topic Re: How to do clustering in mathcad ? in Mathcad

How to do clustering in mathcad ?

Mathcad111 — Thu, 07 Jun 2018 07:46:45 GMT

For example i have deployed some random nodes in (200x200), but the problem is i want to form some random cluster's, like the given graph, please look my mathcad file !

Re: How to do clustering in mathcad ?

-MFra- — Thu, 07 Jun 2018 07:12:18 GMT

Your question is not so clear to me. I do not think the answer you're looking for is as simple as mine ...............

Re: How to do clustering in mathcad ?

Mathcad111 — Thu, 07 Jun 2018 07:46:16 GMT

no i not looking for this solution i have attached modified mathcad file please go through it (inform me if have some question regarding it) !

Re: How to do clustering in mathcad ?

Mathcad111 — Thu, 07 Jun 2018 09:33:54 GMT

I have modified my mathcad but i don't know how to expand for full block !! please check mathcad file !

Re: How to do clustering in mathcad ?

-MFra- — Thu, 07 Jun 2018 10:21:45 GMT

you want something like that expandable as you like. right? in GSM networks, for example, the hexagons are all the same size and adjacent. To the chart, must be added the random positions of the sources, while the antennas are in the vertices. It's been a long time since I've dealt with the subject.

I'm working on it

Re: How to do clustering in mathcad ?

Mathcad111 — Thu, 07 Jun 2018 10:12:05 GMT

Thank for reply, Yes the same!

Re: How to do clustering in mathcad ?

Werner_E — Thu, 07 Jun 2018 10:18:20 GMT

Any additional constraints like same area/size of all clusters or same number of nodes in each cluster?

Do you only need a graphical representation of a hex grid like FM showed or do you need to sort your nodes according to which cluster they are in?

Re: How to do clustering in mathcad ?

-MFra- — Thu, 07 Jun 2018 10:26:58 GMT

Basically you should work in the complex plan. See the following example. I leave you to continue. I do not go further.

Re: How to do clustering in mathcad ?

Mathcad111 — Thu, 07 Jun 2018 10:29:34 GMT

1. There are no constrains so size of the cluster are random

2. Yes i want to find out what's inside the each cluster (say number of node's which is present inside the cluster) !

Re: How to do clustering in mathcad ?

Werner_E — Thu, 07 Jun 2018 10:50:42 GMT

2. Yes i want to find out what's inside the each cluster (say number of node's which is present inside the cluster) !

Clustering a plane with hexagons is quite easy but sorting the nodes and assigning each node to a specific cluster od counting the nodes in each cluster can be quite demanding, given that you want a hexagonal area and not a simple rectangle or even square which would make the task much simpler.

There sure are some clever algorithms to determine if a point is inside a given polygon and it may be even simpler in your case as you have regular hexagons.

Furthermore you would have to define what the count should if a point is exactly on a border between two hexagons or is one of the corners belonging to three hexagons.

If you are happy with an approximation you could simply count the nodes within the circumcircle of a hexagon.

Re: How to do clustering in mathcad ?

Werner_E — Thu, 07 Jun 2018 15:52:29 GMT

For whatever its worth here is a crude way to create a hex grid.

For counting the nodes within a hexagon you might search the forum for a routine a I posted quite a while ago which decides for any polygon if a given point is inside or not. Using a quick search here in the forum did not bring up the thread I have in mind but a routine by Stuart which may serve as well.

Re: How to do clustering in mathcad ?

Mathcad111 — Fri, 08 Jun 2018 05:58:56 GMT

Thank you ! i got some idea how to find the "node" under the hexogen (i'm not sure whether it will work!) let me check!

Re: How to do clustering in mathcad ?

-MFra- — Fri, 08 Jun 2018 07:27:58 GMT

but, on the hypothesis that the hexagons are regular, why do they deform after rotation?

Re: How to do clustering in mathcad ?

LucMeekes — Fri, 08 Jun 2018 07:59:48 GMT

Because, apart from rotating, a different scaling in x- and y- directions is applied...

Luc

Re: How to do clustering in mathcad ?

Werner_E — Fri, 08 Jun 2018 08:15:53 GMT

@-MFra- wrote:

but, on the hypothesis that the hexagons are regular, why do they deform after rotation?

I have not shown how to rotate the grid, I just mentioned that it could be done.

What I showed was just different scaling in x- and y-direction - you would expect "deformation" when doing so 😉

Apart from using different scaling factors the difference in the last two plots is that the left one scales wrt the origin and the right one wrt (-7/-7), which therefore remains the center of the lower left hexagon. Just playing around as I not really sure what exactly is needed.

Re: How to do clustering in mathcad ?

Werner_E — Fri, 08 Jun 2018 10:10:14 GMT

I found a sheet in my archive which compares a couple of different "Point-in-Polygon" algorithms. Its not the routine (based on the Jordan algorithm) I was talking about in my former post but they may serve as well.

I attach the sheet - maybe it can be of use for you.

Re: How to do clustering in mathcad ?

Werner_E — Fri, 08 Jun 2018 13:22:46 GMT

OK, now I found the Jordan routine I was talking about.

I added it in the attached worksheet along with some routines to scale, rotate and translate the grid

and also included an example how you may use the program to count the number of points in one hexagon:

Re: How to do clustering in mathcad ?

Mathcad111 — Sat, 09 Jun 2018 05:10:25 GMT

Apologies for my late reply, it's looks good can we able to extend for multiple hexogen ? and finding the no. of nodes under the cluster (that you have did already for single hexogen)!

Re: How to do clustering in mathcad ?

Mathcad111 — Sat, 09 Jun 2018 06:37:38 GMT

Now it's working for all hexagon (it's small modification are required from what you did already) Big Thanks for all the people!

Re: How to do clustering in mathcad ?

Werner_E — Sat, 09 Jun 2018 08:02:16 GMT

@Mathcad111 wrote:

Apologies for my late reply, it's looks good can we able to extend for multiple hexogen ? and finding the no. of nodes under the cluster (that you have did already for single hexogen)!

The routine will give you the number of nodes in any polygon you feed in.

So you will have to decide for a data structure you'd like to manage the various hexagons with.

Clustering a picture with a hexagon structure is one thing, managing that grid as a bunch of individually addressable areas is another. The grid structure I created consists of a list of vertex coordinates separate by a line of NaN's. So you should have not much troubles to split it into a list of single hexagons which you then could feed in the point counting routine. Maybe a vector consisting of elements representing a hexagon each could be a suitable structure. Depends on your needs and what exactly you have in mind.

You still have not decided what to do if a point lies exactly on the border of the polygon.

My routine will not distinguish between point an a segment of the border (belonging to 2 hexagons) and point being a vertex (belonging to 3 hexagons). If thats an issue the Punkt_in_Polygon and some other routines will have to be modified.