[R-sig-Geo] Create distance 'neighborhood' (zone of indifference) when clustering binary data

Wed Nov 23 18:55:15 CET 2011

On Wed, 23 Nov 2011, Roger Bivand wrote:

> On Wed, 23 Nov 2011, Alberto Gallano wrote:
>
>> Hi Roger,
>> 
>> thanks for your reply. The data I posted is only a subset of my real data,
>> in which there are some points less than 100 meters apart.
>> 
>> To clarify what I want:
>> 
>> 1) I would like to create neighbourhoods of 100 meters within which all
>> points are neighbors. I think my code will do that with the real dataset if
>> I set the upper bounds of dnearneigh to 100.
>> 
>> 2) I want points outside of this 100 meter neighborhood to still be
>> neighbors, *but* with decreasing weight by distance. I believe this is
>> referred to as inverse distance weighting. I may want to accentuate this by
>> using squared inverse distance weighting.
>> 
>> The question is how can I accomplish task 2? Here is my attempt:
>
> Try going out to a sparse matrix with both, then back again:
>
> library(spdep)
> set.seed(1)
> coords <- matrix(runif(1000, 0, 2000), ncol=2)
> nb1 <- dnearneigh(coords, 0, 100)
> nb1
> k1 <- knn2nb(knearneigh(coords, k=1))
> maxD <- max(unlist(nbdists(k1, coords)))
> nb2 <- dnearneigh(coords, 100, maxD)
> set.ZeroPolicyOption(TRUE)
> lw1 <- nb2listw(nb1, style="B")
> mat1 <- as(as_dgRMatrix_listw(lw1), "CsparseMatrix")
> dnb2 <- nbdists(nb2, coords)
> idw2 <- lapply(dnb2, function(x) 1/(x-100))
> # to avoid an abrupt drop, I suggest subracting 100m

This wasn't a good idea, as points with (x-100) < 1 end up with weights > 
1. It would need trapping to reduce them to 1:

idw2 <- lapply(dnb2, function(x) {x100 <- x-100; x100 <- ifelse (x100 < 1, 
1, x100); 1/x100})

Roger

> all(unlist(sapply(idw2, function(x) is.finite(x))))
> lw2 <- nb2listw(nb2, glist=idw2, style="B")
> mat2 <- as(as_dgRMatrix_listw(lw2), "CsparseMatrix")
> mat12 <- mat1 + mat2
> image(mat1)
> image(mat2)
> image(mat12)
> summary(rowSums(mat12))
> summary(colSums(mat12))
> lw12 <- mat2listw(mat12, style="B")
> lw12
> table(card(lw12$neighbours))
>
> Hope this helps,
>
> Roger
>
>> 
>> coords <- cbind(dat$x, dat$y)
>> k1 <- knn2nb(knearneigh(coords))
>> maxD <- max(unlist(nbdists(k1, coords)))
>> datnb <- dnearneigh(coords, 0, maxD)
>> 
>> # general weights - inverse distance squared
>> dlist <- nbdists(datnb, coords)
>> idlist <- lapply(dlist, function(x) (1/x)^2)
>> 
>> datlistw.id2 <- nb2listw(datnb, glist=idlist, style="B", zero.policy=TRUE)
>> 
>> joincount.test(as.factor(dat$present), datlistw.id2, zero.policy=TRUE,
>>  alternative="greater", spChk=NULL, adjust.n=TRUE)
>> 
>> 
>> Does this make sense? It seems so to me. (There is a warning given, but I
>> think that is because my example has so few points).
>> 
>> thank you,
>> 
>> Alberto
>> 
>> 
>> 
>> On Mon, Nov 21, 2011 at 3:29 AM, Roger Bivand <Roger.Bivand at nhh.no> wrote:
>> 
>>> On Sun, 20 Nov 2011, Alberto Gallano wrote:
>>>
>>>  Hi, i'm trying to do join count analysis on binary data, but i'd like to
>>>> create neighborhood's of 'indifference' of 100 meters around each spacial
>>>> point.
>>>> 
>>>> I've been using dnearneigh to create a neighbor list and knearneigh to
>>>> calculate the maximum of the nearest neighbor distances for the upper
>>>> bound
>>>> argument to dnearneigh (so that no observations become islands).
>>>> 
>>>> My question is, how do I create neighborhoods based on distance? Should I
>>>> just input a number into the upper bound argument of dnearneigh, without
>>>> first using knearneigh? If so, what number would correspond to 100 meters
>>>> (Euclidean)? (btw, the coordinates are already projected).
>>>> 
>>> 
>>> If you mean that you define neighbours as points j within 100m of point i,
>>> then:
>>> 
>>> datnb <- dnearneigh(coords, 0, 100)
>>> 
>>> will do this if your coordinates are measured in metres. This doesn't work
>>> for your example, because the closest points are almost 1200m apart, so no
>>> point has any neighbours for this definition. However, your mentioning
>>> neighborhoods of 'indifference' makes me uncertain that this is what you
>>> mean. Do you mean placing a buffer around each point before finding
>>> neighbours?
>>> 
>>> Roger
>>> 
>>> 
>>>> Here is a small subsample of my data and analysis. Thanks,
>>>> 
>>>> Alberto
>>>> 
>>>> 
>>>> 
>>>> # ==========================
>>>> # data
>>>> dat <- structure(list(present = c(0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L,
>>>> 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L), x = c(332940L, 316301L,
>>>> 312714L, 306008L, 312248L, 329276L, 329663L, 341535L, 314761L,
>>>> 332898L, 332957L, 328332L, 312462L, 330063L, 317808L, 336216L,
>>>> 333763L, 315049L, 333855L, 324406L), y = c(4305226L, 4303010L,
>>>> 4316685L, 4309006L, 4319255L, 4311208L, 4316837L, 4306055L, 4301051L,
>>>> 4300625L, 4330342L, 4303420L, 4308292L, 4307181L, 4292904L, 4304336L,
>>>> 4313750L, 4297998L, 4314941L, 4315051L)), .Names = c("present",
>>>> "x", "y"), class = "data.frame", row.names = c(1L, 2L, 3L, 4L, 5L, 6L,
>>>> 7L, 8L, 9L, 10L, 11L, 12L, 13L, 14L, 15L, 16L, 17L, 18L, 19L, 20L))
>>>> 
>>>> 
>>>> library(spdep)
>>>> coords <- cbind(dat$x, dat$y)
>>>> k1 <- knn2nb(knearneigh(coords))
>>>> maxD <- max(unlist(nbdists(k1, coords))) # upper bound distance btw
>>>> neighbors
>>>> datnb <- dnearneigh(coords, 0, maxD)
>>>> summary(datnb)
>>>> print(is.symmetric.nb(datnb))
>>>> 
>>>> datlistw <- nb2listw(datnb, glist=NULL, style="B", zero.policy=TRUE)
>>>> 
>>>> # join count
>>>> joincount.test(as.factor(dat$**present), datlistw, zero.policy=TRUE,
>>>>   alternative="greater", spChk=NULL, adjust.n=TRUE)
>>>> # =========================
>>>>
>>>>        [[alternative HTML version deleted]]
>>>> 
>>>> ______________________________**_________________
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>>>> https://stat.ethz.ch/mailman/**listinfo/r-sig-geo<https://stat.ethz.ch/mailman/listinfo/r-sig-geo>
>>>> 
>>>> 
>>> --
>>> Roger Bivand
>>> Department of Economics, NHH Norwegian School of Economics,
>>> Helleveien 30, N-5045 Bergen, Norway.
>>> voice: +47 55 95 93 55; fax +47 55 95 95 43
>>> e-mail: Roger.Bivand at nhh.no
>>> 
>>> 
>> 
>
>

-- 
Roger Bivand
Department of Economics, NHH Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no