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Dear Meta,

Apologies for the multiple e-mails on this matter. I am happy to inform you that I managed to find out what the difference between the depthmapX and PST Integration values caused that I observed.

I was under the wrong assumption that Turner implemented Standard Closeness Centrality in DepthmapX, hence, I was expecting to get the same results from PST as I would from depthmapX.
However, I had a look at the source code of depthmapX on Github and it turns out that Turner calculates Integration by multiplying the node count before dividing by total depth:

Line 639: row.setValue(integ_col[k], (float)(curs_node_count * curs_node_count / total_depth_conv)); 

(https://github.com/SpaceGroupUCL/depthmapX/blob/master/salalib/segmmodules/segmtulip.cpp#L639)

So while Angular Integration in PST is calculated like this:

depthmapX calculated Angular Integration like this:


I’ve run a simple correlation to prove my point here by comparing depthmapX Integration W2K and PST Angular Integration W2K against NC*NC/TD, see below:

A) using Node Count and Total Depth from PST (As one can see with PST Node Count and Total Depth I arrived with a new value that is almost identical to depthmapX Integration R2 = 0.99):


And B) using Node Count and Total Depth from depthmapX (and here using depthmapX Node Count and Total Depth the value is identical):




I think this is an important distinction, which I also think might be worth emphasising. It also shows Turner’s way of dealing with ‘flipping depth’; He simply weighted the Node Count higher.

Best wishes,
Kimon


On 27 Nov 2019, at 18:15, Krenz, Kimon <[log in to unmask]> wrote:

Dear Meta,

Thanks a lot for your prompt reply and mentioning Hillier et al’s. 2012 paper. 
I am aware the problem of ‘flipping depth' outlined in the Hillier et al’s appendix, but I was under the impression the paper only refers to this in the context of normalised least angle choice (NACH). I did also encounter ‘flipping depth’ in Integration results, particularly in regional models using small metric radii (there was a discussion about the cause of this effect a while ago with Petros Koutsolampros). For what it’s worth, I might also mention that I proposed a method to detect such outlier for Integration in the appendix of my SSS11 paper: https://www.researchgate.net/publication/322255338_Regional_Morphology_The_Emergence_of_Spatial_Scales_in_Urban_Regions.

Having said that, I am not sure this is the particular problem here. 

Because if so, we should observe the effect to a similar magnitude in both PST and depthmapX result. While I can only observe it in the PST version (more so for Ai_W2K than Ai_W2K_Nain). A possible reason might be that the Angular Integration implementation in depthmapX is different to what Turner outlined in his 2007 paper?

Either way, many thanks for taking a look at this!

Best,
Kimon

Dr Kimon Krenz
FHEA

Research Associate
Urban Dynamics Lab
Space Syntax Laboratory

mail.       
[log in to unmask]
web.       
www.kimonkrenz.com

Faculty of the Built Environment
University College London UCL
22 Gordon Street
London WC1H 0QB

On 27 Nov 2019, at 17:07, Meta Berghauser Pont <[log in to unmask]> wrote:

Dear Kimon,
 
Thanks for your email. The problem you raise in the rural areas is referred to as “flipping depth” and is discussed in the appendix of the paper Hillier, B., Yang, T., Turner, A., 2012, “Normalising least angle choice in Depthmap and how it opens up new perspectives on the global and local analysis of city space”, in The Journal of Space Syntax, vol. 3, issue 2, p. 155-193.
 
But I will have a closer look at your data next week and discuss it in the group and then hopefully get back to you with an answer.
 
Kind regards,
Meta
Meta Berghauser Pont
Associate Professor Urban Design
 
Spatial Morphology Group (SMoG)
Chalmers University of Technology
Department of Architecture and Civil Engineering Sven Hultins gata 6 (room SB-K 395)
SE-412 96 Gothenburg, Sweden
 
+46 (0) 73 4233637
 
 
 
 
 
 
From: [log in to unmask] <[log in to unmask]> On Behalf Of Krenz, Kimon
Sent: den 26 november 2019 19:34
To: [log in to unmask]
Subject: Re: New PST for QGIS 3.- released!
 
Dear Meta, 
 
Thanks a lot for sharing the newest version of PST for QGIS 3.- with everyone.
It really is a fantastic tool, particularly when it comes to computation time!
 
I would like to follow up on Yuru’s question about the difference between depthmapX and PST.
As you’ve mentioned; PST allows the same space syntax analysis based on the axial map (or angular analysis based on the road-center-line map).
 
I’ve run a couple of Angular Integration analyses in QGIS using PST and the model of Gothenburg from your tutorial data and came a cross some rather unexpected results.
 
My expectation was that PST Angular Integration would give the same results as depthmapX Angular Segment Integration, however, they appear to not be comparable (r2 < 0.04 and 0.5 respectively).
 
Please see figure 1 below:
 
<image001.png>
 
As far as I understand from the PST manual, the user is forced to use either of two ’normalisation’ methods (1. Turner 2007 and 2. NAIN).
I briefly read Turner 2007 paper cited in the manual (https://journals.sagepub.com/doi/10.1068/b32067) and he mentioned two measures for integration (or closeness) 1. standard angular closeness and 2. weighted angular closeness (page 544):
<image003.png>
Compared to the PST Angular closeness formula (page 11):
<image005.png>
 
The above appear consistent with the formula generally referred to as Closeness Centrality (https://en.wikipedia.org/wiki/Closeness_centrality) a normalised form of Bavelas (1950) Closeness, multiplied by N - 1 (Turner seemed to have dropped the -1?), where N is the number of nodes in the graph. PST also includes a 1+ in the divisor to avoid dividing by 0.
 
However, if it is the same ’standard angular closeness’ Turner referred to in his paper, that is implemented in PST, then why are the results different (r2 = 0.036)? I am sure I am missing something here.
 
A visualisation of the three measures shows that the PST results have high values in more ‘rural’ areas–at the edge of the system–whereas depthmapX does not. This is also an observation that I encountered in other models that I have tested.
 
<image007.png>
 
I have uploaded a couple of files to a dropbox folder, so you can have a look at it (https://www.dropbox.com/sh/uuytgao5u9eblwm/AACf_eKFixYybkF3HMUdnMSPa?dl=0). 
The folder includes a high resolution versions of the figures (GOT_comp_1.png & linear_regression.png), a .CSV file with all data, including the geometry as x1y1x2y2 (GOT_comp.csv), as well as a MapInfo file to be opened in QGIS or depthmapX (GOT_comp.mif & .mid).
Please note: I have renamed the depthmapX variable in the MapInfo file to Integration_R2K.
 
Best wishes,
Kimon
Dr Kimon Krenz
FHEA

Research Associate
Urban Dynamics Lab
Space Syntax Laboratory

mail.       
[log in to unmask]
web.       
www.kimonkrenz.com
Faculty of the Built Environment
University College London UCL
22 Gordon Street
London WC1H 0QB


On 10 Sep 2019, at 09:58, Meta Berghauser Pont <[log in to unmask]> wrote:
 
New PST for QGIS 3.- released!

A new version of the Place Syntax Tool (PST) for QGIS versions 3.- for Windows and MAC is released.

PST is an open source tool for performing spatial analyses. It combines the space syntax description of the urban environment with conventional descriptions of attraction into the combined accessibility analysis tool PST. PST is developed by KTH School of Architecture, Chalmers School of Architecture (SMoG) and Spacescape AB, Sweden.

Download the plugin from the PST page at our website >>>
https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.smog.chalmers.se%2Fpst&amp;data=02%7C01%7C%7Cd101c6e7edea4a34c59a08d735ce8f93%7C1faf88fea9984c5b93c9210a11d9a5c2%7C0%7C0%7C637037033605883443&amp;sdata=7RUd4Kcfs4XUDU94gAFX0gbAd%2FoaqrWdFlqzBgRRoBg%3D&amp;reserved=0 

//
Meta Berghauser Pont
Associate Professor Urban Design

Spatial Morphology Group (SMoG)
Chalmers University of Technology
Department of Architecture and Civil Engineering Sven Hultins gata 6
SE-412 96 Gothenburg, Sweden

+46 (0) 73 4233637

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