number of rows and columns, are capital letters but are scalars (same below)). Solving (2) for A and B, and using the obtained coefficients, we can calculate the L-1 unknown future values ​​{y ｍ＋１ , y ｍ＋２ , ..., y ｍ＋Ｌ－１} can be obtained.

[0048] [Autoreservoir] Alternatively, by constructing a nonlinear transformation F using a neural network as in equation (3) based on equation (2) for spatiotemporal information transformation, the prediction accuracy, robustness, and computational efficiency can be significantly improved.

[0049] As an example, a multi-layer feed-forward neural network F can be applied to the neural network unit, where weights between neurons are randomly assigned in advance.

[0050] An example of an autoreservoir neural network F is shown in Figure 8. This neural network includes three hidden layers and uses the hyperbolic tangent tanh as an activation function. However, this is not limiting and any suitable layers, activation functions, or network structures may be used.

[0051] Throughout the processing of the neural network F, the original D variables X ｔ = (x ｔ １ , x ｔ ２ , …, x ｔ Ｄ )' is a set of D variables F(X ｔ ) = (F １ (X ｔ ), F ２ (X ｔ ), ..., F Ｄ～ (X ｔ ))'. Input X ｔ and output F(X ｔ ) evolves over time. In other words, this method uses the observed high-dimensional data X ｔThe reservoir is the dynamics of a randomly connected recurrent neural network. This is in contrast to conventional reservoir computing, which uses the dynamics of a randomly connected recurrent neural network as the reservoir. In other words, the autoreservoir neural network can be expressed by the following autoreservoir neural network-based space-time transformation equation (t = 1, 2, ..., m): A is an L x D~ matrix, B is a D~ x L matrix, AB = I, I is an L x L identity matrix. F is a nonlinear transformation (constructed by a neural network). D and D~ can be different. A and B are two weight matrices determined based on observed data.

[0052] Given X and F, we solve the autoreservoir neural network-based space-time transformation equation (3) to find the future values ​​of the target variables {y ｍ＋１ , y ｍ＋２ , ..., y ｍ＋Ｌ－１} can be obtained. In this way, multi-step future prediction is possible. Here, D>L is generally required.

[0053] [Application to the embodiment] The spatiotemporal data of multidimensional variables indicating the state of the target (specifically, n-dimensional spatiotemporal data observed at time t) acquired by the acquisition unit 10 of the sign detection device 1 of the present embodiment is expressed as a vector Z ｔ = (z ｔ １ , z ｔ ２ , …, z ｔ ｎ )'. From the multidimensional data vector observed at m times, the matrix (Z １ , Z ２ , …, Z ｍ ) is constructed.

[0054] First, based on the embedding theory, the scalar variable v is transformed from the non-delayed coordinate space to the delayed coordinate space by an L-step delay-time embedding transformation. As a result, the time column vector V for m time points is obtained as follows: ｔ = (v ｔ, v ｔ＋１ , …, v ｔ＋Ｌ－１ )', the matrix (V １ , V ２ , …, V ｍ ) is obtained. Here, the parameter L (>1) is the embedding dimension.

[0055] Spatial data vector Z ｔ and the time column vector V ｔ The following relationship holds between (space-time transformation): Here, Φ is a differentiable nonlinear transformation from an n-dimensional vector space to an L-dimensional vector space. Ψ is a differentiable nonlinear transformation from an L-dimensional vector space to an n-dimensional vector space. Φ·Ψ=I (i.e., the composite transformation of Φ and Ψ is an identity transformation). As mentioned above, when d is the dimension of the original dynamical system or the box-count dimension of the attractor, if n>2d>0 and L>2d>0, then V ｔ can be used to reconstruct dynamics that are topologically equivalent to the original system.

[0056] From the first equation of equation (6), Z ｔ V ｔ That is, the spatial information at one time t (z ｔ １ , z ｔ ２ , …, z ｔ ｎ )' is the time information (v ｔ , v ｔ＋１ , …, v ｔ＋Ｌ－１ )'. Therefore, the dynamics of an n-dimensional system can be expressed using data of one variable.

[0057] Generally, the states and phenomena addressed in this disclosure are nonlinear and exhibit nonstationary temporal changes. In such cases, recent short-term time series data are considered to contain more reliable information about near-future dynamics than time series data from the distant past. Therefore, it is expected that problems caused by nonlinearity and nonstationarity can be alleviated by using high-dimensional short-term data (e.g., data within a sliding time window) based on the time-space transformation equation (6). However, it is difficult to estimate the nonlinear transformations Φ and Ψ using only short-term time series data.

[0058] By constructing the nonlinear transformation F using a neural network, the space-time transformation equation (6) can be approximated to a simpler form (7). Here, P is an L×n-matrix, Q is an n-×L matrix, and PQ=E (E is an L×L identity matrix). F=(F １ , F ２ , ..., F ｎ～ ) is a nonlinear transformation (each F ｋ is a transformation from n-dimensional vector space to real number space).

[0059] The autoreservoir F is actually a multilayer neural network constructed from connected nodes, in which the weights are randomly assigned and pre-fixed (rather than learned) during the computation. Thus, in contrast to equation (6), equation (7) can be solved efficiently.

[0060] As described above, in this embodiment, the transformation from spatiotemporal data to temporal data of the target variable may be a transformation by embedding in a non-time-dilation coordinate space or by embedding in a time-dilation coordinate space.

[0061] The transformation from spatiotemporal data to temporal data of the target variable may be calculated using machine learning, in particular machine learning using the aforementioned autoreservoir neural network.

[0062] The fluctuation analysis unit 30 of this embodiment may calculate the fluctuation of the state of the target by converting the spatiotemporal data into time data of a virtual variable. In particular, the virtual variable may be data representing the movement of the state of the target on a central manifold.

[0063] [Dynamic Network Marker] When a system branches from a stable state and transitions to another stable state, there exists a specific group of variables that satisfy the following three properties immediately before the transition. 1. As the transition approaches, the standard deviation of the variables within the group rises sharply. 2. As the transition approaches, the absolute value of the correlation coefficient between variables within the group rises sharply. 3. As the transition approaches, the absolute value of the correlation between variables within the group and variables outside the group falls sharply. At this point, this variable is called a dynamic network marker (DNM). By focusing particularly on this group within the system, it is possible to efficiently detect signs. As an indicator of this, the dynamic network marker score I is defined as follows: Here, SD ｄ is the average standard deviation of all variables included in the dynamic network marker, PCC ｄ is the average of the absolute values ​​of the correlation coefficients between all pairs of variables included in the dynamic network marker, PCC ０ is the average of the absolute values ​​of the correlation coefficients between all pairs of variables included in the dynamic network marker and those not included in the dynamic network marker. ０ may be removed and replaced with a value of 1.

[0064] Based on the above three properties, it is expected that the numerator of score I will increase and the denominator will decrease as the transition approaches, causing the overall value of score I to rise sharply just before the transition. Therefore, by observing this, it is thought that a sign can be detected.

[0065] In this theory, the equation describing the system is linearly approximated near the equilibrium point, and attention is paid to the behavior of the dominant eigenvector direction of the Jacobian matrix. According to this, each variable x of the system ｉFor the dynamic network marker, if the value of the corresponding component of the dominant eigenvector of the Jacobian matrix immediately before the transition is not 0, it is included in the dynamic network marker, and if it is 0, it is not included in the dynamic network marker. This leads to three properties of the dynamic network marker (for details on dynamic network markers, see, for example, Non-Patent Documents 9 and 10).

[0066] By applying the dynamic network markers described above, in one embodiment, the fluctuation analysis unit 30 may estimate the fluctuation of the spatiotemporal data using the dynamic network markers, thereby enabling the fluctuation of the spatiotemporal data to be estimated efficiently and accurately.

[0067] In one embodiment, the fluctuation analysis unit 30 may start calculating the fluctuation when the deviation estimated by the prediction error analysis unit 20 exceeds a predetermined first threshold. This embodiment is particularly effective for a target in which the deviation between the predicted value and the actual measured value of the time data in the spatio-temporal data occurs before the fluctuation.

[0068] In one embodiment, the state transition of interest may be the occurrence of an earthquake.

[0069] In one embodiment, the sign of a transition in the subject's state may be the occurrence of a pre-disease state, which is a state in which a healthy state transitions to a diseased state.

[0070] In one embodiment, the transformation from the non-dilated coordinate space to the dilated coordinate space is expressed as follows: Φ(Z ｔ ) = V ｔ Z ｔ = Ψ(V ｔ ) Φ·Ψ=I

[0071] In one embodiment, the transformation from the non-dilated coordinate space to the dilated coordinate space is given by PF(Z ｔ ) = V ｔ F (Z ｔ ) = QV ｔIt may be expressed as PQ=E.

[0072] 9 is a flowchart showing the processing steps of a sign detection method according to a second embodiment. This sign detection method detects signs of transitions in the state of an object. This sign detection method includes an acquisition step S1 of acquiring spatio-temporal data of multidimensional variables indicating the state of the object, a prediction error analysis step S2 of estimating the discrepancy between predicted and measured values ​​of the time data, a fluctuation analysis step S3 of estimating fluctuations in the spatio-temporal data, and a sign detection step S4.

[0073] The prediction error analysis step S2 calculates a predicted value by converting the spatiotemporal data of the multidimensional variables into time data of the target variable, which is the variable to be predicted by the sign detection method, and estimates the deviation between the predicted value and the actual measured value.

[0074] The fluctuation analysis step S3 calculates the fluctuation of the state of the object by fluctuation analysis using the spatiotemporal data.

[0075] The precursor detection step S4 detects that the target has a precursor to a state transition when the deviation estimated in the prediction error analysis step S2 exceeds a predetermined first threshold and the fluctuation estimated in the fluctuation analysis step S3 exceeds a predetermined second threshold.

[0076] According to this embodiment, the timing of the sign of a transition in the state of the target can be detected accurately through a procedure.

[0077] The third embodiment is a program that causes a computer to execute a sign detection method including an acquisition step S1 of acquiring spatio-temporal data of multidimensional variables that indicate a state of an object, a prediction error analysis step S2 of estimating a discrepancy between a predicted value and an actual measured value of the time data, a fluctuation analysis step S3 of estimating a fluctuation of the spatio-temporal data, and a sign detection step S4.

[0078] The prediction error analysis step S2 calculates a predicted value by converting the spatiotemporal data of the multidimensional variables into time data of the target variable, which is the variable to be predicted by the sign detection method, and estimates the deviation between the predicted value and the actual measured value.

[0079] The fluctuation analysis step S3 calculates the fluctuation of the state of the object by fluctuation analysis using the spatiotemporal data.

[0080] The precursor detection step S4 detects that the target has a precursor to a state transition when the deviation estimated in the prediction error analysis step S2 exceeds a predetermined first threshold and the fluctuation estimated in the fluctuation analysis step S3 exceeds a predetermined second threshold.

[0081] According to this embodiment, a program that accurately detects the timing of a sign that a target state will transition can be implemented as software.

[0082] The fourth embodiment is a recording medium. This recording medium records a program for causing a computer to execute a sign detection method, including an acquisition step S1 of acquiring spatio-temporal data of multidimensional variables indicating a state of a target, a prediction error analysis step S2 of estimating a discrepancy between a predicted value and an actual measured value of the time data, a fluctuation analysis step S3 of estimating fluctuations in the spatio-temporal data, and a sign detection step S4.

[0083] The prediction error analysis step S2 calculates a predicted value by converting the spatiotemporal data of the multidimensional variables into time data of the target variable, which is the variable to be predicted by the sign detection method, and estimates the deviation between the predicted value and the actual measured value.

[0084] The fluctuation analysis step S3 calculates the fluctuation of the state of the object by fluctuation analysis using the spatiotemporal data.

[0085] The precursor detection step S4 detects that the target has a precursor to a state transition when the deviation estimated in the prediction error analysis step S2 exceeds a predetermined first threshold and the fluctuation estimated in the fluctuation analysis step S3 exceeds a predetermined second threshold.

[0086] According to this embodiment, it is possible to record a program on a recording medium that accurately detects the timing of a sign that a state of an object will transition.

[0087] [Verification] To verify the effectiveness of the technology disclosed herein, signs of earthquake occurrence were detected by applying spatiotemporal information transformation to multidimensional spatiotemporal data on wide-area movements of the Earth's surface obtained from crustal movement observation instruments using GNSS in various locations, seismometers in various locations, etc. The spatiotemporal data used was data obtained by analyzing earthquakes that occurred in five high-risk seismic zones and regions: Ibaraki Prefecture in Japan, west-central Hokkaido (around Iburi), Miyagi Prefecture, Sichuan Province in China, and south-central Alaska in the United States.

[0088] The results are shown in Table 1. Table 1

[0089] As can be seen from Table 1, the technology disclosed herein detected precursors of future earthquakes for 1,380 earthquakes with magnitudes of 3 to 5 with an average accuracy of 93.21% and a specificity of 99.00%. Furthermore, for 417 strong earthquakes with magnitudes of over 5, it detected precursors of future earthquakes with an average accuracy of 98.41% and a specificity of 99.02%. Furthermore, for strong earthquakes with magnitudes of over 5, early warning signals were identified an average of 6.23 days before the earthquake when based on daily GNSS data, and an average of 5.75 hours before the earthquake when based on 5-minute seismic waveform records.

[0090] As shown in Table 1, this verification showed that both TPR (True Positive Rate) and FPR (False Positive Rate) can stably detect signs of an earthquake, especially for strong earthquakes of magnitude 5 or greater.

[0091] Table 2 compares existing methods (M1 to M10) with the technology of the present disclosure for detecting precursors of earthquakes occurring in the same areas as those in Table 1. Table 2

[0092] The existing methods listed in Table 2 are as follows: Method 1 (M1): A real-time outlier detection method based on a window-based forecasting model. Method 2 (M2): A supervised machine learning algorithm for GNSS positioning time series forecasting. Method 3 (M3): A method based on the randomness of outliers in GPS time series. Method 4 (M4): The GPS Interactive Time Series Analysis (GITSA) software program developed for visualization and analysis of GPS time series in geodesy and geodynamics research. Method 5 (M5): An artificial neural network (ANN) for earthquake warning using real-time GNSS data. Method 6 (M6): A deep learning algorithm called WANEH. This method detects anomalies in time series data by combining wavelets with neural networks and Hilbert transforms. Method 7 (M7): A method based on martingale theory to extract anomalies from continuous GPS data as precursors to earthquakes. Method 8 (M8): A graphical method for detecting outliers in routine measurement time series data. Method 9 (M9): Support Vector Regression (SVR), a supervised machine learning algorithm. Method 10 (M10): Delayed Long Short-Term Memory (dLSTM), an anomaly detection method for time series data.

[0093] As can be seen from Table 2, the technology disclosed herein can detect signs of an earthquake with higher accuracy than existing earthquake prediction methods.

[0094] [Integration of Disease Prevention and Pre-Disease Medical Science] One notable effect expected to be achieved by this technology is the integration of disease prevention and pre-disease medical science. FIG. 10 is a schematic diagram illustrating the definition of pre-disease. The top panel shows the conventional definition of pre-disease, while the bottom panel shows the definition of pre-disease as disclosed herein. Conventionally, the pre-disease state has been considered to exist between the healthy state and the diseased state, but the exact timing of the pre-disease state has not always been clear. In contrast, the present disclosure collects data from the period leading up to the pre-disease state, thereby accurately capturing the signs of the transition from the healthy state to the pre-disease state. This enables the integration of ultra-early disease prediction and prevention (i.e., extending healthy lifespan and preventing disease, with the ability to detect deviations from the healthy state through prediction error analysis) with DNB theory (i.e., discovering the pre-disease state on the time axis from the healthy state to the diseased state) (DNB theory; see, for example, Non-Patent Document 10).

[0095] FIG. 11 is a schematic diagram showing the integration of DNB theory analysis and prediction theory analysis. Both DNB theory analysis and prediction theory analysis collect multivariate measurement big data by measuring biological systems. However, DNB theory analysis detects signs of state transitions through fluctuation analysis, which allows for pre-disease detection. On the other hand, prediction theory analysis (i.e., spatiotemporal information transformation learning) detects signs of deviation from a healthy state through prediction error analysis, which enables early disease prediction and prevention. By integrating DNB theory analysis and prediction theory analysis, the technology disclosed herein paves the way for ultra-early disease prediction and prevention, which was previously unrealizable.

[0096] The present invention has been described above based on the embodiments. These embodiments are merely examples, and it will be understood by those skilled in the art that various modifications are possible in the combination of each component and each treatment process, and that such modifications are also within the scope of the present invention.

[0097] When understanding the abstract technical ideas of the embodiments and modifications, the technical ideas should not be interpreted as being limited to the contents of the embodiments and modifications. The above-described embodiments and modifications are merely illustrative examples, and many design modifications, such as changes, additions, and deletions of components, are possible. In the embodiments, the contents in which such design modifications are possible are emphasized by adding the notation "embodiment." However, design modifications are also permitted even in contents without such notation.

[0098] The technology disclosed herein can be used for predictions in a wide range of natural and social fields, such as earthquake prediction, early detection and treatment of diseases, development of new drugs, development of medical equipment, prediction of traffic congestion, prediction of sudden climate changes, prediction of stock price fluctuations, and prediction of political upheaval.

[0099] 1. Sign detection device; 10. Acquisition unit; 20. Prediction error analysis unit; 30. Fluctuation analysis unit; 40. Sign detection unit; S10. Acquisition step; S20. Prediction error analysis step; S30. Fluctuation analysis step; S40. Sign detection step.

Claims

1. An indication detection device for detecting indications of a transition in the state of an object, comprising: an acquisition unit for acquiring spatio-temporal data of a multidimensional variable indicating the state of the object; a prediction error analysis unit for estimating a deviation between a predicted value and an actual measured value of temporal data in the spatio-temporal data; a fluctuation analysis unit for estimating fluctuations in the spatio-temporal data; and an indication detection unit, wherein the prediction error analysis unit calculates the predicted value by converting the spatio-temporal data of the multidimensional variable into temporal data of a target variable, which is a variable of the object to be predicted by the indication detection device, and estimates the deviation between the predicted value and the actual measured value, the fluctuation analysis unit calculates the fluctuation of the state of the object by fluctuation analysis using the spatio-temporal data, and the indication detection unit detects that the object has an indication of a state transition when the deviation estimated by the prediction error analysis unit exceeds a predetermined first threshold and the fluctuation estimated by the fluctuation analysis unit exceeds a predetermined second threshold.

2. The symptom detection device according to claim 1, characterized in that the transformation from the spatio-temporal data to the temporal data of the target variable is a transformation by embedding in a non-time-delay coordinate space or by embedding in a time-delay coordinate space.

3. The symptom detection device according to claim 2, characterized in that the conversion from the spatiotemporal data to the time data of the target variable is calculated using machine learning.

4. The symptom detection device according to claim 1, characterized in that the fluctuation analysis unit calculates the fluctuation of the state of the target by converting the spatio-temporal data into time data of a virtual variable based on the spatio-temporal data.

5. The symptom detection device according to claim 4, wherein the virtual variables are data representing the movement of the state of the target on a central manifold.

6. The symptom detection device according to claim 1, characterized in that the fluctuation analysis unit estimates the fluctuation of the spatio-temporal data using a dynamic network marker.

7. The symptom detection device according to claim 6, characterized in that the fluctuation analysis section calculates the fluctuation when the deviation estimated by the prediction error analysis section exceeds a predetermined first threshold value.

8. The symptom detection device according to claim 1, characterized in that the target state transition is the occurrence of an earthquake.

9. The sign detection device according to claim 1, characterized in that the sign of a transition in the subject's state is the occurrence of a pre-disease state, which is a state in which a healthy state transitions to a diseased state.

10. The transformation from the non-time-dilated coordinate space to the time-dilated coordinate space is ｔ is a vector at time t in the non-delay coordinate space, V ｔ is a vector at time t in the time-delay coordinate space, Φ and Ψ are nonlinear transformations, and I is an identity transformation. ｔ ) = V ｔ Z ｔ = Ψ (V ｔ 4. The symptom detection device according to claim 3, wherein the magnitude of the difference between the magnitude of the impulse response and the impulse response is expressed as follows: Φ·Ψ=I.

11. The transformation from the non-time-delay coordinate space to the time-delay coordinate space is expressed as follows: PF(Z ｔ ) = V ｔ F (Z ｔ ) = QV ｔ 11. The symptom detection device according to claim 10, wherein PQ is expressed as E.

12. A sign detection method for detecting signs of a transition in the state of an object, comprising: an acquisition step of acquiring spatio-temporal data of a multidimensional variable indicating the state of the object; a prediction error analysis step of estimating a deviation between a predicted value and an actual measured value of time data in the spatio-temporal data; a fluctuation analysis step of estimating fluctuations in the spatio-temporal data; and a sign detection step, wherein the prediction error analysis step calculates the predicted value by converting the spatio-temporal data of the multidimensional variable into time data of a target variable, which is a variable of the object to be predicted by the sign detection method, and estimates the deviation between the predicted value and the actual measured value; the fluctuation analysis step calculates fluctuations in the state of the object by fluctuation analysis using the spatio-temporal data; and the sign detection step detects that the object has a sign of a state transition when the deviation estimated in the prediction error analysis step exceeds a predetermined first threshold and the fluctuation estimated in the fluctuation analysis step exceeds a predetermined second threshold.

13. A program for causing a computer to execute a method for detecting signs of a transition in the state of an object, comprising: an acquisition step of acquiring spatio-temporal data of multidimensional variables indicating the state of the object; a prediction error analysis step of estimating a deviation between a predicted value and an actual measured value of time data in the spatio-temporal data; a fluctuation analysis step of estimating fluctuations based on the spatio-temporal data; and an indication detection step, wherein the prediction error analysis step calculates the predicted value by converting the spatio-temporal data of the multidimensional variable into time data of a target variable, which is a variable of the object to be predicted by the program, and estimates the deviation between the predicted value and the actual measured value; the fluctuation analysis step calculates fluctuations in the state of the object by fluctuation analysis using the spatio-temporal data; and the indication detection step detects that the object has a sign of a state transition when the deviation estimated in the prediction error analysis step exceeds a predetermined first threshold and the fluctuation estimated in the fluctuation analysis step exceeds a predetermined second threshold.

14. A recording medium having recorded thereon a program for causing a computer to execute a method for detecting a sign of a transition in the state of an object, the program comprising: an acquisition step of acquiring spatio-temporal data of a multidimensional variable indicating the state of the object; a prediction error analysis step of estimating a deviation between a predicted value and an actual measured value of time data in the spatio-temporal data; a fluctuation analysis step of estimating a fluctuation based on the spatio-temporal data; and an indication detection step, wherein the prediction error analysis step calculates the predicted value by converting the spatio-temporal data of the multidimensional variable into time data of a target variable which is a variable of the object to be predicted by the program, and estimates the deviation between the predicted value and the actual measured value; the fluctuation analysis step calculates the fluctuation of the state of the object by fluctuation analysis using the spatio-temporal data; and the indication detection step detects that the object has a sign of a state transition when the deviation estimated in the prediction error analysis step exceeds a predetermined first threshold value and the fluctuation estimated in the fluctuation analysis step exceeds a predetermined second threshold value.

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