Time Series Prediction Model of Landslide Displacement Using Mean-Based Low-Rank Autoregressive Tensor Completion
Motoki Kazama
Round 1
Reviewer 1 Report
1. After the introduction section, there should be a section presenting the objectives of the research in a concise manner.
2. The graphs presenting the results have to be redone as they do not have appropriate legends.
3. The discussions section has to be extensively improved providing a clear presentation of the pros of the algorithm presented. Preferably, results have to be embedded in the discussion section.
Author Response
Dear Editors and Reviewers,
We sincerely thank the Editors and the Reviewers for your careful and timely review and valuable comments on our manuscript (Manuscript ID: applsci-2233768). These comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We carefully considered and revised the article based on the opinions of Reviewers. The revised manuscript of the paper has been revised in review mode and the important revisions are marked in red. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:
Point 1: After the introduction section, there should be a section presenting the objectives of the research in a concise manner.
Response 1: Thank you for providing these insights. We have added the content of the research objectives after the introduction. Modified as follows: The purpose of this study is to establish a new method for completing and predicting landslide displacement data based on MLATC. In this paper, the causes of data loss of landslide displacement are analyzed. Taking the Shuizhuyuan landslide in the Three Gorges Reservoir area as an example, the data completion and prediction algorithm are designed by using MLATC. Then, the landslide displacement data is divided into training set and test set, and the random missing and non-random missing are selected for corresponding data completion and prediction. The designed model can achieve accurate completion and prediction of landslide displacement. Finally, a comparative analysis with existing models verifies the effectiveness of the model.
Point 2: The graphs presenting the results have to be redone as they do not have appropriate legends.
Response 2: Thank you for your suggestion. Our previous graphs may not have been well represented and only the legend was illustrated in the manuscript. Therefore, we have redrawn all the graphs showing the results to clearly represent the results of the graphs.
Point 3: The discussions section has to be extensively improved providing a clear presentation of the pros of the algorithm presented. Preferably, results have to be embedded in the discussion section.
Response 3: Thanks to the reviewer for your meticulous and careful review. We have revised the Discussion section and the Conclusion section, adding the results to the Discussion section, and discussed the advantages of the proposed algorithm. Modified as follows:
Discussion
Affected by the complex environment in the field, there will be missing data in the process of landslide monitoring, which will affect the accurate analysis of landslide displacement. In landslide disaster monitoring, landslide displacement deformation is relatively complex, and the displacement changes of each deformation area on the landslide are not the same. From the analysis of landslide local deformation characteristics, there is a certain correlation between the daily displacement deformation of different monitoring points. In addition, landslide displacement is a continuous cumulative process, and the landslide displacement occurring in the preceding period will have a certain influence on the landslide displacement occurring subsequently. Therefore, in order to better realize landslide data completion and prediction, a novel model based on MLATC method is proposed, and the RM and NM cases are designed respectively, so as to verify the validity and reliability of the designed model. In addition, from the construction of the model, the initial time series matrix is converted into a third-order tensor structure. Under the assumption that the time series data satisfy approximate low-rankness, the time series completion and prediction problem is transformed into low-rank tensor completion and prediction. The tensor-based completion method fully considers the time series of landslide displacement data, which not only preserves the correlation between different displacements, but also better fits the landslide displacement deformation characteristics, making the displacement completion more accurate.
To verify the effectiveness of the algorithm, a comparative analysis with the existing RTMF and HALRTC models was performed. The MAPE and RMSE of the MLATC model are 0.9066, 0.9196 and 0.7676, 0.9880 for the NM5% and RM5% data completion, respectively. Similarly, the MAPE and RMSE for NM5% and RM5% data prediction are 1.1079, 3.6676 and 1.1084, 3.6774, respectively. The analysis results show that under the conditions of 5%, 10%, 20%, and 40% missing data, the data completion and prediction effects of the MLATC model are better than those of other models, which also confirms the significant data completion and prediction effects of the MLATC model. In this study, the data prediction and the data completion of time series are used in the same way. The prediction experiment of time series is to treat the displacement data to be predicted as the missing values of the data set, then for data prediction is also in principle to complete the data complementary task. Therefore, data completion is the basic iterative calculation of the original data on the whole of the time series, while the time series prediction will process the experimental data to be predicted as the missing value. This part of the missing data will not participate in the iterative calculation of the model by default, and the cycle and iterative calculation are realized in the way of rolling prediction, which will result in a loss in the amount of data. The MAPE and RMSE values of NM and RM also show that the prediction effect of the MLATC model is lower than that of data completion, but both can achieve satisfactory results, which are more in line with the actual needs of landslide monitoring.
Conclusion
A novel method for landslide displacement data completion and prediction based on MLATC model is proposed for missing landslide displacement data and time series prediction. The tensor structure in the MLATC model well perpetuates the structural information of landslide spatio-temporal data in the time dimension, makes full use of the correlation of landslide displacement time series in different time scales, and solves the problem of serious data loss caused by the destruction for the original matrix structure. The data completion and prediction models are implemented in a tensor structure framework, combining VAR models and autoregressive paradigms, and different proportions of random and non-random missing cases are selected for experimental analysis. The experimental results of Shuizhuyuan landslide prove that the model can also achieve the effective completion of missing data and displacement trend prediction of landslide displacement time series without the need of complete original landslide displacement data. The reliability and accuracy of the model data completion and prediction are verified, further improving the feasibility of the model, which likewise helps to issue timely and accurate early warning forecast signals to remind people in the danger area to evacuate and avoid casualties and property damage. The method can be extended and applied in data completion and prediction of such landslides.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper.
We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
Best regards,
Corresponding author: Chenhui Wang
E-mail: wangchenhui@mail.cgs.gov.cn
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This study is a paper on the theme of repairing missing landslide time histories using low-rank autoregressive tensor completion.
The method may be novel. However, since there is little need to repair missing landslide data sections, the problem setting itself as an application of the method is a problem. Indeed, when landslide displacement monitoring is used for warning, there is no need to reproduce slip displacements that have already occurred in the past. Moreover, it is self-evident that landslide displacement data will be data that monotonically increases when dealing with significant deformation, and there is no need to know precise changes in displacement over time. In many cases it is sufficient to linearly interpolate the missing intervals. In addition, the usefulness of spatial interpolation is also poor, as landslide data are rarely acquired spatially.
As a result of this research, it is necessary to concretely show what kind of usefulness can be obtained for landslide displacement time series monitoring.
Author Response
Dear Editors and Reviewers,
Thank you very much and the Reviewers for your careful and timely review and valuable comments on our manuscript (Manuscript ID: applsci-2233768). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We carefully considered and revised the article based on the opinions of Reviewers. The revised manuscript of the paper has been revised in review mode and the important revisions are marked in red. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:
Point 1: This study is a paper on the theme of repairing missing landslide time histories using low-rank autoregressive tensor completion.
Response 1: We would like to express our great appreciation to Reviewers for comments on our manuscript.
Point 2: The method may be novel. However, since there is little need to repair missing landslide data sections, the problem setting itself as an application of the method is a problem. Indeed, when landslide displacement monitoring is used for warning, there is no need to reproduce slip displacements that have already occurred in the past. Moreover, it is self-evident that landslide displacement data will be data that monotonically increases when dealing with significant deformation, and there is no need to know precise changes in displacement over time. In many cases it is sufficient to linearly interpolate the missing intervals. In addition, the usefulness of spatial interpolation is also poor, as landslide data are rarely acquired spatially.
Response 2: Thanks to the reviewer for the suggestion. (1) Landslide monitoring data at some point is required for data recovery, especially the complex environment in the field can lead to missing landslide data. In order to deeply analyze the landslide displacement change process, it is necessary to obtain the complete landslide data set, and the proposed method is precisely to solve the missing data problem of landslides. (2) The deformation of landslide displacement is closely related to the deformation occurred in the past, and we also make full use of historical deformation data when doing displacement completion and prediction, from which we can mine the deformation characteristics and then obtain a good displacement prediction model. (3) As mentioned by the reviewer, the magnitude of the deformation of landslide displacement is caused by a variety of factors, and probably we will pay more attention to the situation when the landslide displacement appears to be significantly deformed. However, in order to understand the whole process of deformation of landslide displacement, it is also necessary to design effective displacement completion and prediction methods with high accuracy. (4) In most cases, linear interpolation can indeed meet the data complementary needs, and our proposed tensor-based method precisely considers the spatial relationship between various points on the landslide. We try to explore the spatial relationship of displacement deformation between each monitoring point, and then observe the landslide deformation as a whole to achieve a good overall displacement prediction.
Point 3: As a result of this research, it is necessary to concretely show what kind of usefulness can be obtained for landslide displacement time series monitoring.
Response 3: Thanks to the reviewer for your meticulous and careful review. The significance of landslide displacement prediction is that unknown monitoring data can be predicted based on existing monitoring data. In order to verify the reliability and stability of the prediction model, researchers often select known landslide displacement monitoring data to verify the validity of the designed model. Firstly, the landslide displacement time series prediction can grasp the local displacement deformation trend of each monitoring point of the landslide. Secondly, the overall deformation trend of landslide displacement can be analyzed in depth by understanding the displacement correlation relationship of each monitoring point. In addition, in the actual landslide monitoring, the landslide displacement time series do have data missing, so it is necessary to construct a suitable method for data recovery. This paper is based on this comparative analysis of existing research methods to achieve displacement prediction simultaneously based on the completion of displacement. Finally, effective landslide displacement and deformation prediction can issue timely and accurate early warning forecast signals to remind people in dangerous areas to evacuate and avoid casualties and property losses. The relevant content we have modified and added improvements in the Discussion and Conclusion. Modified as follows:
Discussion
Affected by the complex environment in the field, there will be missing data in the process of landslide monitoring, which will affect the accurate analysis of landslide displacement. In landslide disaster monitoring, landslide displacement deformation is relatively complex, and the displacement changes of each deformation area on the landslide are not the same. From the analysis of landslide local deformation characteristics, there is a certain correlation between the daily displacement deformation of different monitoring points. In addition, landslide displacement is a continuous cumulative process, and the landslide displacement occurring in the preceding period will have a certain influence on the landslide displacement occurring subsequently. Therefore, in order to better realize landslide data completion and prediction, a novel model based on MLATC method is proposed, and the RM and NM cases are designed respectively, so as to verify the validity and reliability of the designed model. In addition, from the construction of the model, the initial time series matrix is converted into a third-order tensor structure. Under the assumption that the time series data satisfy approximate low-rankness, the time series completion and prediction problem is transformed into low-rank tensor completion and prediction. The tensor-based completion method fully considers the time series of landslide displacement data, which not only preserves the correlation between different displacements, but also better fits the landslide displacement deformation characteristics, making the displacement completion more accurate.
To verify the effectiveness of the algorithm, a comparative analysis with the existing RTMF and HALRTC models was performed. The MAPE and RMSE of the MLATC model are 0.9066, 0.9196 and 0.7676, 0.9880 for the NM5% and RM5% data completion, respectively. Similarly, the MAPE and RMSE for NM5% and RM5% data prediction are 1.1079, 3.6676 and 1.1084, 3.6774, respectively. The analysis results show that under the conditions of 5%, 10%, 20%, and 40% missing data, the data completion and prediction effects of the MLATC model are better than those of other models, which also confirms the significant data completion and prediction effects of the MLATC model. In this study, the data prediction and the data completion of time series are used in the same way. The prediction experiment of time series is to treat the displacement data to be predicted as the missing values of the data set, then for data prediction is also in principle to complete the data complementary task. Therefore, data completion is the basic iterative calculation of the original data on the whole of the time series, while the time series prediction will process the experimental data to be predicted as the missing value. This part of the missing data will not participate in the iterative calculation of the model by default, and the cycle and iterative calculation are realized in the way of rolling prediction, which will result in a loss in the amount of data. The MAPE and RMSE values of NM and RM also show that the prediction effect of the MLATC model is lower than that of data completion, but both can achieve satisfactory results, which are more in line with the actual needs of landslide monitoring.
Conclusion
A novel method for landslide displacement data completion and prediction based on MLATC model is proposed for missing landslide displacement data and time series prediction. The tensor structure in the MLATC model well perpetuates the structural information of landslide spatio-temporal data in the time dimension, makes full use of the correlation of landslide displacement time series in different time scales, and solves the problem of serious data loss caused by the destruction for the original matrix structure. The data completion and prediction models are implemented in a tensor structure framework, combining VAR models and autoregressive paradigms, and different proportions of random and non-random missing cases are selected for experimental analysis. The experimental results of Shuizhuyuan landslide prove that the model can also achieve the effective completion of missing data and displacement trend prediction of landslide displacement time series without the need of complete original landslide displacement data. The reliability and accuracy of the model data completion and prediction are verified, further improving the feasibility of the model, which likewise helps to issue timely and accurate early warning forecast signals to remind people in the danger area to evacuate and avoid casualties and property damage. The method can be extended and applied in data completion and prediction of such landslides.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper.
We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
Best regards,
Corresponding author: Chenhui Wang
E-mail: wangchenhui@mail.cgs.gov.cn
Author Response File: Author Response.pdf
Reviewer 3 Report
This is a very interesting approach in time series prediction. I recommend this article for publication. However, I have concerns and suggestions to improve this contribution:
My major comment is the presentation of the Figures: Please add legends to the Figures. Also, the line size is so thick that it is impossible to distinguish between the single data sets. The captions do not explain the content, it is very difficult to locate the features described in the text in the figures.
Also, for the tables: please explain in the caption what can be found in the tables.
An additional section on symbols and notation and also abbreviations would be useful.
Be careful with the use of the term climate when you mean weather.
Line 53: please clarify what you mean with 'based on small-scale problems'
Please define the term 'better'. You often say one is better than the other without having explained what you consider being 'better'.
In Sec. 3.4 it would be easier for the readers to have the same order: 1. random missing, 2. non-random missing
Author Response
Dear Editors and Reviewers,
Thank you very much and the Reviewers for your careful and timely review and valuable comments on our manuscript (Manuscript ID: applsci-2233768). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We carefully considered and revised the article based on the opinions of Reviewers. The revised manuscript of the paper has been revised in review mode and the important revisions are marked in red. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:
Point 1: My major comment is the presentation of the Figures: Please add legends to the Figures. Also, the line size is so thick that it is impossible to distinguish between the single data sets. The captions do not explain the content, it is very difficult to locate the features described in the text in the figures.
Response 1: Thanks to the reviewer for the suggestion. We are very sorry for our negligence of not adding legends to the Figures. We have redrawn all Figures of the analysis results. And the relevant Figure legends are also clearly explained in the captions.
Point 2: Also, for the tables: please explain in the caption what can be found in the tables.
Response 2: Thanks to the reviewer for the suggestion. We have modified the captions to clearly explain the contents of the table.
Point 3: An additional section on symbols and notation and also abbreviations would be useful.
Response 3: Thanks to the reviewer for the suggestion. We have added Descriptions of the main symbols and abbreviations in the revised manuscript.
Point 4: Be careful with the use of the term climate when you mean weather.
Response 4: Thanks to the reviewer for the suggestion. We have made correction according to the Reviewer’s comments. Modified as follows: Frequent occurrence of extreme weather increases the likelihood of landslides.
Point 5: Line 53: please clarify what you mean with 'based on small-scale problems'.
Response 5: Thanks to the reviewer for the suggestion. The term 'based on small-scale problems' here refers specifically to the size of the data volume and data dimensions, which may not be clear, and we have re-written it. Modified as follows: For the problem of completing and predicting missing landslide data, most traditional time series models have focused on models such as regression analysis and exponential smoothing.
Point 6: Please define the term 'better'. You often say one is better than the other without having explained what you consider being 'better'.
Response 6: Thank you for the suggestion. The term 'better' refers to the relatively 'better' evaluation metrics of the prediction model. We have clarified this in the paper. Modified as follows: Moreover, the MLATC model is compared with the High-Accuracy Low-Rank Tensor Completion (HALRTC) and Temporal Regularized Matrix Factorization (TRMF) methods. The completion and prediction results with a smaller MAPE and RMSE are considered to be better.
Point 7: In Sec. 3.4 it would be easier for the readers to have the same order: 1. random missing, 2. non-random missing.
Response 7: Thank you for the suggestion. To facilitate the readers ' understanding, we have reordered the random missing and non-random missing. The random missing case is described first, followed by the non-random missing case.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper.
We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
Best regards,
Corresponding author: Chenhui Wang
E-mail: wangchenhui@mail.cgs.gov.cn
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
There is a need for an easy-to-understand explanation of how this method can be used not only to complement existing data, but also to predict future warnings.
Author Response
Dear Editors and Reviewers,
Thank you very much and the reviewers for your careful and timely review and valuable comments on our manuscript (Manuscript ID: applsci-2233768). We carefully considered and revised the article based on the opinions of Reviewers. The revised manuscript of the paper has been revised in review mode and the important revisions are marked in red. The main corrections in the paper and the responds to the Reviewer’s comments are as flowing:
Point 1: There is a need for an easy-to-understand explanation of how this method can be used not only to complement existing data, but also to predict future warnings.
Response 1: Thanks to the reviewer for the suggestion. We provided a brief explanation in the revised manuscript. Modified as follows: In this study, the completion and prediction model were constructed by considering the intrinsic correlation between landslide displacement data and using the low-rankness of the completion tensor. Data completion is an iterative calculation of the landslide displacement time series based on the entire original data. In order to verify the effectiveness of the data completion model, random and non-random data missing cases are designed, and time series prediction is based on the predicted experimental data as the missing value, which also belongs to a special case of missing data. By default, this part of the experimental data is not involved in iterative calculations. Therefore, the data prediction for time series is the same as the method used for data completion. The model is implemented in a rolling prediction method with cyclic and iterative computation, which leads to a loss in the amount of data in the prediction case.
We tried our best to improve the manuscript and made some changes in the manuscript. These changes will not influence the content and framework of the paper.
We appreciate for Editors/Reviewers’ warm work earnestly, and hope that the correction will meet with approval.
Once again, thank you very much for your comments and suggestions.
Best regards,
Corresponding author: Chenhui Wang
E-mail: wangchenhui@mail.cgs.gov.cn
Author Response File: Author Response.pdf
Reviewer 3 Report
Thank you for providing the revised version.
Author Response
Dear Editors and Reviewers,
Thank you very much and the Reviewers for your careful and timely review and valuable comments on our manuscript (Manuscript ID: applsci-2233768). Thanks for the Reviewer's suggestions. All your suggestions are very important. They have important guiding significance to my thesis writing and scientific research work.
Point 1: Thank you for providing the revised version.
Response 1: We would like to express our great appreciation to Reviewer for comments on our manuscript.
We appreciate for Editors/Reviewers’ warm work earnestly.
Thank you again for your advice, hoping to learn more from you.
Best regards,
Corresponding author: Chenhui Wang
E-mail: wangchenhui@mail.cgs.gov.cn
Author Response File: Author Response.pdf
