Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The identification of correlation  in large datasets is of high importance.  Some high-dimensional datasets might present cyclic correlations, that are elusive to identify. Counting with adequate tools to detect such correlations is of the essence. In this contribution, authors define a methodology to detect cyclic correlations that relies  on graphical representations, mainly correlation graphs and chains.

Authors clearly define the relevant terms and deeply describe the main ideas. A relevant description of related work is presented and connected to the new proposal. Figs. 1 to 4 lead the reader to the main ideas through examples.

The results are encouraging, as shown by author's exploration of a handful of datasets. The interpretability of the achieved chains and graphs is, in my opinion, the most relevant aspect of the proposal.

 

Some minor issues:

-Pearson correlation is a well-known parameter, perhaps it is not needed to explicitly show it as in eq. 1. The same applies for the Spearman and Kendalll correlations.

- Authors relied on RMSE, which is a good evaluation metric. However, no details about this decision are offered. Can authors elaborate about their decision?

Author Response

COMMENT 1: Pearson correlation is a well-known parameter, perhaps it is not needed to explicitly show it as in eq. 1. The same applies for the Spearman and Kendall correlations.

AUTHOR RESPONSE: Thank you for your comment, which we agree with. However, we felt, that with the inclusion of the equations and a brief discussion of the coefficients, the work offered more comprehensive view of the correlation analysis.

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COMMENT 2: Authors relied on RMSE, which is a good evaluation metric. However, no details about this decision are offered. Can authors elaborate about their decision?

AUTHOR RESPONSE: Thank you for your valuable comment. We selected RMSE mainly for the following two properties of the measure - it provides the results in the same unit as input data and it inflates the large regression errors (which in turn causes overall error to grow). 

The manuscript has been updated to include the idea behind the selection of the metric as follows:

This metric has been selected for its two main properties - firstly, RMSE provides results (error rate) measured in the same unit as the attributes of the studied datasets, which makes it convenient for further evaluation and interpretation; secondly, RMSE inflates the influence of large regression errors in the model, which is desirable in the tuning process of the systems for the lowest possible error rate.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors presented a publication on Correlation Cycles in Multidimensional Datasets, indicating that its use allows for minimizing errors in regression models. The article has a well-developed methodology and adequately presented results and conclusions and the prospect of further research. I believe that the article meets the requirements and can be considered for further publication.

Author Response

We are very thankful to the review for their kind assessment of the presented work.

Reviewer 3 Report

Comments and Suggestions for Authors

NOTES:
• Data ordering problems are of great importance in machine learning. Therefore, the subject of the work is relevant in applications.
• This work focuses on the definition, identification and exploration of so-called correlation cycles.
• The proposed concept is evaluated in predictive analysis tasks in the context of three comparative data sets from the engineering area: sensor data set, superconductivity data set and energy farm data set. Python models are considered.
• In the analyzed examples, the authors show that the method using deconstructed correlation cycles achieves a lower error rate in 83% of regression cases compared to the same regression models without considering the cycle.
• The quality of the decision-making process is measured by one of the standardized error metrics. For the purposes of this work, the root mean square error (RMSE) – see (7).
• The corresponding comparison of RMSE for the three considered regressors with and without the use of deconstructed correlation cycles is given in Table 3.

SUGGESTED additions:
• Machine learning is of interest to researchers of various disciplines who do not understand the language of computer scientists. I suggest that in the conclusion or in the introduction you explain in simple and understandable language for the average reader the benefits of using the methods proposed in this work.

Author Response

COMMENT 1: Machine learning is of interest to researchers of various disciplines who do not understand the language of computer scientists. I suggest that in the conclusion or in the introduction you explain in simple and understandable language for the average reader the benefits of using the methods proposed in this work.

AUTHOR RESPONSE: Thank you for your valuable suggestion, which we fully agree will highlight the usability of the method and better the readability of the article. The conclusion section of the manuscript has been updated with the following text:

These findings lead to two main utilizations of the proposed method of correlation cycles. Since modern datasets contain a large amount of attributes, the building of models on such data is computationally expensive. This motivates the feature selection task, where a subset of attributes from input data with strong decision-making potential is selected. Hence, the proposed method of correlation cycles can be used to identify subsets of attributes fitting for the mentioned decision-making models.

The other use of the proposed method lies in the possibility of indirect identification of complex relationships in data that are not easily measurable via conventional correlation analysis. Correlation cycles can be used as a technique for the determination of such complex functional multiattribute dependencies, which can be utilized in other data analysis processes based on machine and deep learning methods.