the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Oct 2021
Unsupervised classification of simulated magnetospheric regions
Maria Elena Innocenti
Jorge Amaya
Joachim Raeder
Romain Dupuis
Banafsheh Ferdousi
Giovanni Lapenta
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- Final revised paper (published on 08 Oct 2021)
- Supplement to the final revised paper
- Preprint (discussion started on 03 Jun 2021)
- Supplement to the preprint
Interactive discussion
Status: closed
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RC1: 'Comment on angeo-2021-33', Anonymous Referee #1, 23 Jun 2021
Anonymous review of Unsupervised classification of simulated magnetospheric regions by Innocenti et al for Annales Geophysicae
In the manuscript under review, the authors have applied machine learning, more specifically self-organizing maps (SOMs), to the question of identifying the magnetospheric regions in which space plasma measurements were made. They propose that their method could be applied to deciding which parts of large measurement databases be downlinked at high resolution, a very real issue for space missions. In this study, they apply the SOM method and K-means clustering to simulation data generated by the OpenGGCM-CTIM-RCM code, a global MHD simulation of the Earth's magnetosphere. They show the method is capable of successfully classifying several magnetospheric plasma regions, and perform comparisons of input data preparation on classification results.
The manuscript is well written, describes new science results, and is of high interest to the community. The application does not contain brilliant breakthroughs as such, but is a valuable addition and a useful parameter study. There are only a few clarifications and improvements to the discussion to suggest before recommending publication, which I have divided below into major and minor suggestions.
Major points:
L94-95: Please explicitly state that the boundary conditions vary with time. Are all boundary cells surrounding the simulation domain always at the same value, varying identically with time?
L157: Please clarify the data point selection. Is it randomized? Is there any selection based on Y or Z?
Figures and analysis: Although the polar plane is very interesting in many ways and should indeed play a role in the study, the equatorial plane could be considered even more relevant, particularly considering the orbits of recent significant space missions. I strongly urge that you present also equatorial plane plots early on to show the strength of the method.
Table 2: Instead of multiplying values in the latter two feature sets, could all sets perhaps be re-normalized to a norm of 1? This would make comparison easier.
Kneedle determination of optimal cluster count: did you attempt changing the number of clusters to see how robust the method is? Would setting k=6 merge clusters 1 and 4? How would this change the misclassified cluster 5 points at the bow shock for F1?
What about setting k=5, would clusters 1,4 and 5 merge? I believe a written description of such a test without figures would suffice.Could you please add some quantitative estimate of the agreement between different feature sets? This would be particularly useful if you also included comparison against the pure K-clustering approach, to show how much improvement SOMs bring to the table. For this purpose, I think manually merging some clusters (e.g. 1,4,5) would be acceptable.
L372: Since you talk of lessons learned, I was surprised that you did not describe attempts using the logarithm of magnitude of B, instead going with the quasi-arbitrary clipping procedure. Please try out log(B) if not already attempted, and at least briefly report the results.
Conclusions: I would like to see some more discussion about relevance and limitations. An important point to discuss, albeit outside the scope of the current paper, is the identification of small structures inside larger domains (e.g. the tail current sheet within the boundary layer) and the points of transition between domains. The latter might arise naturally from this method, the former not so much. Some mention of this should be included. Also, there has been no discussion of the drastic difference between MHD simulation descriptions of plasma parameters and the values measured by spacecraft or hybrid simulation methods, namely kinetic effects, noise, and/or instrumentation limitations. Some of these are touched upon in Amaya(2020), but they are quite relevant to the discussion here as well, if this method is indeed to become a first step in any actual classification approach.
Minor points:
Abstract: I would recommend you mention comparisons against the K-clustering event here, as well as the use of PCA to reduce input data.
L14: Introduction to machine learning: Perhaps some more general, canonical paper could be cited?
L30: how has the data magnitude changed when compared with Cluster, the Van Allen probes, ISEE-1, etc?
L90: Please clarify in better detail the simulation set-up. Is this the domain size of the whole simulation, or the portion of it shown in figure 1? In section 4 you state you use only the relevant portion of the simulation for post-processing SOM analysis. What is the spatial resolution of the simulation?
L119: The indicated magnetic field clipping value does not make much sense. Is the intention to keep the same ratio between the three components and the original signs, but re-scale the magnetic field vector to a magnitude of 100 nT? Please rephrase.
L129: is the lattice really of type R^2? The visualizations show a hexagonal grid.
L131: I recommend you briefly mention that from available plasma variable you select n features for the SOM method to use, so that the R^n notation is meaningful.
L135: Could this be better described (to the layman) as altering the feature values of the code word so that the distance ws for the winning element becomes smaller? Similarly, consolidation of terms might make it easier to read, e.g. data entry vs input data point vs input point - these are probably all the same thing, i.e. a list of features associated with a point of measurement.
L143: is the numerator of the exponent in formula (3) the integer lattice neighbor distance, up to a value of sigma(tau)?
L201: Is the K-means clustering performed based on the final code words of each node?
L282: I would suggest briefly mentioning the sunward inner magnetosphere misclassification already here.
L286: This should probably be Bx, not Bz?
L299: Since the cluster numbering is arbitrary, you could perhaps re-order the colors to match the earlier ordering to assist the reader.
Figure 7: What time value is this? (for the caption, not just the text)
L337: Please clarify if these are trained with t0+210 or with mixed time data?
Figures 8 and 9, main text: The ordering, going from the top row of Fig8 to two rows of Fig9, back to the bottom row of Fig8, and then to the last row of Fig9 is counter-intuitive. This could surely be improved.
L367-368: Please briefly mention what F7 and F8 added
L416: More comparison with Amaya(2020) of the results and potential future avenues would be good - it was only very briefly cited before.
L447: Do you have any references to indicate what direction non-linear feature correlation analysis in deciding a dimensionality reduction could take? What about the addition of non-local features, such as spatial and temporal derivatives, curls etc?
L448: Are dynamic SOMs a reasonable approach to automatic classification, or do they require user validation after every re-learning?
Citation: https://doi.org/10.5194/angeo-2021-33-RC1 -
AC1: 'Reply on RC1', Maria Elena Innocenti, 08 Jul 2021
We thank the reviewer for the useful comments, that will help improving our work. We answer to the comments below, rewriting the reviewer’s comment for clarity.
Major points:
L94-95: Please explicitly state that the boundary conditions vary with time. Are all boundary cells surrounding the simulation domain always at the same value, varying identically with time?
The manuscript will be edited as follows:
The OpenGGCM-CTIM-RCM boundary conditions require the specification of the three components of the solar wind velocity and magnetic field, the plasma pressure and the plasma number density at 1 AU. Boundary conditions in the sunward direction vary with time. They are interpolated to the appropriate simulated time from ACE observations (Stone et al., 1998), and applied identically to the entire sunward boundary.
L157: Please clarify the data point selection. Is it randomized? Is there any selection based on Y or Z?
We have randomly selected 1 % of the points included in the −40 < x/RE < 18, −Ly < y/RE < Ly, −Lz < z/RE < Lz subdomain, seeding the random selection to be sure to be able to retrieve the same dataset if needed. No selection based on y or z has been used.
This will be clarified in the manuscript as follows:
The selection of these points is randomized, and the seed of the random number generator is fixed to ensure that results can be reproduced. Tests with different seeds and with an higher number of training points did not result into significantly different classification results.
Figures and analysis: Although the polar plane is very interesting in many ways and should indeed play a role in the study, the equatorial plane could be considered even more relevant, particularly considering the orbits of recent significant space missions. I strongly urge that you present also equatorial plane plots early on to show the strength of the method.
In the revised version of the manuscript, we will introduce equatorial plane results, now shown for the first time in Figure 7, in Figure 4 as well. Furthermore, we will add validation plots for the F1 feature set in the equatorial plane in Figure 6, which in the old version of the manuscript shows only the meridional plane.
The plots we will add are shown in Figure 1 (added as supplement). They are consistent with the classification in the meridional plane at the same times. Also the mis-classifications are consistent: also in the equatorial plane we see mis-classification of a few bow shock points, which are classified as inner magnetosheath (orange), and mis-classification of a few inner magnetosphere points as inner magnetosheath plasma at t0 + 225 minutes (orange).
Table 2: Instead of multiplying values in the latter two feature sets, could all sets perhaps be re-normalized to a norm of 1? This would make comparison easier.
We will remove the renormalization for the first two feature sets.
Kneedle determination of optimal cluster count: did you attempt changing the number of clusters to see how robust the method is? Would setting k=6 merge clusters 1 and 4? How would this change the misclassified cluster 5 points at the bow shock for F1? What about setting k=5, would clusters 1,4 and 5 merge? I believe a written description of such a test without figures would suffice.
Short answer: k = 6 merges the three magnetosheath clusters into two, the other clusters are left unaltered. With k = 5, the boundary layer cluster disappears, and the points that mapped to it are assigned to the clusters mapping to inner magnetospheric (this is mostly the case of current sheet plasma), magnetosheath or lobe plasma. In all cases, we keep seeing few bow shock points mis-classified as inner magnetosheath plasma.
In the pdf added as supplement, we examine in some details and with plots the classification results in the meridional and equatorial plane with k = 6 and k = 5. We propose to add that as an Appendix in the revised manuscript.
Could you please add some quantitative estimate of the agreement between different feature sets? This would be particularly useful if you also included comparison against the pure K-clustering approach, to show how much improvement SOMs bring to the table. For this purpose, I think manually merging some clusters (e.g. 1,4,5) would be acceptable.
We would avoid manually merging clusters, as it would defy the purpose of unsupervised classification. In the new Appendix we propose to add a comparison of SOM + K-means vs pure K-means classification with k = 5 and k = 6 as well, as suggested. We do not observe significant differences in SOM+ K-means and pure K-means classification with k = 5. With k = 6 (as already observed with k = 7), the SOM+ K-means classification is more robust to the mis-classification of inner magnetospheric plasmas.
L372: Since you talk of lessons learned, I was surprised that you did not describe attempts using the logarithm of magnitude of B, instead going with the quasi-arbitrary clipping procedure. Please try out log(B) if not already attempted, and at least briefly report the results.
We will add a new feature set, F10, where log(|B|) is used as a feature, instead of clipped |B|. The new validations plots are reported here in Figure 2 added as supplement.
As you can see comparing F1, F9 and F10, F10 looks remarkably similar to F1 in the internal regions, including the mis-classification of some inner magnetospheric points as magnetosheath plasma at t0 + 225 minutes. The three magnetosheath cluster vary at the three different times depicted with respect to F1. This behavior, and the pattern of classification of magnetosheath plasma in F9, shows that the magnetic field is a feature of relevance in classification especially for magnetosheath regions. F10 classification results show that the blue cluster in F9 originates from the clipping procedure. This somehow artificial procedure is however beneficial for inner magnetospheric points, which are not mis-classified in that case.
Conclusions: I would like to see some more discussion about relevance and limitations. An important point to discuss, albeit outside the scope of the current paper, is the identification of small structures inside larger domains (e.g. the tail current sheet within the boundary layer) and the points of transition between domains. The latter might arise naturally from this method, the former not so much. Some mention of this should be included. Also, there has been no discussion of the drastic difference between MHD simulation descriptions of plasma parameters and the values measured by spacecraft or hybrid simulation methods, namely kinetic effects, noise, and/or instrumentation limitations. Some of these are touched upon in Amaya(2020), but they are quite relevant to the discussion here as well, if this method is indeed to become a first step in any actual classification approach.
We will add this discussion to the Conclusions:
In this paper, we have classified large scale simulated regions. However this is only one of the classification activities one may want to be able to perform on simulated, or observed, data. Other activities of interest may be the classifi- cation of meso-scale structures, such as dipolarizing flux bundles or reconnection exhausts. This seems to be within the purview of the method, assuming that an appropriate number of clusters is used, and that the simulations used to produce the data are resolved enough. To increase the chances of meaningful classification of meso-scale structures, one may consider applying a second round of unsupervised classification on the points classified in the same, large-scale cluster. Another activity of interest could be the identification of points of transition between domains. Such an activity appears challenging in the absence, among the features used for the clustering, of spatial and temporal derivatives. We purposefully refrained from using them among our training features, since we are aiming for a local classification model, that does not rely on higher resolution sampling either in space or time.
We will edit L420 as follows:
As a first step towards the application of this methodology to spacecraft data, we verify its performance on simulated magnetospheric data points obtained with the MHD code OpenGGCM-CTIM-RCM. We choose to start with simulated data since they offer several distinct advantages. First of all, we can for the moment bypass issues, such as instrument noise and instrument limitations, that are unavoidable with spacecraft data. Data analysis, de-noising, pre-processing is a fundamental component of ML activities. With simulations, we have access to data from a controlled environment that need minimal pre-processing, and allow us to focus on the ML algorithm for the time being. Furthermore, the time/ space ambiguity that characterizes spacecraft data is not present in simulations, and it is relatively easy to qualitatively verify classification performance by plotting the classified data in the simulated space. Performance validation can be an issue for magnetospheric unsupervised models working on spacecraft data. A model such as ours, trained and validated against simulated data points, could be part of an array of tests against which unsupervised classifications of magnetospheric data could be bench marked.
The code we are using to produce the simulation is MHD. This means that kinetic processes are not included in our work, and that variables available in observations, such as parallel and perpendicular temperatures and pressures, moments separated by species, are not available to us at this stage. This is certainly a limitation of our current analysis. This limitation is somehow mitigated by the fact that we are focusing on classification on large scale regions. Future work, on kinetic simulations and spacecraft, will assess the impact of including “kinetic” variables among the classification features.
Minor points:
Abstract: I would recommend you mention comparisons against the K-clustering event here, as well as the use of PCA to reduce input data.
We will add the following sentences to the abstract:
The dimensionality of the data is reduced with Principal Component Analysis before classification. ... We validate our classification results by plotting the classified data in the simulated space, and by comparing with K-means classification.
L14: Introduction to machine learning: Perhaps some more general, canonical paper could be cited?
The sentence will be edited as follows:
The growing amount of data produced by measurements and simulations of different aspects of the heliospheric environment 25 has made it fertile ground for applications rooted in Artificial Intelligence, AI, and Machine Learning, ML (Bishop, 2006, Goodfellow et al, 2016). The use of ML in space weather nowcasting and forecasting is addressed in particular in Camporeale (2019).
L30: how has the data magnitude changed when compared with Cluster, the Van Allen probes, ISEE-1, etc?
We will add this sentence to the manuscript:
The four-spacecraft Cluster mission (Escoubet et al., 2001) has been investigating the Earth’s magnetic environment and its interaction with the solar wind for over 20 years. Laakso et al. (2010), introducing a publicly accessible archive for high-resolution Cluster data, expected it to exceed 50 TB.
L90: Please clarify in better detail the simulation set-up. Is this the domain size of the whole simulation, or the portion of it shown in figure 1? In section 4 you state you use only the relevant portion of the simulation for post- processing SOM analysis. What is the spatial resolution of the simulation?
The description of the simulation set up will be updated as follows:
OpenGGCM-CTIM-RCM uses a stretched Cartesian grid, which in this work has 325x150x150 cells, sufficient for our large scale classification purposes, while running for few hours on a modest number of cores. The point density increases in the Sunwards direction and in correspondence with the magnetospheric plasma sheet, the “interesting” region of the simulation for our current purposes. The simulation extends from −3000 RE to 18 RE in the Earth-Sun direction, from −36 RE to +36 RE in the y and z direction. RE is the Earth’s mean radius, the Geocentric Solar Equatorial (GSE) coordinate system is used in this study.
In this work, we won’t be analyzing the entire simulation, but the subset with coordinate −40 < x/RE < 18, i.e. the magnetosphere / solar wind interaction region and the near magnetotail.L119: The indicated magnetic field clipping value does not make much sense. Is the intention to keep the same ratio between the three components and the original signs, but re-scale the magnetic field vector to a magnitude of 100 nT? Please rephrase.
The intention of the clipping procedure was to cap the maximum magnitude of the magnetic field module to 100 nT, while retaining information on the sign of each magnetic field component. The respective ratios of the origina field components are lost with this procedure, since each of them is arbitrarily set a fixed value. Any negative effects of this procedure is limited to feature set F5 (old labelling, F7 new labelling), the only one which uses the clipped magnetic field components. Comparing the F5 (F7) validation plots with F1, it appears that the clipping procedure did not have a major influence on classification results.
L129: is the lattice really of type R2? The visualizations show a hexagonal grid.
The lattice is of type R2 . To clarify the visualization, this sentence will be added to the text:
The node location in the lattice can use a Cartesian pattern, but most applications relocate the nodes in a hexagonal arrangement in order to feature equidistant points to the six closest neighbouring nodes.
L131: I recommend you briefly mention that from available plasma variable you select n features for the SOM method to use, so that the Rn notation is meaningful.
The following text will be added to the manuscript:
n is therefore the number of plasma variables that we select, among the available ones, for our classification experiment.
L135: Could this be better described (to the layman) as altering the feature values of the code word so that the distance ws for the winning element becomes smaller? Similarly, consolidation of terms might make it easier to read, e.g. data entry vs input data point vs input point - these are probably all the same thing, i.e. a list of features associated with a point of measurement.
The comments will be incorporated in the manuscript as follows:
SOMs learn by moving the winning element closer to the data entry, based on their relative distance, and on a iter- ation number-dependent learning rate ε(τ), with τ the progression of samples being presented to the map for training: the feature values of the winning element are altered as to reduce the distance between the “updated” winning element and the data entry.
Indeed, data entry, input data and input point are the same thing. We will add a clarification statement in the manuscript:
Notice that, in the rest of the manuscript, we will use terms such as “data point”, “data entry”, “input point” interchangeably.
L143: is the numerator of the exponent in formula (3) the integer lattice neighbor distance, up to a value of sigma(tau)?
σ(τ) is the value of the lattice neighbor width, which is not necessarily an integer. σ(τ) decreases with the iteration number (τ) to ensure that the map converges at the end of the training.
L201: Is the K-means clustering performed based on the final code words of each node?
Yes.
L282: I would suggest briefly mentioning the sunward inner magnetosphere misclassification already here.
We prefer to complete our line of thought before introducing the inner magnetosphere mis-classification, which is mentioned just a few lines below
L286: This should probably be Bx, not Bz?
yes, corrected
L299: Since the cluster numbering is arbitrary, you could perhaps re-order the colors to match the earlier ordering to assist the reader.
The colors of the clusters will be re-ordered to match F1.
Figure 7: What time value is this? (for the caption, not just the text)
t0 + 210 minutes. It will be made clear in text and caption.
L337: Please clarify if these are trained with t0+210 or with mixed time data?
They are trained with t0 + 210 minutes data. This will be clarified in the manuscript.
Figures 8 and 9, main text: The ordering, going from the top row of Fig8 to two rows of Fig9, back to the bottom row of Fig8, and then to the last row of Fig9 is counter-intuitive. This could surely be improved.
The labelling of the feature sets will be changed and the description of classification results with different features improved.
L367-368: Please briefly mention what F7 and F8 added
What F7 and F8 (old feature set labelling, F4 and F5 with the new labelling) add to the the feature list is mentioned in the paragraph before L367 in the old manuscript. If the comment refers instead to the rationale for adding F7 and F8 to the feature list, the idea is to verify if quantities which are meaningful for the human observer, such as Mach number, Alfven speed, plasma beta, hinder or help the unsupervised classification. As per the tests presented, the difference is not major.
L416: More comparison with Amaya(2020) of the results and potential future avenues would be good - it was only very briefly cited before.
This will be added to the conclusions:
In Amaya 2020, more advanced pre-processing techniques were experimented with, which will most probably prove useful when we will move to the more challenging environment of spacecraft observations (as opposed to simulations). Furthermore, Amaya 2020 employed windows of time in the classification, which we have not used in this work in favor of an “instantaneous” approach. In future work, we intend to verify which approach gives better results.
L447: Do you have any references to indicate what direction non-linear feature correlation analysis in deciding a dimensionality reduction could take? What about the addition of non-local features, such as spatial and temporal derivatives, curls etc?
We will try non-linear feature correlation analysis as part of future work. As such, we do not think we are in a position to speculate on results of this activity at this point in time.
Regarding the addition of non local features: in this work, we preferred a local, instantaneous approach, which gave good results with identification of large-scale magnetospheric regions. It may be unavoidable to introduce spatial and temporal derivatives if we decide to use a similar approach for the identification of boundaries between magnetospheric regions, or meso- and small-scale processes.L448: Are dynamic SOMs a reasonable approach to automatic classification, or do they require user validation after every re-learning?
If the learning parameters are the same, the net casted by the DSOM has the same rigidity for any random initial- ization of the initial code word (node) locations. The final maps can potentially show slightly different arrangements, but as a net the SOM will cover the same area of the N-dimensional space. This has not been tested thoroughly in this paper but will be added to our future analysis.
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AC2: 'Reply on AC1 / 2', Maria Elena Innocenti, 14 Jul 2021
We will add an estimate on the agreement between the different classification experiments, with F1 as reference.
The SOMS + K-means classification and the pure K-means classification of the training dataset at time t0 + 210 minutes (depicted in Figure 7) classify 92.15 % of the points in the same cluster, 92.74 % if the two magnetosheath clusters just downstream the bow shock are considered the same. This is because different classification mostly occurs for inner magnetospheric clusters, see Fig. 7.
In the table in the supplemental material , we report the % of points classified in the same cluster as for F1 (second column) for the different feature sets used. Third column (header "M"): the two magnetosheath clusters downstream the bow shock are considered one
Notice: the feature set numbering is changed with respect to the submitted manuscript, to match the labeling in the new version.
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AC2: 'Reply on AC1 / 2', Maria Elena Innocenti, 14 Jul 2021
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AC1: 'Reply on RC1', Maria Elena Innocenti, 08 Jul 2021
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RC2: 'Comment on angeo-2021-33', Anonymous Referee #2, 01 Jul 2021
In the manuscript under review the authors have applied unsupervised machine learning algorithms to analyse global magnetospheric simulation data obtained from OpenGGCM-CTIM-RCM code. The automated classification process uses principal component analysis for input data dimension reduction, self-organizing maps for training of an artificial neural network and K-means for cluster extraction from the trained neural network. These unsupevised machine learning algorithms offer an automated way to determine clusters in the physical simulation data. The results shown in the paper are surely of great interest to space physics. The paper also displays the advantages and performance of the unsupervised clustering algorithm.
The paper contains interesing results, but contains no new method development, rather it presents an automated algorithm comprised of multiple unsupervised clustering algorithms. The application of methods is in overall well executed and explained.
There are points for revision that need to be addressed before advising for publication and minor suggestions for consideration. They are listed as following.
Major comments:
1. The authors do not discuss the stochastic nature of artificial neural networks, their sensitvity to initial conditions and convergence to local minima. Clarification for this issue would be needed to the section discussing Self Orgainzing Maps.
2. The nature of the hyper-parameters of the Self Organizing Maps are only briefly discussed in Section 3, more clarification on their influence to the algorithms performance is needed. A case study is done in appendix A, but a more theoretical description of the nature of the hyper-parameters should be added.
3. In Section 3 the authors do not mention what distance metric is used for the matching rule in Equation (1) and updating rule in Equation (2) of the SOM.
4. Clarification should be added about how the authors initialized the neural map of the SOM.
5. The influence of sampling of input data during learning needs to be discussed.
6. The authors should describe how much confidence they have in the result of the SOM.
7. In Section 4.2 the model validation is done only by visual inspection. The colors of similar clusters differ from image to image. This fact also makes the readability of the figure very hard, as the eye automatically matches colors. A quantitative measure should be introduced for the robustness of the SOM. To discuss Figure 7 data, one could simply calculate for each result comparison pair for the same data a percentage of similarly labelled data points. Human labelling of the 7 clusters is already previously done (Figure 4 panel (d)). The same labeling system could be used for the K-means classification results displayed on Figure 7.
8. Clarify what time snapshots and data is analysed on Figure 8. Do the panels on the figure correspond to the same dataset with different training features? Clusters depicted on Figure 8 follow different coloring schemes, which diminish the readability of the results. To better quantify the comparison of independent algorithm results on the same data a quantitative measure should be added. Similarly to the previous comment 7, Figure 4 panel (d) labeling system can be applied to all results. One could count the fraction of similarly labelled input data points for each compared pair of independent results for the same data.
9. Similar quantitative robustness measure should be added for the comparison of independent results for the same data in Figure 9.
10. Use the same coloring scheme for all cluster analysis results (Fig 6 – Fig 9) as different colors lose information in Figures. In Figure 4 a labelling system with colors is created, which could be used for all figures. Only visual comparison of clusters over multiple images throughout the paper with different color coding is tiresome.
11. The comparison of panels between Figure 4, Figure 6, Figure 7, Figure 8 and Figure 9 would be easier if all the captions of the panel names would contain the time snapshot information. Panels on the Figure 6 have different sizes, panel sizes on a Figure should be uniform.
Minor suggestions and questions:
L167: Does the dimension of the input data influence the training time of the map considerably? Are there other metrics that could possibly influence it more? Can the PCA be used to intialize the neural map of the SOM? Is the main motivation for input data dimensionality reduction to have more reliable results from training of the SOM?
Fig 3: the name of panel (a) is in different size.
Fig 4: the style of panel descriptions differ in the Caption. A more uniform style would increase the readability of the figure.
Fig 7: the name of panel (b) is in different size.
Citation: https://doi.org/10.5194/angeo-2021-33-RC2 -
AC3: 'Reply on RC2', Maria Elena Innocenti, 14 Jul 2021
We thank the reviewer for their comments, that helped improve our work. We reply here in details, reporting the reviewer's comments in bold for easy reading.
Major comments:
1. The authors do not discuss the stochastic nature of artificial neural networks, their sensitvity to initial conditions and convergence to local minima. Clarification for this issue would be needed to the section discussing Self Orgainzing Maps.
To clarify the issue, the following sentences will be added to the manuscript:
It is useful to remark that, even if the same data are used to train different SOMs, the trained networks can differ (and most probably will), due e.g. to the stochastic nature of artificial neural networks and to their sensitivity to initial conditions. If the initial positions of the map nodes are randomly set (as in our case), maps will evolve differently, even if the same data are used for the training.
We have verified that SOMs trained starting from different initial node positions give comparable classification results, even if the nodes that map to the same magnetospheric points are located at different coordinates in the map. The reason for this comparable classification results is that the ‘net’ created by a well-converged SOM will always have a similar coverage and neighbouring nodes will always be located at similar distances with respect to their neighbours (if the data do not change). Hence, while the final map might look different, the classes and their properties will produce very similar end results. We refer the reader to Amaya et al. (2020) for exploration of the sensitivity of the SOM method to the parameters and to initial condition, and for a study of the rate and speed of convergence of the SOM.
2. The nature of the hyper-parameters of the Self Organizing Maps are only briefly discussed in Section 3, more clarification on their influence to the algorithms performance is needed. A case study is done in appendix A, but a more theoretical description of the nature of the hyper-parameters should be added.
We refer the reader to Amaya et al (2020) for the study of the convergence of the method with different parameters.
3. In Section 3 the authors do not mention what distance metric is used for the matching rule in Equation (1) and updating rule in Equation (2) of the SOM.
We use the Euclidean norm. The manuscript will be updated accordingly.
4. Clarification should be added about how the authors initialized the neural map of the SOM.
The initial nodes are randomly distributed. We have verified that SOMs trained with the same data starting from different initial node distribution give comparable results.
5. The influence of sampling of input data during learning needs to be discussed.
This issue will be clarified in the manuscript as follows:
The selection of these points is randomized, and the seed of the random number generator is fixed to ensure that results can be reproduced. Tests with different seeds and with an higher number of training points did not give significantly different classification results.
6. The authors should describe how much confidence they have in the result of the SOM.
As we will describe in the revised Conclusions, we are at the moment quite happy with the classification results we obtain, because they map well to our knowledge of the system and appear to be quite robust to temporal variations in the simulated magnetosphere. The fact that a good subset of the features we tested gives comparably good results also points in the direction of a robust procedure on simulated data. Of course the real test for the method will be using spacecraft data, which will be extremely more challenging in terms of instrument noise, instrument limitations, presence of kinetic processes.
7. In Section 4.2 the model validation is done only by visual inspection. The colors of similar clusters differ from image to image. This fact also makes the readability of the figure very hard, as the eye automatically matches colors. A quantitative measure should be introduced for the robustness of the SOM. To discuss Figure 7 data, one could simply calculate for each result comparison pair for the same data a percentage of similarly labelled data points. Human labelling of the 7 clusters is already previously done (Figure 4 panel (d)). The same labeling system could be used for the K-means classification results displayed on Figure 7.
The colors in all plots will be matched to those of F1, to simplify visual comparisons of results.
We will add this while commenting figure 7:
To compare the two classification methods quantitatively, we calculate the number of points which are classified in the same cluster with SOMs plus K-means vs pure K-means classification. 92.15 % of the points are classified in the same cluster, 92.74 % if the two magnetosheath clusters just downstream the bow shock are considered the same. These percentage are calculated on the entire training dataset at time t0 + 210 minutes, of which cuts are depicted in the panels in Figure 7.
8. Clarify what time snapshots and data is analysed on Figure 8. Do the panels on the figure correspond to the same dataset with different training features? Clusters depicted on Figure 8 follow different coloring schemes, which diminish the readability of the results. To better quantify the comparison of independent algorithm results on the same data a quantitative measure should be added. Similarly to the previous comment 7, Figure 4 panel (d) labeling system can be applied to all results. One could count the fraction of similarly labelled input data points for each compared pair of independent results for the same data.
In the submitted manuscript, Figure 8 depicted classification with different sets of training features of the training data points. In the new version, we will show results for the same validation dataset as Figure 6. In both cases, t = t0 +210 minutes. Results do not differ significantly between the two sets of pictures. The colors in the new picture will be changed to match the cluster description in Figure 4.
We will add a table with the % of data classified in the same cluster as F1, see Table 3 in supplementary material. The manuscript will be edited as follows:
In Table 3, second column (“S”), we report the percentage of data points classified in the same cluster as F1 for each of the feature sets of Table 1, for the validation dataset at t0 + 210 minutes. In the third column (“M”), we consider cluster 1 and 4 as a single cluster: in the previous analysis, we remarked that cluster 1 and 4 (the two magnetosheath clusters just downstream the bow shock) map to the same kind of plasma. We keep this into account when comparing classification results with F1.
The metrics depicted in Table 3 cannot be used to assess the quality of the classification per se, since we are not comparing against ground truth, but merely against another classification experiment. However, it gives us a quantitative measure of how much different classification experiments agree.
9. Similar quantitative robustness measure should be added for the comparison of independent results for the same data in Figure 9.
Done, see table.
10. Use the same coloring scheme for all cluster analysis results (Fig 6 – Fig 9) as different colors lose information in Figures. In Figure 4 a labelling system with colors is created, which could be used for all figures. Only visual comparison of clusters over multiple images throughout the paper with different color coding is tiresome.
Done.
11. The comparison of panels between Figure 4, Figure 6, Figure 7, Figure 8 and Figure 9 would be easier if all the captions of the panel names would contain the time snapshot information. Panels on the Figure 6 have different sizes, panel sizes on a Figure should be uniform.
The time snapshot information will be added to all captions, and labels will be made uniform. We will also add (T) and (V) to the caption, to label the training and validation datasets.
Minor suggestions and questions:
L167: Does the dimension of the input data influence the training time of the map considerably? Are there other metrics that could possibly influence it more? Can the PCA be used to intialize the neural map of the SOM? Is the main motivation for input data dimensionality reduction to have more reliable results from training of the SOM?
In our experience, it is the number of points, rather than the number of features, that influences the training time the most, so the main motivation for dimensionality reduction was in fact not training time (even if that helped) but rather, as the reviewer suggests, generating a more reliable training dataset. The correlation analysis (and previous knowledge) made clear that several of the magnetospheric variables in fact carry the same information on the state of the plasma, and we aimed at compressing that information in a lower number of features, while preserving a high percentage of the variance of the original dataset.
PCA can certainly be used to initialize the SOM map, but in this case we chose random initialization.
Fig 3: the name of panel (a) is in different size.
Fig 4: the style of panel descriptions differ in the Caption. A more uniform style would increase the readability of the figure.
Fig 7: the name of panel (b) is in different size.We will improve figure presentation in the revised version.
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AC3: 'Reply on RC2', Maria Elena Innocenti, 14 Jul 2021
Peer review completion
