Estimating the Major Cluster by Mean-Shift with Updating Kernel

Round 1

Reviewer 1 Report

Overall this is an interesting update to an existing method and one which could be tested in various ways, some of which the authors touch upon.

However they have demonstrated the potential improvements offered by the method and this is good to see. I might like a more theoretical discussion of the role of the scale factor, thought the authors acknowledge that this is beyond the scope of this article. - The revisions relate to the language used to present the ideas which would benefit from substantial proof reading as in several places it is not always clear what the author's meaning is.
- The new method and the range of experiments used in order to justify it are the aspects of the paper which are most engaging and make it a worthy contribution.

Author Response

Thank you for your comments. We have corrected our revised manuscript by English native speaker’s proofreading. In revised manuscript, the corrections related to reviewers’ comments are shown in red. Because there are many corrections to the grammar and word spelling, we have not marked them. Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

In this work the authors deal with the construction of a mean-shift-type algorithm with updating kernels. At the best of my knowledge the results are original, the numerical section show the performances of the presented ideas that are introduced only at a formal level.  

Even if typos and overall English make the article very hard to read I would like to ask several questions to the authors:

1) In 2.1 you suppose a kind of symmetry for outliers since the mode is not biased by the presence of outliers, how the method performs in the absence of this heuristic hypothesis?

2) How you estimate $\hat{\mu}_N$ in the first step of the algorithm?

3) $\mu_W$ and $\sigma_W$ are not estimated quantities, please make it clear in the text. 

4) Your considerations on the drawbacks of the standard method is quite heuristic, please stick to rigorous considerations. Furthermore, how you compute the errors in Figure 1? Make the label in x and y axis explicit. 

5) The validity of the approximation in equation (17) is unclear to me. In the best option it is an approximation (therefore avoid to use the "=" symbol), in the worst option its validity is limited to nice supersymmetric situations. 

6) The extension to the multidimensional case is somehow trivial, I would suggest to write an Appendix. 

7) In the numerical tests all the images are almost not readable. Please specify always what you have in the x and y axis. it would be interesting to adopt the introduced technique for other kernels like the uniform of something biased. 

Author Response

Thank you for your comments. We have corrected our revised manuscript by English native speaker’s proofreading. In revised manuscript, the corrections related to reviewers’ comments are shown in red. Because there are many corrections to the grammar and word spelling, we have not marked them. Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The authors answered in a satisfactory way to my questions. 

I suggest publication after a further style check of the work and minor revisions.

In the following my remarks:

1) The authors did not modify the figures to improve the readability of the paper. I suggest to specify all the labels in the x and y axis (as already observed), for example: fig.1, fig. 3, fig. 4 etc... Please add the label to EACH axis. As it is, the work is not well done. 

2) It is not clear to me why $\sigma^2$ is at the denominator in (7)-(9).

Further comments: please add a space between the last letter and the citation bracket. 

Author Response

Thank you for your comments. According to your advice, we have corrected our manuscript carefully. All the corrections are marked in red in revised manuscript. Please see the attachment.

Author Response File: Author Response.docx