Few comments (up to section Diagnostic 2)

[okayama1]

Abstract:

• • Abstract: A reference to “Guided tour” should be included. It is a bit odd to add a 
reference to pp and not to guided tour.
• • Abstract: We propose (instead of implement) a data collection object? Or we propose and implement a data collection object derived during the optimisation process of the projection pursuit guided …
• • Abstract: Why are you introducing visual diagnostics? To examine the performance of the optimization procedure, right? That needs to be included.
• • Abstract: Comma before “to assess” is not needed
• • Key words: visual diagnostics

Introduction:

• • You can remove the equations and just keep the text
• • Interesting structures in high dimensional … such as clusters or outliers among others…. (3rd paragraph)
• • Is this sentence fully accurate? A view is interesting if it can show some structures of the data other than a normal distribution, e.g., bi-modality, clustering and outliers.
• • Last paragraph page 1: these diagnostic plots can be used to query the performance of different optimisers

• • Optimisation methods:

• • Here our interest is on constrained optimisation problems as defined in () (you don’t need to specified if it is in the introduction) where it is not possible …
• • A large class of methods use the gradient ….--> what for? You are missing that point on that sentence. Also if you mention a large class of methods, you should provide a reference.
• • On the limited complexity of the constraints I don’t understand what you mean here.
• • As it will be shown Missing subject (it) in this sentence
• • This sentence is a bit off here. You are talking about something that it will be described in the next section. That is confusing: “As will be shown in the next section, the independent variables in our optimisation problem are the entries of a projection matrix and the computational time required to perform differentiation on a matrix could impede the render of tour animation” you need to put yourself in the shoes of someone that is not as familiar with this topic as you.
• • This is not a clear Hence, gradient-based methods are not the focus of this paper and considerations will be given to derivative-free methods.
• • Is there any general reference to derivative-free methods that you could add on page 2, third paragraph?
• • 4th paragraph: the global optimum can be attained under mild conditions. do you mean mild regularity conditions? Projection pursuit guided tour:
• • Projection pursuit guided tour combines two different methods (projection pursuit and guided tour) what for? With the aim of exploring interesting features in a high dimensional space.
• • Add a references for tour and guided tour
• • Second paragraph page 2 and it is used (missing subject it)
• • An interesting projection shows structures that are non-normal and this has been argued for two reasons: Theoretical proofs An interesting projection shows structures that are non-normal. Diaconis ….
• • The sentence starting with Legendre index (Friedman and Tukey, 1974), Hermite index (Hall et al., 1989), and natural Hermite It is just too long please cut it in smaller bits. Otherwise it is hard to read
• • In page 3 on the last paragraph you talked about tour and grand tour in more detail which is good. However, I feel that you have been talking about those concepts earlier. I wonder if we could move this paragraph a bit earlier in this section?

Optimisation in the tour:

• • it forms a Stiefel manifold. is there any reference for this claim?
• • What is it display in the animation? Some readers will not be familiar with that 4) The optimisation should be fast to compute since the tour animation is viewed by the users during the optimisation. the tour animation (where the projections are visualized) is typically used by the users to inspect the optimisation steps (or something along those lines) Existing algorithms:
• • Three optimisers have been implemented three optimisers for ?
• • This is not very clear the optimiser outputs (do you mean selects?) Al for guided tour to construct an interpolation path. Visual diagnostics:
• • four types of diagnostic plots are presented four types of diagnostic plots to investigate the optimiser performance are presented
• • In the section, examples are provide to demonstrate how the visual diagnostics can be used to inspect and reveal issues in the projection pursuit optimisation. Data structure for diagnostics
• • Three main pieces of information are recorded during the projection pursuit optimisation procedure
• • State S What is state S? (information related to the optimisation steps?)
• • What do you mean here? Multiple iterators index the information collected at different levels:
• • You are talking about inner and outer loop --? j and l are the counter of the outer and inner loop respectively. But for someone who is not familiar with the algorithm inner and outer loop is a bit ambiguous. Is there way where you could add a bit of intuition for those so people who are not familiar with the code can understand what you are talking about?
• • Is this really necessary here? The construction of diagnostic plots adopts the core concept of grammar of graphics (Wickham, 2010) in ggplot2. In grammar of graphics, plots are not produced by calling the commands, named by the appearance of the plot, i.e., boxplot and histogram, but by the concept of stacked layers. Seeing plots as stacked layers gives analysts the freedom to compose plots with multiple elements on hand.

Diagnostic 1

• • i.e that is, we want to summarise the increase of the index values over different iterations, and?
• • How many tries How many searches?
• • This is achieved using the search plot function: (Which search plot function?) In this function a boxplot is used to display the distribution ….
• • Search plot function do we have a name for it?
• • This is not clear where the selected basis (corresponding to the highest index value) is always shown as a point.
• • I don’t understand this In case of few tries at a given iteration showing the data points directly may be
• • This paragraph is not clear Additional annotations are added to facilitate better reading of the plot and these include 1) the number of points searched in each iteration can be added as text label at the bottom of each iteration; 2) the anchor bases to interpolate are connected and highlighted in a larger size; and 3) the colour of the last iteration is in a grey scale to indicate no better basis found in this iteration.
• • Figure 3 This figure displays the index values as the
• • When you describe a figure in the text, you need to tell the reader what are the bits at which the reader should be looking at and how to interpret those bits: Figure 2 shows an example of the search plot for CRS (left) and SA (right). We can observe that both optimisers find better bases during the first few iterations and then require longer time (iterations) to find this is not clear one in the later iterations (optimal bases?). Diagnostic 2
• • Another interesting feature to examine visually are the changes/improvements on the index value between interpolating bases. Interpolation bases are using to display the projections in the tour animation (or something along these lines)

[huizezhang-sherry]

Abstract:

• added
• changed
• added
• changed
• Di recommended picking keywords from topics in CRAN Task Views: https://cran.r-project.org/web/views/

[huizezhang-sherry]

Introduction:

• I commented out the second paragraph of introduction but still leave it in the .rmd in case we want to reuse it.
• ???
• I think it is not wrong @Di @uschiLaa
• I don't like the word "query" since it gives a connotation to web technology. I change it to "examine the performance of different optimisers"

[huizezhang-sherry]

Optimisation method:

• removed
• changed it to "Gradient-based methods are commonly used to optimise an objective function, with the most notable one being the gradient ascent (descent) method. Although these methods are popular, ... "
• I think we wrote that one together a while back then and I also feel like it can be clearer. I remove the bit "and on the limited complexity of the constraints"
• (next three points) we will need to talk about these points face-to-face/ over zoom
• Another reference added for random search
• changed

[huizezhang-sherry]

Projection pursuit guided tour:

• changed
• added
• already mentioned and changed in ursula's notes
• I have an attempt on making the sentence easier to understand
• In this section I have the structure of an opening paragraph, a para for projection pursuit, and a para for tour/ guided tour. Where do you want this paragraph to be moved to?

[huizezhang-sherry]

Optimisation in tour:

• This is a textbook result I can cite the one that I read: Optimization algorithms on matrix manifolds
• ???

Existing algorithms:

• ???
• ???

Visual diagnostics:

• I shortened this opening paragraph since the main purpose of this section is to introduce the data structure and 4 types of plot. "demonstrate how the visual diagnostics can be used to inspect and reveal issues in the projection pursuit optimisation" is the theme for the next section, "Diagnosing an optimiser"

Data structure for diagnostics

• changed
• we will talk about the state, iterator, and matrix in eq 2 in the meeting
• the last paragraph becomes less necessary for now - I commented it out

[huizezhang-sherry]

Diagnostic 1:

• changed
• how many bases need to be sampled
• (next two points) changed
• changed it to "accepted basis"
• I added some punctuation here: " In the case of few tries at a given iteration, showing the data points directly may be preferred over the boxplot"
• this paragraph describes other elements in the plot: the text label, line connection of the accepted basis, and greyscale for the last iteration. These are necessary.
• Figure 3 belongs to diagnostic 2 so where is "This figure displays the index values as the" from?
• This caption has been changed already

Diagnostic 2:

• changed

[okayama1]

I have done few changes directly on the paper and you are good to go! The paper looks great !