CN116187443B - Causal strength detection method and detection device based on multidimensional symbol dynamics - Google Patents
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Abstract
The invention relates to the technical field of data processing, in particular to a causal strength detection method and device based on multidimensional symbol dynamics. The causal strength detection method comprises the steps of firstly constructing attractors in a phase space according to a time sequence, then calculating nearest neighbors of the element points based on a Manhattan distance calculation method aiming at each element point in the attractors, calculating a first mode corresponding to each nearest neighbor, carrying out average processing on the first modes of all the nearest neighbors of each element point to obtain an average mode of each element point, obtaining a real average mode and a predicted average mode of each element point according to the average mode, and calculating causal strength values according to the real average mode and the predicted average mode. The causal strength detection method can improve the detection efficiency of causal strength values.
Description
Technical Field
The invention relates to the technical field of data processing, in particular to a causal strength detection method and device based on multidimensional symbol dynamics.
Background
The prior art includes methods for detecting causal relationships between variables, which can be mainly classified into qualitative process models and data-driven models. Qualitative process methods such as directed graph-based models typically require domain knowledge of an expert to represent the causal relationships, however, knowledge acquisition and causal relationship determination are very difficult and time consuming. Therefore, the data-driven method is widely used.
The prior art graininess causality check is considered one of the earliest data-driven causality detection methods. In the gland causal relationship test, if the prediction accuracy of one variable can be improved by combining the information of another variable, there is a causal relationship between the two variables. However, the lanjie causal relationship test is usually based on a linear regression model for causal relationship detection, requiring that the variables detected are independent of each other. Therefore, it cannot function in complex nonlinear systems with coupled variables and therefore has poor applicability.
Another detection method in the prior art is a causal relation detection method of transfer entropy proposed based on the concept of information entropy, and the method characterizes the causal relation between two variables by detecting that one variable reduces the uncertainty of the other variable. The method is suitable for linear and nonlinear systems, is sensitive to parameter changes, and cannot be normally detected when the parameter exceeds a certain range. In addition, the transfer entropy causality detection method has very high computational complexity and large time consumption in implementation, so the detection effect is low.
Another causality detection method in the prior art is a convergence cross mapping algorithm, and the method can detect causality in a complex nonlinear system with coupling and is widely applied in various fields. However, the converged cross-mapping algorithm intelligently detects whether a causal relationship exists, and cannot verify the causal type and causal strength.
It can be seen that the detection methods in the prior art have certain technical defects and have a large room for improvement.
Disclosure of Invention
The invention provides a causal strength detection method and a causal strength detection device based on multidimensional symbol dynamics, which are used for solving the technical problem of low detection efficiency of the detection method in the prior art.
The invention provides a causal strength detection method based on multidimensional symbol dynamics, which comprises the following steps:
Constructing attractors in the phase space according to the time sequence;
Calculating nearest neighbors of the element points based on a Manhattan distance calculation method aiming at each element point in the attractor, calculating a first mode corresponding to each nearest neighbor, carrying out average processing on the first modes of all nearest neighbors of each element point to obtain an average mode of each element point, and obtaining a real average mode and a predicted average mode of each element point according to the average mode;
and calculating a causal intensity value according to the real average mode and the predicted average mode.
According to the causal strength detection method based on multidimensional symbol dynamics, the causal strength detection method further comprises the following steps of:
And filling the causal intensity values into a multi-dimensional mode matrix to obtain a causal intensity distribution map.
According to the causal strength detection method based on multidimensional symbol dynamics, the causal strength detection method further comprises the following steps before constructing attractors in a phase space according to a time sequence: environmental information affecting the causal relationship is quantized to the time series.
According to the causal intensity detection method based on multidimensional symbol dynamics, the attractor in the phase space is constructed according to a time sequence, and the causal intensity detection method comprises the following steps:
and constructing attractors in the phase space along three coordinate axis directions of the phase space through the time sequence and the time delay.
The causal strength detection method based on multidimensional symbol dynamics provided by the invention further comprises the following steps: and determining a causal type from the causal intensity value, wherein the causal type comprises a positive causal, a negative causal and a dark causal.
The invention also provides a causal strength detection device based on multidimensional symbol dynamics, which comprises:
a first processing unit for constructing attractors in a phase space according to a time sequence;
The second processing unit is used for calculating nearest neighbors of the element points based on a Manhattan distance calculation method aiming at each element point in the attractor, calculating a first mode corresponding to each nearest neighbor, carrying out average processing on the first modes of all nearest neighbors of each element point to obtain an average mode of each element point, and obtaining a real average mode and a predicted average mode of each element point according to the average modes;
And the third processing unit is used for calculating a causal strength value according to the real average mode and the prediction average mode.
According to the causal strength detection device based on multidimensional symbol dynamics provided by the invention, the causal strength detection device further comprises:
And a fourth processing unit, configured to fill the causal intensity value into a multidimensional pattern matrix after obtaining the causal intensity value, and obtain a causal intensity distribution map.
According to the causal strength detection device based on multidimensional symbol dynamics provided by the invention, the causal strength detection device further comprises:
a quantization unit for quantizing the environmental information affecting the causal relationship into a time series before constructing the attractors in the phase space from said time series.
According to the causal strength detection device based on multidimensional symbol dynamics provided by the invention, the causal strength detection device further comprises:
a fifth processing unit for determining a causal type from the causal intensity value, the causal type comprising a dark causal and a bright causal.
The invention also provides a computer program product comprising a computer program which when executed by a processor implements a causal strength detection method based on multidimensional symbol dynamics as defined in any one of the above.
According to the causal strength detection method based on multidimensional symbol dynamics, attractors in a phase space are firstly constructed according to a time sequence, then nearest neighbors of the element points are calculated according to a Manhattan distance calculation method aiming at each element point in the attractors, a first mode corresponding to each nearest neighbor is calculated, the first modes of all nearest neighbors of each element point are subjected to average processing to obtain an average mode of each element point, a real average mode and a predicted average mode of each element point are obtained according to the average mode, and causal strength values are calculated according to the real average mode and the predicted average mode. The causal strength detection method can improve the detection efficiency of causal strength values.
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In order to more clearly illustrate the invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a causal strength detection method based on multidimensional symbolic dynamics according to an embodiment of the present invention;
FIG. 2 is a second flow chart of a causal strength detection method based on multidimensional symbolic dynamics according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a multi-dimensional pattern matrix according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a causal strength detection device based on multidimensional symbolic dynamics according to an embodiment of the present invention;
Fig. 5 is a schematic diagram of an entity structure of an electronic device according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The application applies symbol dynamics to causal intensity detection, and provides a set of methods for separating and calculating different causal modes of a complex system based on traditional phase space reconstruction, wherein the method defines three causal modes: positive causality, negative causality, and dark causality, positive causality representing the promotion of one variable to another, negative causality representing the inhibition, and dark causality representing the fuzzy causality. The mode causal detection method can detect the type and intensity of causal relation of two variables.
However, in real scenes, causal relationships are closely linked to the external environment, e.g. soil moisture affects predator-prey interactions in the soil animal community, population migration contributes to the spread of Covid-19, but the spread efficiency is different in winter and summer. The general causal detection algorithm can only detect the causal relation between a pair of time sequences, and cannot be used for carrying out fine-grained characterization on the causal relation strength by combining environmental factors.
The invention provides a causal strength detection method based on multi-dimensional symbol dynamics based on the influence of environmental factors on causal strength, which comprises the steps of firstly constructing attractors in a phase space according to a time sequence, then calculating nearest neighbors of element points based on a Manhattan distance calculation method aiming at each element point in the attractors, calculating a first mode corresponding to each nearest neighbor, weighting and summing the first modes of all nearest neighbors of each element point by using the Manhattan distance, and symbolizing to obtain a real average mode of each element point, wherein a predicted average mode calculated by the real average mode, and the percentage of the predicted average mode consistent with the real average mode are causal strength. The causal strength detection method can improve the detection efficiency of causal strength values and has stronger applicability.
In embodiments of the present invention, "at least one" means one or more, and "a plurality" means two or more. "and/or", describes an association relationship of an association object, and indicates that there may be three relationships, for example, a and/or B, and may indicate: there are three cases, a alone, a and B together, and B alone, wherein a, B may be singular or plural. In the text description of the present invention, the character "/" generally indicates that the front-rear associated object is an or relationship.
The causal strength detection method based on multidimensional symbol dynamics provided by the invention will be described in detail by the following several specific examples. It is to be understood that the following embodiments may be combined with each other and that some embodiments may not be repeated for the same or similar concepts or processes.
Fig. 1 is a schematic flow chart of a causal strength detection method based on multi-dimensional symbol dynamics according to an embodiment of the present invention, and fig. 2 is a second schematic flow chart of a causal strength detection method based on multi-dimensional symbol dynamics according to an embodiment of the present invention, where the causal strength detection method based on multi-dimensional symbol dynamics may be executed by software and/or hardware devices. The hardware device may be an embedded device, or a personal computer, or a server, for example. For example, referring to fig. 1, the causal intensity detection method based on multidimensional symbol dynamics may include:
s101, constructing an attractor in a phase space according to a time sequence.
Illustratively, prior to constructing the attractor in the phase space from the time series, further comprising: environmental information affecting the causal relationship is quantified as a time series, such as temperature, humidity, solar intensity, etc., measured at intervals. In other words, in this embodiment, the environment information is quantized into a time series, and the time series is converted into a multi-dimensional symbol pattern by using the method of reconstructing the attractor by using the time series delay, so as to perform causal detection based on the multi-dimensional symbol pattern.
The general time sequence is mainly studied in the time domain, and for the chaotic time sequence, the establishment and the prediction of a chaotic model are carried out in a phase space, and the phase space reconstruction is an important step in the chaotic time sequence processing. This example constructs the attractor by time-series delay.
For example, in this embodiment, causal strength under environmental influence is detected based on multidimensional symbol dynamics, and attractor reconstruction is performed based on three time sequences, so as to obtain M x、My、Mz. Specifically, assuming that the time sequence of the power system M map is { X (i): i=1, 2..n }, the present invention reconstructs an E-dimensional attractor M x from the time sequence and the time delay τ, the time delay vector is as follows:
x(t)＝<X(t),X(t-τ),...,X(t-(E-1)τ)> (1)
Similarly, the delay vectors of attractors M y and M z are the following formulas (2) and (3):
y(t)＝<Y(t),Y(t-τ),...,Y(t-(E-1)τ)> (2)
z(t)＝<Z(t),Z(t-τ),...,Z(t-(E-1)τ)> (3)
subsequently, a causal relationship test of Y to X under the influence of Z will be described as an example.
S102, calculating nearest neighbors of the element points based on a Manhattan distance calculation method aiming at each element point y (t) in the attractor M y, calculating a first mode corresponding to each nearest neighbor, weighting and summing the first modes of all nearest neighbors of each element point by using the Manhattan distance, and symbolizing to obtain a real average mode of each element point y (t), and obtaining a real average mode of z (t) and x (t) in the same way. And then calculating a prediction average mode of x (t) based on the real average modes of z (t) and y (t), wherein the percentage of the prediction average mode of x (t) consistent with the real average mode is causal strength.
For example, for each element point y (t) in attractor M y, the following process is performed:
In order to equally treat each point of the attractor, the invention uses Manhattan distance (MANHATTAN DISTANCE) to calculate the distance between two points, and the formula is as follows:
In the formula (4), y (t 1) and y (t 2) respectively represent any two points, and for each point in the E-dimensional attractor, there are e+1 nearest neighbors. The first mode calculation formula for each nearest neighbor is as follows:
wherein,
The true average pattern calculation method for y (t) is as follows:
Py(t)＝signature(Sy(t))(7)
Wherein:
Wherein d is the Manhattan distance, The first pattern for each nearest neighbor.
The defining method of the modes is shown in formulas (10) and (11), and the arrow combinations in different directions represent different modes:
When e=2, the number of the cells,
When e=3, the number of the cells is,
The following describes the calculation method of the average pattern signature: let y (t) have 4 nearest neighbors as shown below when e=3:
The first pattern of four nearest neighbors s 1,s2,s3,s4 is assumed as follows:
the calculation method of the average pattern is as shown in formula 11:
the true average pattern of x (t), z (t) is similarly available.
To calculate causal intensities under the influence of { Z } from { Y } to { X }, the present embodiment defines a K+1-dimensional pattern multidimensional pattern as follows:
The average pattern of x (t) under the influence of { Z } is predicted by P yz The formula is as follows:
wherein,
Same theory can calculate
By the method, the real average mode and the prediction average mode of each adjacent point in the attractor M x can be obtained, and the real average mode and the prediction average mode can reflect the causal relationship of { Y } on { Y } under the influence of { Z }.
S103, calculating a causal strength value according to the real average mode and the prediction average mode.
Optionally, after calculating the calculated causal intensity value, determining a causal type from the causal intensity value, the causal type including positive causal, negative causal, and dark causal.
Illustratively, a predictive average pattern is calculated for each pointAnd the real average mode P xz(t), wherein the percentage of the predicted average mode consistent with the real average mode is the intensity of the current mode. By filling in the cause and effect pattern matrix (fig. 3 when e=1) in this process.
Calculating the causal relationship and intensity of the { Y } and the { X } under different modes according to the following formula (20) by calculating Z by the method, wherein the formula is as follows:
Where erf is the error extrusion function.
FIG. 3 is a schematic diagram of a multi-dimensional pattern matrix provided in an embodiment of the present invention, and optionally, after calculating the causal relationship and intensity of { X } and { Y }, the multi-dimensional pattern matrix shown in FIG. 3 is constructed according to the causal relationship and intensity, and different color depths in the matrix represent the mean value of causal intensities of Z in different patterns. For example, different color depths represent the mean of the positive causal intensity, the mean of the negative causal intensity, and the mean of the dark causal intensity of Z in different modes, respectively.
The causal intensity uses the mean of the causal intensity of the principal diagonal:
negative causal intensity uses the average of the anti-diagonal causal intensities:
The average value of the other areas is the dark causal intensity.
Aiming at scenes (such as an ecological system and a social system) with great influence on states of components and relationships among the components and complex and changeable environments, the embodiment is not limited to causal relationship detection of two time sequences, but adds an environment time sequence, codes the environment time sequence into a multidimensional mode and realizes fine-granularity causal strength detection along with environmental changes. The embodiment can obtain the relation between the causal strength change and the environmental change, and has better interpretability. In addition, the embodiment is inspired by symbol dynamics, and the time sequence wave is symbolized, so that the stability of the method of the embodiment is enhanced, and noise interference can be effectively treated.
The causal strength detection device based on multi-dimensional symbol dynamics provided by the invention is described below, and the causal strength detection device based on multi-dimensional symbol dynamics described below and the causal strength detection method based on multi-dimensional symbol dynamics described above can be correspondingly referred to each other.
FIG. 4 is a schematic structural diagram of a causal strength detection device based on multi-dimensional symbolic dynamics according to an embodiment of the present invention, for example, please refer to FIG. 4, the causal strength detection device 40 based on multi-dimensional symbolic dynamics may include:
a first processing unit 401 for constructing attractors in a phase space according to a time sequence.
The second processing unit 402 is configured to calculate, for each element point in the attractor, a nearest neighbor point of the element point based on a manhattan distance calculation method, calculate a first mode corresponding to each nearest neighbor point, perform an average process on the first modes of all nearest neighbors of each element point, obtain an average mode of each element point, and obtain a real average mode and a predicted average mode of each element point according to the average mode.
A third processing unit 403 for calculating a causal intensity value based on the real average pattern and the predicted average pattern.
Optionally, the causal intensity detection device 40 based on multidimensional symbol dynamics further comprises:
And a fourth processing unit, configured to fill the causal intensity values into the multidimensional pattern matrix after the causal intensity values are obtained, and obtain a causal intensity distribution map.
Optionally, the causal intensity detection device 40 based on multidimensional symbol dynamics further comprises:
a quantization unit for quantizing the environmental information affecting the causal relationship into a time series before constructing the attractors in the phase space from the time series.
Optionally, the causal intensity detection device 40 based on multidimensional symbol dynamics further comprises:
A fifth processing unit for determining a causal type from the causal intensity value, the causal type comprising a positive causal, a negative causal and a dark causal.
The causal strength detection device 40 provided in the embodiment of the present invention may implement the technical scheme of the causal strength detection method based on multi-dimensional symbol dynamics in any of the above embodiments, and its implementation principle and beneficial effects are similar to those of the causal strength detection method based on multi-dimensional symbol dynamics, and may refer to the implementation principle and beneficial effects of the causal strength detection method based on multi-dimensional symbol dynamics, which will not be described herein.
Fig. 5 is a schematic entity structure diagram of an electronic device according to an embodiment of the present invention, where, as shown in fig. 5, the electronic device may include: processor (processor) 501, communication interface (Communications Interface) 502, memory (memory) 503, and communication bus 504, wherein processor 501, communication interface 502, memory 503 complete communication with each other through communication bus 504. The processor 501 may invoke logic instructions in the memory 503 to perform a causal strength detection method based on multidimensional symbolic dynamics, the method comprising: constructing attractors in the phase space according to the time sequence; calculating nearest neighbors of the element points based on a Manhattan distance calculation method aiming at each element point in the attractor, calculating a first mode corresponding to each nearest neighbor, carrying out average processing on the first modes of all nearest neighbors of each element point to obtain an average mode of each element point, and obtaining a real average mode and a predicted average mode of each element point according to the average mode; and calculating a causal intensity value according to the real average mode and the predicted average mode.
Further, the logic instructions in the memory 503 described above may be implemented in the form of software functional units and may be stored in a computer readable storage medium when sold or used as a stand alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
In another aspect, the present invention also provides a computer program product comprising a computer program, the computer program being storable on a non-transitory computer readable storage medium, the computer program, when executed by a processor, being capable of performing the causal strength detection method based on multidimensional symbol dynamics provided by the methods described above, the method comprising: constructing attractors in the phase space according to the time sequence; calculating nearest neighbors of the element points based on a Manhattan distance calculation method aiming at each element point in the attractor, calculating a first mode corresponding to each nearest neighbor, carrying out average processing on the first modes of all nearest neighbors of each element point to obtain an average mode of each element point, and obtaining a real average mode and a predicted average mode of each element point according to the average mode; and calculating a causal intensity value according to the real average mode and the predicted average mode.
In yet another aspect, the present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, is implemented to perform the method of causal strength detection based on multidimensional symbol dynamics provided by the methods described above, the method comprising: constructing attractors in the phase space according to the time sequence; calculating nearest neighbors of the element points based on a Manhattan distance calculation method aiming at each element point in the attractor, calculating a first mode corresponding to each nearest neighbor, carrying out average processing on the first modes of all nearest neighbors of each element point to obtain an average mode of each element point, and obtaining a real average mode and a predicted average mode of each element point according to the average mode; and calculating a causal intensity value according to the real average mode and the predicted average mode.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (7)
1. A causal intensity detection method based on multidimensional symbol dynamics, comprising:
constructing attractors in a phase space along three coordinate axis directions of the phase space through time sequences and time delays, wherein the number of the attractors is three;
calculating nearest neighbors of the element points based on a Manhattan distance calculation method aiming at each element point in the attractor, calculating a first mode corresponding to each nearest neighbor, carrying out weighted summation on the first modes of all nearest neighbors of each element point by using Manhattan distances, and carrying out symbolization to obtain a real average mode of each element point;
determining a predicted average mode of the element points in the current attractor based on the real average modes of the element points of at least two other attractors for the element points in any attractor; determining the percentage of the consistency of the predicted average mode of the element points in the current attractor and the real average mode of the element points in the current attractor as the causal intensity value of the element points in the current attractor;
Wherein prior to constructing the attractor in the phase space from the time series, further comprises: environmental information affecting the causal relationship is quantized to the time series.
2. The causal intensity detection method based on multidimensional symbolic dynamics according to claim 1, further comprising, after deriving the causal intensity value:
And filling the causal intensity values into a multi-dimensional mode matrix to obtain a causal intensity distribution map.
3. The multi-dimensional symbol dynamics-based causal strength detection method of claim 1, further comprising: and determining a causal type from the causal intensity value, wherein the causal type comprises a positive causal, a negative causal and a dark causal.
4. A causal intensity detection device based on multidimensional symbol dynamics, comprising:
The first processing unit is used for constructing attractors in a phase space along three coordinate axis directions of the phase space through time sequences and time delays, and the number of the attractors is three;
The second processing unit is used for calculating nearest neighbors of the element points based on a Manhattan distance calculation method aiming at each element point in the attractor, calculating a first mode corresponding to each nearest neighbor, carrying out weighted summation on the first modes of all nearest neighbors of each element point by using Manhattan distances, and carrying out symbolization to obtain a real average mode of each element point;
The third processing unit is used for determining a prediction average mode of the element points in the current attractor based on the real average modes of the element points of at least two other attractors aiming at the element points in any attractor; determining the percentage of the consistency of the predicted average mode of the element points in the current attractor and the real average mode of the element points in the current attractor as the causal intensity value of the element points in the current attractor;
the causal strength detection device further comprises:
a quantization unit for quantizing the environmental information affecting the causal relationship into a time series before constructing the attractors in the phase space from said time series.
5. The multi-dimensional symbol dynamics-based causal strength detection device of claim 4, further comprising:
And a fourth processing unit, configured to fill the causal intensity value into a multidimensional pattern matrix after obtaining the causal intensity value, and obtain a causal intensity distribution map.
6. The multi-dimensional symbol dynamics-based causal strength detection device of claim 4, further comprising:
a fifth processing unit for determining a causal type from the causal intensity value, the causal type comprising a dark causal and a bright causal.
7. A computer program product comprising a computer program which, when executed by a processor, implements a causal strength detection method based on multidimensional symbol dynamics as claimed in any one of claims 1 to 3.
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| JPH0844699A (en) * | 1994-07-29 | 1996-02-16 | Meidensha Corp | Nonlinear time-series data predicting device |
| CN109886409A (en) * | 2019-02-15 | 2019-06-14 | 南京信息工程大学 | A kind of quantitative causality determination method of multidimensional time-series |
| CN114036736A (en) * | 2021-11-05 | 2022-02-11 | 大连理工大学 | Cause and effect network learning method based on local granger cause and effect analysis |
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