GNNWR: An Open-Source Package of Spatiotemporal Intelligent Regression Methods for Modeling Spatial and Temporal Non-Stationarity

Yin, Ziyu; Ding, Jiale; Liu, Yi; Wang, Ruoxu; Wang, Yige; Chen, Yijun; Qi, Jin; Wu, Sensen; Du, Zhenhong

doi:https://doi.org/10.5194/gmd-2024-62

Preprints

https://doi.org/10.5194/gmd-2024-62

Preprints

Submitted as: development and technical paper

29 May 2024

Submitted as: development and technical paper |

| 29 May 2024

Status: a revised version of this preprint was accepted for the journal GMD and is expected to appear here in due course.

GNNWR: An Open-Source Package of Spatiotemporal Intelligent Regression Methods for Modeling Spatial and Temporal Non-Stationarity

Ziyu Yin, Jiale Ding, Yi Liu, Ruoxu Wang, Yige Wang, Yijun Chen, Jin Qi, Sensen Wu, and Zhenhong Du

Abstract. Spatiotemporal regression is a crucial method in geography for discerning spatiotemporal non-stationarity in geographical relationships, which has found widespread application across diverse research domains. This study implements two innovative spatiotemporal intelligent regression models, namely geographically neural network weighted regression (GNNWR) and geographically and temporally neural network weighted regression (GTNNWR), integrating the spatiotemporal weighted framework and neural networks. Demonstrating superior accuracy and generalization capabilities in large-scale data environments compared to traditional methods, these models have emerged as prominent tools. To facilitate the seamless application of GNNWR and GTNNWR in addressing spatiotemporal non-stationary processes, a Python-based package, GNNWR, has been developed. This article details the implementation of these models and introduces the GNNWR package, enabling users to efficiently apply these cutting-edge techniques. Validation of the package is conducted through two case studies. The first case involves the verification of GNNWR using air quality data from China, while the second employs offshore dissolved silicate concentration data from Zhejiang Province to validate GTNNWR. The results of the case studies underscore the effectiveness of the GNNWR package, yielding outcomes of notable accuracy. This contribution anticipates a significant role for the developed package in supporting future research that leverages big data and spatiotemporal regression techniques.

Received: 29 Mar 2024 – Discussion started: 29 May 2024

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.

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Ziyu Yin, Jiale Ding, Yi Liu, Ruoxu Wang, Yige Wang, Yijun Chen, Jin Qi, Sensen Wu, and Zhenhong Du

Status: closed

RC1:
'Comment on gmd-2024-62', Anonymous Referee #1, 05 Jun 2024
This paper presents an open-source Python package, GNNWR, which incorporates spatiotemporal intelligent regression techniques to model spatial and temporal non-stationarity. The package includes two models: geographically weighted neural network regression (GNNWR) and geographically and temporally weighted neural network regression (GTNNWR). These models utilize neural networks to improve accuracy and generalization over traditional methods, particularly in large-scale data settings. The GNNWR package provides a complete workflow for data preprocessing, model training, and result computation, making advanced spatiotemporal regression techniques more accessible to users.

The followings should be addressed before publication.

Part of the content in the ‘Model Review’ section of the article is somewhat similar to the content found in ‘Geographically and Temporally Neural Network Weighted Regression for Modeling Spatiotemporal Non-Stationary Relationships’, especially lines 80-85. Please correct.

The article provides a detailed description of the usage workflow for the package within the application case. However, incorporating a clear flowchart to depict the package’s operation would greatly benefit the readers.

It is recommended to add statistical characteristics of regression coefficients to the model result information. These statistical characteristics provide an overall understanding of the regression coefficients, which is a very important part for users to understand the model results.

In the package, it is mentioned that only the neural network part of the model is saved during the model saving process. It is necessary to introduce to the readers what content is included in this neural network part.

The article mentions that the “predict_weight” function in the model library can output relevant information. In addition to the spatial weight, all other relevant information should be detailed in the article.

Please review the article for instances where abbreviations are used without being fully expanded. For instance, the abbreviation "PReLU" is encountered for the first time on line 194 without its full name being provided.

There are several formatting issues within the equations that the authors need to review and correct.

(1) There is a missing ‘for i = 1, 2, …, n’ in the second line of Equation 5 on Page 5.

(2) In Equation 11 on Page 5, the equals signs across the two lines are not aligned, whereas in all other equations the equals signs are aligned.
Citation: https://doi.org/10.5194/gmd-2024-62-RC1
RC2:
'Comment on gmd-2024-62', Anonymous Referee #2, 13 Jun 2024
This manuscript introduces a Python package named GNNWR, which integrates two neural network-based models, GNNWR and GTNNWR, to enhance the accuracy and interpretability of spatiotemporal data analysis. The GNNWR package is validated using case studies involving air quality and offshore dissolved silicate concentration data. The results, evaluated through various performance metrics, demonstrate the package's robustness and efficacy in capturing both spatial and temporal patterns. The comprehensive implementation and validation demonstrate the potential of this package as a valuable tool in the field of spatiotemporal modeling. Still, there are some points that need to be improved:
Since the GNNWR and GTNNWR are models that have been proposed in other articles. This article should focus less on the model review, while highlight the design and usage of the newly developed package.

Chapter 3 is named as "Usage Example", but it contains class design, function usage, and other content that is outside the scope of Usage Example. Therefore, I suggest to use a more appropriate chapter name.

The usage example for GNNWR and GTNNWR in Sections 3.2 and 3.3 can be further divided into subsections for easier reading.

The design of optimizers is mentioned in both the GNNWR and GTNNWR sections. In L197, a range of optional optimizers are indicated, while in L345, the passage in focus on explaining the SGD optimizer. Is the choice of optimizer model-dependent (determined by GNNWR or GTNNWR)? If so, then it should be specified in the article, if not, then it might be better to arrange all the discussion about optimizers in consecutive paragraphs

The fonts in the subscripts of the formulas need to be checked further, i.e., the "OLR" in formulas 3, 4, and 7 have both roman and italic types.

In L116, "the symbol ⊗ represents the operator", what is "the operator"?

In Figure 2, the abbreviations (STPNN&STWNN) and their full names are duplicated, instead, detailed descriptions about the network (i.e. the ds and dst nodes) should be added.

L325, the word "function" is in the same font as function name "init_dataset".
Citation: https://doi.org/10.5194/gmd-2024-62-RC2
RC3: 'Comment on gmd-2024-62', Anonymous Referee #3, 17 Jun 2024

The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2024-62/gmd-2024-62-RC3-supplement.pdf

Citation: https://doi.org/10.5194/gmd-2024-62-RC3
RC4:
'Comment on gmd-2024-62', Anonymous Referee #4, 17 Jun 2024
The manuscript presents the development and validation of the GNNWR package, which includes novel spatiotemporal intelligent regression models, namely GNNWR and GTNNWR. These models are designed to handle spatial and temporal non-stationarity using neural networks within a spatiotemporal weighted framework. The paper is well-structured and provides detailed explanations of the models and their applications. However, there are several areas that require clarification and improvement. The abstract is concise and informative, but it would benefit from a brief mention of the key results from the case studies to highlight the effectiveness of the proposed models.
General Comments:
The introduction provides a comprehensive overview of the importance of spatiotemporal regression and the limitations of existing methods. It effectively sets the stage for the introduction of the GNNWR and GTNNWR models. However, the manuscript mentions traditional methods but does not provide a detailed comparative analysis. Please find the general comments below:
Please specify the traditional methods.

It might be helpful to explicitly state the primary contributions of this work in the introduction to clearly differentiate it from previous research.

A brief explanation of how these weights are derived using the SWNN would enhance understanding.

For the GTNNWR model, the process of integrating the STPNN and STWNN should be explained with more detail, particularly the way spatiotemporal distances are calculated and used.

The case studies provided (air quality data from China and offshore dissolved silicate concentration data from Zhejiang Province) are appropriate for demonstrating the models' capabilities. However, the results section should include more detailed comparisons with traditional methods to better highlight the advantages of GNNWR and GTNNWR. Add a table or figure that directly compares the performance metrics (e.g., mean squared error, R-squared) of GNNWR and GTNNWR against traditional methods like OLS, GWR, and other spatiotemporal models. It would be beneficial to include visualizations of the results (e.g., maps or plots) to illustrate the models' performance and the spatial/temporal patterns they capture.

Ensure that any mention of parallel processing clearly explains its relevance and application within the context of the research. For instance, explain how parallel processing contributes to efficiency and performance in the GNNWR model or mention in limitations.

The manuscript does not discuss the computational efficiency of the proposed models. Please provide benchmarks comparing the training and prediction times of GNNWR and GTNNWR with those of traditional models. Discuss strategies for improving efficiency, such as parallel processing.

The conclusion summarizes the findings but does not address limitations or future work in detail. Potential limitations of the current models are not discussed. Acknowledge limitations such as computational demands, data requirements, and model interpretability. Discuss how these might be addressed in future work.

Specific Comments:
Matrices and vectors in the entire manuscript should be denoted by boldface uppercase letters (e.g., Eq. 12).

In Eqs. 1, 7, and 2, 3, please clarify the distinction between and .

Please review the sentence in lines 87-89 to enhance clarity.

In line 85, the sentence needs a period after the equation. Please check the whole manuscript (e.g., lines 93, 96).

In lines 4, 28, 43, and more, each word of abbreviations should begin with a capital letter.

In Eqs. 3, 4, and 6, why do you need to use the symbol “×”?

In Eq. 1, what do p and n represent?

Please check all symbols shown in the manuscript and mentioned in the text (such as 𝑦̂𝑖, 𝑤, i, j, etc.).

In Eq. 5, what is the range of values for “j”?
Citation: https://doi.org/10.5194/gmd-2024-62-RC4
AC1: 'Comment on gmd-2024-62', Sensen Wu, 14 Aug 2024

The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2024-62/gmd-2024-62-AC1-supplement.pdf

Citation: https://doi.org/10.5194/gmd-2024-62-AC1

Status: closed

RC1:
'Comment on gmd-2024-62', Anonymous Referee #1, 05 Jun 2024
This paper presents an open-source Python package, GNNWR, which incorporates spatiotemporal intelligent regression techniques to model spatial and temporal non-stationarity. The package includes two models: geographically weighted neural network regression (GNNWR) and geographically and temporally weighted neural network regression (GTNNWR). These models utilize neural networks to improve accuracy and generalization over traditional methods, particularly in large-scale data settings. The GNNWR package provides a complete workflow for data preprocessing, model training, and result computation, making advanced spatiotemporal regression techniques more accessible to users.

The followings should be addressed before publication.

Part of the content in the ‘Model Review’ section of the article is somewhat similar to the content found in ‘Geographically and Temporally Neural Network Weighted Regression for Modeling Spatiotemporal Non-Stationary Relationships’, especially lines 80-85. Please correct.

The article provides a detailed description of the usage workflow for the package within the application case. However, incorporating a clear flowchart to depict the package’s operation would greatly benefit the readers.

It is recommended to add statistical characteristics of regression coefficients to the model result information. These statistical characteristics provide an overall understanding of the regression coefficients, which is a very important part for users to understand the model results.

In the package, it is mentioned that only the neural network part of the model is saved during the model saving process. It is necessary to introduce to the readers what content is included in this neural network part.

The article mentions that the “predict_weight” function in the model library can output relevant information. In addition to the spatial weight, all other relevant information should be detailed in the article.

Please review the article for instances where abbreviations are used without being fully expanded. For instance, the abbreviation "PReLU" is encountered for the first time on line 194 without its full name being provided.

There are several formatting issues within the equations that the authors need to review and correct.

(1) There is a missing ‘for i = 1, 2, …, n’ in the second line of Equation 5 on Page 5.

(2) In Equation 11 on Page 5, the equals signs across the two lines are not aligned, whereas in all other equations the equals signs are aligned.
Citation: https://doi.org/10.5194/gmd-2024-62-RC1
RC2:
'Comment on gmd-2024-62', Anonymous Referee #2, 13 Jun 2024
This manuscript introduces a Python package named GNNWR, which integrates two neural network-based models, GNNWR and GTNNWR, to enhance the accuracy and interpretability of spatiotemporal data analysis. The GNNWR package is validated using case studies involving air quality and offshore dissolved silicate concentration data. The results, evaluated through various performance metrics, demonstrate the package's robustness and efficacy in capturing both spatial and temporal patterns. The comprehensive implementation and validation demonstrate the potential of this package as a valuable tool in the field of spatiotemporal modeling. Still, there are some points that need to be improved:
Since the GNNWR and GTNNWR are models that have been proposed in other articles. This article should focus less on the model review, while highlight the design and usage of the newly developed package.

Chapter 3 is named as "Usage Example", but it contains class design, function usage, and other content that is outside the scope of Usage Example. Therefore, I suggest to use a more appropriate chapter name.

The usage example for GNNWR and GTNNWR in Sections 3.2 and 3.3 can be further divided into subsections for easier reading.

The design of optimizers is mentioned in both the GNNWR and GTNNWR sections. In L197, a range of optional optimizers are indicated, while in L345, the passage in focus on explaining the SGD optimizer. Is the choice of optimizer model-dependent (determined by GNNWR or GTNNWR)? If so, then it should be specified in the article, if not, then it might be better to arrange all the discussion about optimizers in consecutive paragraphs

The fonts in the subscripts of the formulas need to be checked further, i.e., the "OLR" in formulas 3, 4, and 7 have both roman and italic types.

In L116, "the symbol ⊗ represents the operator", what is "the operator"?

In Figure 2, the abbreviations (STPNN&STWNN) and their full names are duplicated, instead, detailed descriptions about the network (i.e. the ds and dst nodes) should be added.

L325, the word "function" is in the same font as function name "init_dataset".
Citation: https://doi.org/10.5194/gmd-2024-62-RC2
RC3: 'Comment on gmd-2024-62', Anonymous Referee #3, 17 Jun 2024

The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2024-62/gmd-2024-62-RC3-supplement.pdf

Citation: https://doi.org/10.5194/gmd-2024-62-RC3
RC4:
'Comment on gmd-2024-62', Anonymous Referee #4, 17 Jun 2024
The manuscript presents the development and validation of the GNNWR package, which includes novel spatiotemporal intelligent regression models, namely GNNWR and GTNNWR. These models are designed to handle spatial and temporal non-stationarity using neural networks within a spatiotemporal weighted framework. The paper is well-structured and provides detailed explanations of the models and their applications. However, there are several areas that require clarification and improvement. The abstract is concise and informative, but it would benefit from a brief mention of the key results from the case studies to highlight the effectiveness of the proposed models.
General Comments:
The introduction provides a comprehensive overview of the importance of spatiotemporal regression and the limitations of existing methods. It effectively sets the stage for the introduction of the GNNWR and GTNNWR models. However, the manuscript mentions traditional methods but does not provide a detailed comparative analysis. Please find the general comments below:
Please specify the traditional methods.

It might be helpful to explicitly state the primary contributions of this work in the introduction to clearly differentiate it from previous research.

A brief explanation of how these weights are derived using the SWNN would enhance understanding.

For the GTNNWR model, the process of integrating the STPNN and STWNN should be explained with more detail, particularly the way spatiotemporal distances are calculated and used.

The case studies provided (air quality data from China and offshore dissolved silicate concentration data from Zhejiang Province) are appropriate for demonstrating the models' capabilities. However, the results section should include more detailed comparisons with traditional methods to better highlight the advantages of GNNWR and GTNNWR. Add a table or figure that directly compares the performance metrics (e.g., mean squared error, R-squared) of GNNWR and GTNNWR against traditional methods like OLS, GWR, and other spatiotemporal models. It would be beneficial to include visualizations of the results (e.g., maps or plots) to illustrate the models' performance and the spatial/temporal patterns they capture.

Ensure that any mention of parallel processing clearly explains its relevance and application within the context of the research. For instance, explain how parallel processing contributes to efficiency and performance in the GNNWR model or mention in limitations.

The manuscript does not discuss the computational efficiency of the proposed models. Please provide benchmarks comparing the training and prediction times of GNNWR and GTNNWR with those of traditional models. Discuss strategies for improving efficiency, such as parallel processing.

The conclusion summarizes the findings but does not address limitations or future work in detail. Potential limitations of the current models are not discussed. Acknowledge limitations such as computational demands, data requirements, and model interpretability. Discuss how these might be addressed in future work.

Specific Comments:
Matrices and vectors in the entire manuscript should be denoted by boldface uppercase letters (e.g., Eq. 12).

In Eqs. 1, 7, and 2, 3, please clarify the distinction between and .

Please review the sentence in lines 87-89 to enhance clarity.

In line 85, the sentence needs a period after the equation. Please check the whole manuscript (e.g., lines 93, 96).

In lines 4, 28, 43, and more, each word of abbreviations should begin with a capital letter.

In Eqs. 3, 4, and 6, why do you need to use the symbol “×”?

In Eq. 1, what do p and n represent?

Please check all symbols shown in the manuscript and mentioned in the text (such as 𝑦̂𝑖, 𝑤, i, j, etc.).

In Eq. 5, what is the range of values for “j”?
Citation: https://doi.org/10.5194/gmd-2024-62-RC4
AC1: 'Comment on gmd-2024-62', Sensen Wu, 14 Aug 2024

The comment was uploaded in the form of a supplement: https://gmd.copernicus.org/preprints/gmd-2024-62/gmd-2024-62-AC1-supplement.pdf

Citation: https://doi.org/10.5194/gmd-2024-62-AC1

Ziyu Yin, Jiale Ding, Yi Liu, Ruoxu Wang, Yige Wang, Yijun Chen, Jin Qi, Sensen Wu, and Zhenhong Du

Data sets

Replication package for GNNWR v0.1.11: A Python package for modeling spatial temporal non-stationary Ziyu Yin et al. https://doi.org/10.5281/zenodo.10890255

Model code and software

GNNWR v0.1.11: A Python package for modeling spatial temporal non-stationary Ziyu Yin et al. https://doi.org/10.5281/zenodo.10890176

Ziyu Yin, Jiale Ding, Yi Liu, Ruoxu Wang, Yige Wang, Yijun Chen, Jin Qi, Sensen Wu, and Zhenhong Du

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Oct 2024	56	91	0	147
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Short summary

In geography, understanding how relationships between different factors change over time and space is crucial. This study implements two neural network-based spatiotemporal regression models as well as an open-sourced Python package named GNNWR, to accurately capture the varying relationships between factors. This makes it a valuable tool for researchers in various fields, such as environmental science, urban planning, and public health.


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