Notes to finalise

[uschiLaa]

• Second paragraph of introduction: I think we discussed this in the last meeting so I did not make any change here, but I am not really happy with this in the introduction (too much technical detail and notation), maybe we can move this partly into next section?
• Is there a solution to avoid section numbers in the overview paragraph? The numbers don’t appear in the headers, but having the cross-linking is useful.
• Paragraph two of „optimization methods“: is the problem for using gradient methods really the matrix? I would think it is about the objective function depending both on the projection matrix and the empiric data distribution
• Paragraph two of „Projection pursuit guided tour“: not clear what the second reason to look for non-normal is.
• Check section „existing algorithms“ for updated names and acronyms (I think I fixed these but it would be good for you to check)

[uschiLaa]

• Is it possible to make better use of the notation from Eq 2 when describing the diagnostics plots? E.g. for diagnostics 1 you do not show search bases, is there anything in your notation to refer to these?
• Fig 2: can you comment on the distribution of index values? Maybe say what value of alpha is used, that at later iterations the median index of sampled bases increases somewhat (at least for SA this seems to be the case), but we still sample a lot of „bad“ bases.
• Would be good to add one or two sentences about the holes index and reference in the „simulation setup“ section, since this is the main index used in the study.
• Search polish points listed below Fig 10: maybe specify how the distance between bases is defined, and is this really percentage change or relative change?
• Title labels in Fig 11 needs to be updated.

[huizezhang-sherry]

• I commented out the second paragraph of introduction but still leave it in the .rmd in case we want to reuse it.
• I also noticed this and is there any guideline provided by R Journal on this issue @dicook
• the objective function is dependent on both the projection matrix and the data and then ... ?
• fixed
• reviewed, thanks for this!

[huizezhang-sherry]

• I think the purpose of having this matrix notation here is to demonstrate the data structure. Initially, there were some writings on how each variable is mapped onto the ggplot elements for each plot, but later we removed it. I'm thinking if it is better to print out a data object instead.
• added
• added. Also, I'm thinking in Fig 2-4 and 8-10, I'm specific about what dataset is used with what index on 1/2D projection. I'm concerned whether it is necessary to give this information in the caption....
• The code in search_polish is polish_pdiff <- (best_row$index_val - cur_index) / cur_index and I think percentage change and relative change is the same thing?
• updated

[uschiLaa]

From what I see there are three points not fully settled:

point 3 from the first list: I was thinking that getting the gradient of the index function for all projections and any dataset would in general not be possible, which goes beyond the problem of having many free parameters (the entries of the projection matrix you currently mention)

point 3 of the second list: I think its good to have this information in the caption as is

point 4 from the second list: its just a question of units, percentage would be out of 100% but relative change is a fraction, so maximum is 1

[huizezhang-sherry]

• why it is in general impossible?
• ✔️
• TODO: change to "relative change"

[huizezhang-sherry]

settled