CN111539155B - Phenomenon-oriented time-space correlation mode analysis and visualization method - Google Patents

Phenomenon-oriented time-space correlation mode analysis and visualization method Download PDF

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CN111539155B
CN111539155B CN202010314044.7A CN202010314044A CN111539155B CN 111539155 B CN111539155 B CN 111539155B CN 202010314044 A CN202010314044 A CN 202010314044A CN 111539155 B CN111539155 B CN 111539155B
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CN111539155A (en
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李小和
孙建成
屈展
王萍
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Xian Shiyou University
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Abstract

A phenomenon-oriented time-space correlation mode analysis and visualization method comprises the steps of firstly dividing a time-space sequence into a plurality of time regions along the time direction, extracting characteristics of each time region, then utilizing the extracted characteristics and corresponding phenomenon data to carry out model solution by adopting a linear support vector machine, and finally realizing micro visualization and macro visualization according to the solved model; by the method, the invention can explore the mode or knowledge related to the specific phenomenon in the spatio-temporal data and present the mode or knowledge in an intuitive and easily understood form by a graphical method.

Description

Phenomenon-oriented time-space correlation mode analysis and visualization method
Technical Field
The invention belongs to the technical field of machine learning and pattern recognition, and particularly relates to a phenomenon-oriented spatiotemporal correlation pattern analysis and visualization method.
Technical Field
Spatio-temporal data generally includes three elements, spatial location information, temporal information, and variables describing real-world phenomena. To explore the regularity of spatio-temporal data, meaningful knowledge or patterns need to be obtained from the measured data. In many cases, data visualization can be an effective means of exploring knowledge or patterns from highly dynamic and continuous spatiotemporal data.
Exploiting the knowledge implicit in spatiotemporal data is beneficial from the point of view. From this perspective, data visualization may take two forms: and (4) representing and exploring. The data is displayed in an intuitive way based on the visualization of the representation, and the answer "what" can be answered. For example, what is the rainfall variation in different regions, months or years? The answer "what" is typically the first step in analyzing the data. The next step is to answer "why", which is what the exploration-based visualization can answer. Visual analytics has become an important method of understanding and insights into large complex data sets over the past decade. Visual analytics focus on analytical reasoning through an interactive visual interface. This is a dynamic, iterative process in which the answer to "what" and "why" behind the data can be found. The visualization method is widely applied to space-time data analysis.
The first law in Tobler geography holds that "everything is related, except that nearby things are more closely related". Researchers comprehensively consider time and space position factors and carry out deeper research on the time and space data analysis and visualization method. However, sometimes we need to mine, explore, etc. patterns or knowledge implied in spatio-temporal data related to a particular phenomenon. The definition of "phenomenon" here depends on the field of application. For example, what weather conditions in a given area affect the rainfall in the given area over a given period of time, where "phenomenon" refers to rainfall in the given area; what is the relationship between the occurrence of tornadoes in one area and the weather in other areas? Here, the "phenomenon" refers to tornado. Therefore, when analyzing the spatio-temporal data sequence, the method is a problem worthy of exploration by combining with a specific phenomenon to research a phenomenon-oriented spatio-temporal data correlation mode analysis and visualization method.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a phenomenon-oriented space-time correlation mode analysis and visualization method. By the method, the mode or knowledge related to the specific phenomenon in the spatio-temporal data can be explored and presented in an intuitive and easily understood form through a graphical method.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a phenomenon-oriented spatio-temporal correlation mode analysis and visualization method comprises the following steps:
1. to analyze the length T, spatial position { s } i Multivariate spatio-temporal sequence of i =1,2, \8230;, M }
Figure BDA0002458805420000021
And visualizing the pattern or knowledge associated with the particular phenomenon, using a sliding window of length N to->
Figure BDA0002458805420000022
Sequence of divisions K time zones along the time direction into a sequence of->
Figure BDA0002458805420000023
Figure BDA0002458805420000031
In formula (1):
Figure BDA0002458805420000032
is t j Time of day, spatial position s i The measured data, Q is the number of measured variables;
Figure BDA0002458805420000033
in the formula (2):
Figure BDA0002458805420000034
for the k-th time region at spatial position s i The measured data of (a);
Figure BDA0002458805420000035
in formula (3):
Figure BDA0002458805420000036
for the kth time region t j Time of day at spatial position s i The measured data of (a);
2. feature extraction: from the sequence to the time region k
Figure BDA0002458805420000037
Extracting features
Figure BDA0002458805420000038
3. For the time region K (K =1,2, \ 8230;, K), the spatial position s i (i =1,2, \8230;, M) construct a vertical (4) regression model:
Figure BDA0002458805420000039
in formula (4): x is the input of the model;
4. selecting a regression model of the formula (4) as a linear regression, wherein the regression model is shown as the formula (5);
Figure BDA00024588054200000310
in formula (5): x is the input to the model and,
Figure BDA00024588054200000311
is a coefficient of the linear model>
Figure BDA00024588054200000312
p = M (M + 1)/2, b is a constant,<·>represents->
Figure BDA00024588054200000313
Dot product in space;
5. for input x k And an output
Figure BDA00024588054200000314
Solving the vector of the model formula (5) to obtain the vector of the formula (8) by adopting a linear support vector machine
Figure BDA00024588054200000315
Figure BDA00024588054200000316
Figure BDA00024588054200000317
In formula (7):
Figure BDA0002458805420000041
for the kth time region t j Time position s i (ii) phenomenon data of (iii);
Figure BDA0002458805420000042
in formula (8): alpha is alpha i,j And
Figure BDA0002458805420000043
is a spatial position s i Lagrange multipliers of the site model;
6. microscopic visualization: to spatial position s i Time region k, vector
Figure BDA0002458805420000044
Conversion to mxm symmetric matrix
Figure BDA0002458805420000045
Figure BDA0002458805420000046
The upper triangle of (a) is the vector->
Figure BDA0002458805420000047
The components are arranged line by line to obtain a set>
Figure BDA0002458805420000048
To a matrix>
Figure BDA0002458805420000049
M rows and n columns of elements, by spatial position s m And spatial position s n The connecting lines between the lines represent that the depth of the line color represents the size of a value, and the larger the value is, the darker the line color is, so that microscopic visualization is realized;
7. macroscopic visualization: symmetric matrix for time region K (K =1,2, \8230;, K)
Figure BDA00024588054200000410
According to the formula (9), the average value is->
Figure BDA00024588054200000411
Then according to equation (10), make a pair->
Figure BDA00024588054200000412
Vector based on the row sum shown in formula (11)>
Figure BDA00024588054200000413
According to>
Figure BDA00024588054200000414
The macroscopic visualization of the time region k can be realized by drawing the contour line;
Figure BDA00024588054200000415
Figure BDA00024588054200000416
in the formula (10), the compound represented by the formula (10),
Figure BDA00024588054200000417
is a matrix->
Figure BDA00024588054200000418
M rows and n columns of elements;
Figure BDA00024588054200000419
in the step two, in the characteristic extraction,
Figure BDA00024588054200000420
the calculation adopts the following specific steps:
first, using the distance metric g (-) a matrix is calculated according to equation (12)
Figure BDA00024588054200000421
M rows n columns elements>
Figure BDA00024588054200000422
Get MxM matrix>
Figure BDA00024588054200000423
Figure BDA00024588054200000424
In formula (12): the distance metric g (-) takes the euclidean distance;
secondly, utilizing a regularized graph Laplacian method, and performing the following steps according to equations (13) and (14)
Figure BDA00024588054200000425
Conversion into a symmetrical positive decision matrix->
Figure BDA0002458805420000051
Figure BDA0002458805420000052
Figure BDA0002458805420000053
In the formula (14), the regularization parameter lambda is more than 0, and I is an identity matrix;
thirdly, symmetrical positive definite matrix
Figure BDA0002458805420000054
The space is a Riemann manifold which is based on equation (15)>
Figure BDA0002458805420000055
Manifold from the location Riemann>
Figure BDA0002458805420000056
Mapping to £ er>
Figure BDA0002458805420000057
Inner reference point->
Figure BDA0002458805420000058
Is located in the cutting plane->
Figure BDA0002458805420000059
Inner point->
Figure BDA00024588054200000510
Figure BDA00024588054200000511
In formula (15): the logarithm operation of the matrix is to logarithm each element of the matrix;
the fourth step is to divide the M × M symmetric matrix according to equations (16) and (17)
Figure BDA00024588054200000512
Conversion into a vector>
Figure BDA00024588054200000513
p＝M(M+1)/2；/>
Figure BDA00024588054200000514
Figure BDA00024588054200000515
In formula (17): b i,j (i =1,2, \8230;, M; j =1,2, \8230;, M) is the i row and j column elements of an M by M symmetric matrix b.
The invention provides a visual analysis method for exploring space-time data, finding out relevant modes or knowledge between a specific spatial position of a specific phenomenon and other spatial positions, and presenting the relevant modes or knowledge in an intuitive and easily understood form. In the invention, the mining of relevant patterns in data is focused, and more importantly, the patterns related to specific phenomena are focused.
Drawings
Fig. 1 is a riemann manifold and tangent plane.
FIG. 2 is a visualization of spatiotemporal correlation patterns oriented to temperature phenomena.
FIG. 3 is a global mode visualization under temperature phenomena.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
A phenomenon-oriented spatio-temporal correlation mode analysis and visualization method comprises the following steps:
1. to analyze the spatial position { s } of length T i Multivariate spatio-temporal sequence of i =1,2, \8230;, M }
Figure BDA0002458805420000061
And visualizing the pattern associated with the particular phenomenon, using a sliding window of length N to->
Figure BDA0002458805420000062
Sequence of divisions K time zones along the time direction into a sequence of->
Figure BDA0002458805420000063
Figure BDA0002458805420000064
In formula (1):
Figure BDA0002458805420000065
is t j Time of day, spatial position s i The measured data, Q is the number of measured variables;
Figure BDA0002458805420000066
in formula (2):
Figure BDA0002458805420000067
for the k-th time region at spatial position s i The measured data of (a);
Figure BDA0002458805420000068
in formula (3):
Figure BDA0002458805420000069
for the kth time region t j Time of day at spatial position s i The measured data of (a);
2. characteristic extraction: from the sequence to the time region k
Figure BDA00024588054200000610
Extracting features
Figure BDA00024588054200000611
In the step two, in the characteristic extraction,
Figure BDA00024588054200000612
the calculation adopts the following specific steps:
first, a matrix is calculated according to equation (12) using the distance metric g (·)
Figure BDA00024588054200000613
M rows n columns elements>
Figure BDA00024588054200000614
Get the MxM matrix->
Figure BDA00024588054200000615
/>
Figure BDA00024588054200000616
In formula (12): the distance metric g (-) takes the euclidean distance;
secondly, utilizing a regularized graph Laplacian method, and performing the following steps according to equations (13) and (14)
Figure BDA0002458805420000071
Conversion into a symmetrical positive decision matrix>
Figure BDA0002458805420000072
Figure BDA0002458805420000073
Figure BDA0002458805420000074
In formula (14): the regularization parameter lambda is greater than 0, and I is an identity matrix;
thirdly, a symmetric positive definite matrix
Figure BDA0002458805420000075
The space is a Riemann manifold which is based on equation (15)>
Figure BDA0002458805420000076
Manifold from the location Riemann>
Figure BDA0002458805420000077
Mapping to £ er>
Figure BDA0002458805420000078
Internal reference point>
Figure BDA0002458805420000079
Is located in the cutting plane->
Figure BDA00024588054200000710
Inner point->
Figure BDA00024588054200000711
Figure BDA00024588054200000712
In formula (15): the logarithm operation of the matrix is to logarithm each element of the matrix.
Figure BDA00024588054200000713
And &>
Figure BDA00024588054200000714
The corresponding relationship between them is shown in fig. 1. In the figure, a dotted line γ is a geodesic distance, and a solid line is a euclidean distance;
fourthly, the M multiplied by M symmetric matrix is formed according to the formulas (16) and (17)
Figure BDA00024588054200000715
Conversion into a vector>
Figure BDA00024588054200000716
Figure BDA00024588054200000717
p＝M(M+1)/2；
Figure BDA00024588054200000718
Figure BDA00024588054200000719
In formula (17): b i,j (i =1,2, \8230;, M; j =1,2, \8230;, M) is the i row and j column elements of the M symmetric matrix b.
3. For the time region K (K =1,2, \ 8230;, K), the spatial position s i (i =1,2, \8230;, M) construct a vertical (4) regression model:
Figure BDA00024588054200000720
in formula (4): x is the input of the model;
4. selecting the regression model of formula (4) as a linear regression, as shown in formula (5):
Figure BDA0002458805420000081
in formula (5): x is the input of the model, vector
Figure BDA0002458805420000082
Is a coefficient of the linear model>
Figure BDA0002458805420000083
Figure BDA0002458805420000084
p = M (M + 1)/2, b is a constant term,<·>represents->
Figure BDA0002458805420000085
Dot product in space;
5. for input x k And an output
Figure BDA0002458805420000086
Solving the coefficient vector of the model formula (5) to the coefficient vector of the formula (8) by adopting a linear support vector machine
Figure BDA0002458805420000087
/>
Figure BDA0002458805420000088
Figure BDA0002458805420000089
In formula (7):
Figure BDA00024588054200000810
for the kth time region t j Time position s i (ii) phenomenon data of (iii);
Figure BDA00024588054200000811
in formula (8): alpha is alpha i,j And
Figure BDA00024588054200000812
is a spatial position s i Lagrange multipliers of the site model;
6. microscopic visualization: for spatial position s i Time region k, vector
Figure BDA00024588054200000813
Conversion to mxm symmetric matrix
Figure BDA00024588054200000814
Figure BDA00024588054200000815
The upper triangle of (a) is the vector->
Figure BDA00024588054200000816
The components are arranged line by line to obtain a set>
Figure BDA00024588054200000817
To a matrix>
Figure BDA00024588054200000818
M rows and n columns of elements, by spatial position s m And spatial position s n The connecting lines between the lines represent that the depth of the line color represents the size of a value, and the larger the value is, the darker the line color is, so that microscopic visualization is realized;
fig. 2 is a microscopic visualization of hourly meteorological data for 102 observatory stations in the united states in 2016. Selected characteristics are average temperature, total precipitation, total solar energy, average infrared surfaceTemperature and average relative humidity. Each observation station has 8768 sampling points, divided into 4 time zones. 4 observation points were selected for analysis. The phenomenon is the average temperature of the observation points. FIG. 2 contains 16 subgraphs, corresponding to
Figure BDA00024588054200000819
Except alaska and hawaii, each sub-graph against a map of the united states shows how the climate in the region of a circle affects the temperature of a square point in a given place. The shade of the spatial position connecting line indicates the matrix->
Figure BDA0002458805420000091
The dark color indicates that high temperatures are observed and the light color indicates low temperatures. In FIG. 2, for ease of illustration, the @isomitted>
Figure BDA0002458805420000092
The smaller absolute value of the component. Some important patterns can be found in fig. 2. For example, the high temperatures in most regions are highly correlated with some regions in the southwest; the temperature of some regions is associated with remote regions rather than adjacent regions (see the last two rows of fig. 2). These phenomena provide important information that can be used to help and guide us in revealing hidden rules behind the phenomena;
7. macroscopic visualization: symmetric matrix for time region K (K =1,2, \8230;, K)
Figure BDA0002458805420000093
Evaluation of the mean value according to formula (9)>
Figure BDA0002458805420000094
Then, according to equation (10), the matrix is +>
Figure BDA0002458805420000095
The sum by row results in the vector ≥ according to equation (11)>
Figure BDA0002458805420000096
According to>
Figure BDA0002458805420000097
Drawing contours enables macroscopic visualization of the time region K (K =1,2, \8230;, K);
Figure BDA0002458805420000098
Figure BDA0002458805420000099
in the formula (10), the compound represented by the formula (10),
Figure BDA00024588054200000910
is a matrix->
Figure BDA00024588054200000911
M rows and n columns of elements.
Figure BDA00024588054200000912
FIG. 3 is a macroscopic visualization, the graph being based on
Figure BDA00024588054200000913
Drawing a contour line. The year round data serves as a time region. In the figure, the black spot is the meteorological observation point, and is based on the weather>
Figure BDA00024588054200000914
Corresponding to the i-th observation point, the color gray scale represents->
Figure BDA00024588054200000915
Different values of (a). Different regions show different types of climate. Comparison with the U.S. Koppen climate type map shown in Wikipedia shows that under some typical climate conditions, such as hot desert climate in the southwest region, oceanic climate in the northwest pacific region, and wet subtropical climate in the southeast region, there is a high degree of unityCausing the disease. This consistency verifies the effectiveness of the method to some extent. Further, it is believed that more climate observers can obtain more detailed and meaningful results. />

Claims (2)

1. A phenomenon-oriented spatio-temporal correlation mode analysis and visualization method is characterized by comprising the following steps:
1. to analyze the length T, spatial position { s } i Multivariate spatio-temporal sequence of i =1,2, \8230;, M }
Figure FDA0002458805410000011
And visualizing the pattern or knowledge associated with the particular phenomenon, using a sliding window of length N to->
Figure FDA0002458805410000012
Sequence of divisions K time zones along the time direction into a sequence of->
Figure FDA0002458805410000013
Figure FDA0002458805410000014
In formula (1):
Figure FDA0002458805410000015
is t j Time of day, spatial position s i The measured data, Q is the number of measured variables;
Figure FDA0002458805410000016
in formula (2):
Figure FDA0002458805410000017
at spatial position s for the kth time region i Measurement ofData;
Figure FDA0002458805410000018
in formula (3):
Figure FDA0002458805410000019
for the kth time region t j Time of day at spatial position s j The measured data of (a);
2. feature extraction: from the sequence to the time region k
Figure FDA00024588054100000110
Extracting features
Figure FDA00024588054100000111
3. For the time region K (K =1,2, \ 8230;, K), the spatial position s i (i =1,2, \8230;, M) construct a vertical (4) regression model:
Figure FDA00024588054100000112
in formula (4):
Figure FDA00024588054100000113
is the input of the model;
4. selecting a regression model of the formula (4) as a linear regression, wherein the regression model is shown as the formula (5);
Figure FDA0002458805410000021
in formula (5): x is the input to the model and,
Figure FDA0002458805410000022
is a coefficient of the linear model>
Figure FDA0002458805410000023
p = M (M + 1)/2, b is a constant,<·>represents->
Figure FDA0002458805410000024
A dot product in space;
5. for input
Figure FDA0002458805410000025
Output->
Figure FDA0002458805410000026
Solving the vector of the model formula (5) to obtain the vector of the formula (8) by adopting a linear support vector machine
Figure FDA0002458805410000027
Figure FDA0002458805410000028
Figure FDA0002458805410000029
In formula (7):
Figure FDA00024588054100000210
for the kth time region t j Time position s i (ii) phenomenon data of (iii);
Figure FDA00024588054100000211
in formula (8): alpha is alpha i,j And
Figure FDA00024588054100000212
is a spatial position s i Lagrange multipliers of the site model; />
6. Microscopic visualization: for spatial position s i Time region k, vector
Figure FDA00024588054100000213
Symmetrical matrix which is converted into MxM->
Figure FDA00024588054100000214
The upper triangle of (a) is the vector->
Figure FDA00024588054100000215
The components are arranged line by line to obtain a set>
Figure FDA00024588054100000216
To the matrix->
Figure FDA00024588054100000217
M rows and n columns of elements, by spatial position s m And spatial position s n The connecting lines between the lines represent that the depth of the line color represents the size of a value, and the larger the value is, the darker the line color is, so that microscopic visualization is realized;
7. macroscopic visualization: symmetric matrix for time region K (K =1,2, \8230;, K)
Figure FDA00024588054100000218
Evaluation of the mean value according to formula (9)>
Figure FDA00024588054100000219
Then according to equation (10), make a pair->
Figure FDA00024588054100000220
The sum by row results in the vector ≥ according to equation (11)>
Figure FDA00024588054100000221
According to>
Figure FDA00024588054100000222
The macroscopic visualization of the time region k can be realized by drawing the contour line;
Figure FDA00024588054100000223
Figure FDA00024588054100000224
in the formula (10), the compound represented by the formula (10),
Figure FDA00024588054100000225
is a matrix->
Figure FDA00024588054100000226
M rows and n columns of elements;
Figure FDA0002458805410000031
2. the method of claim 1, wherein the spatiotemporal correlation pattern analysis and visualization is a spatiotemporal correlation model,
in the step two, in the characteristic extraction,
Figure FDA0002458805410000032
the calculation adopts the following specific steps:
first, a matrix is calculated according to equation (12) using the distance metric g (·)
Figure FDA0002458805410000033
M rows and n columns of elements->
Figure FDA0002458805410000034
Get the MxM matrix->
Figure FDA0002458805410000035
Figure FDA0002458805410000036
In formula (12): the distance metric g (-) takes the euclidean distance;
secondly, utilizing a regularized graph Laplacian method to convert the data into a normalized graph according to the formulas (13) and (14)
Figure FDA0002458805410000037
Conversion into symmetrical positive definite matrix
Figure FDA0002458805410000038
Figure FDA0002458805410000039
Figure FDA00024588054100000310
In the formula (14), the regularization parameter lambda is more than 0, and I is an identity matrix;
thirdly, symmetrical positive definite matrix
Figure FDA00024588054100000311
Is located in a space which is a Riemann manifold which combines +>
Figure FDA00024588054100000312
Manifold from the location Riemann>
Figure FDA00024588054100000313
Mapping to £ er>
Figure FDA00024588054100000314
Inner reference point->
Figure FDA00024588054100000315
Is located in the cutting plane->
Figure FDA00024588054100000316
Inner point->
Figure FDA00024588054100000317
/>
Figure FDA00024588054100000318
In formula (15): the logarithm operation of the matrix is to logarithm each element of the matrix;
fourthly, the M multiplied by M symmetric matrix is formed according to the formulas (16) and (17)
Figure FDA00024588054100000319
Conversion into a vector>
Figure FDA00024588054100000320
Figure FDA00024588054100000321
p＝M(M+1)/2；
Figure FDA00024588054100000322
Figure FDA00024588054100000323
In formula (17): b i,j (i =1,2, \8230;, M; j =1,2, \8230;, M) is the i row and j column elements of a symmetric M by M matrix b.
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