Title: Calculation of the OPTICS Cordillera
Version: 1.0-3
Date: 2024-09-22
Author: Thomas Rusch ORCID iD [aut, cre], Patrick Mair ORCID iD [ctb], Kurt Hornik ORCID iD [ctb]
Maintainer: Thomas Rusch <thomas.rusch@wu.ac.at>
Description: Functions for calculating the OPTICS Cordillera. The OPTICS Cordillera measures the amount of 'clusteredness' in a numeric data matrix within a distance-density based framework for a given minimum number of points comprising a cluster, as described in Rusch, Hornik, Mair (2018) <doi:10.1080/10618600.2017.1349664>. We provide an R native version with methods for printing, summarizing, and plotting the result.
Depends: R (≥ 3.1.2),
Imports: dbscan
Suggests: cluster, scatterplot3d, MASS, R.rsp
VignetteBuilder: R.rsp
License: GPL-2 | GPL-3
LazyData: true
URL: https://r-forge.r-project.org/projects/stops/
RoxygenNote: 7.3.1
Encoding: UTF-8
NeedsCompilation: no
Packaged: 2024-09-22 15:10:48 UTC; trusch
Repository: CRAN
Date/Publication: 2024-09-22 16:00:01 UTC

cordillera: The OPTICS Cordillera

Description

A package for calculating the OPTICS Cordillera. The package contains various functions, methods and classes for calculating and plotting the OPTICS Cordillera and an interface to ELKI's OPTICS.

Details

The stops package provides these main functions:

Methods: For most of the objects returned by the high-level functions S3 classes and methods for standard generics were implemented, including print, summary, plot.

References:

Authors: Thomas Rusch

Maintainer: Thomas Rusch

Author(s)

Maintainer: Thomas Rusch thomas.rusch@wu.ac.at (ORCID)

Other contributors:

See Also

Useful links:

Examples

data(CAClimateIndicatorsCountyMedian)

res<-princomp(CAClimateIndicatorsCountyMedian[,3:52])
res
summary(res)

library(scatterplot3d)
scatterplot3d(res$scores[,1:3])

irisrep3d<-res$scores[,1:3]
irisrep2d<-res$scores[,1:2]


#OPTICS in dbscan version
library(dbscan)
ores<-optics(irisrep2d,minPts=15,eps=100)
plot(ores)
#OPTICS cordillera for the 2D representation
cres2d<-cordillera(irisrep2d,minpts=15)
cres2d
summary(cres2d)
plot(cres2d)

#OPTICS cordillera for the 3D representation
cres3d<-cordillera(irisrep3d,minpts=15)
cres3d
summary(cres3d)
plot(cres3d)

Climate Change Indicators of Californian Counties

Description

A dataset containing observed and projected indicators of climate change related natural hazards for 58 Californian counties. The values are actually the medians of the predicted distribution over spatial measurement points. It is a compiled data set from three sources and that has been aggregated to the county level. The projected data were derived under two different IPCC climate change scenarios (A2, the high emission scenario and B1, the moderate emission scenario). It further contains the county value of the California social vulnerability index.

Format

A data frame with 58 rows and 52 variables

county

The county name identifier.

vuln_CA

The vulnerability index of Cooley et al. (2012).

degFB1

County average 95th percentile daily maximum temperature in Fahrenheit from May 1 to September 30 over the historical period (1971-2000) under the climate scenario B1. These are averaged values for 4 different climate models. The source was Table 7 of Cooley et al. (2012).

heatB1_71_00

Projected average number of days where the daily maximum temperature exceeds the high-heat threshold (see above) over period 1971-2000. Projections are based on the B1 scenario and are averaged for four downscaled climate models. The source was Table 7 of Cooley et al. (2012).

heatB1_10_39

Projected average number of days where the daily maximum temperature exceeds the high-heat threshold (see above) over period 2010-2039. Projections are based on the B1 scenario and are averaged for four downscaled climate models. The source was Table 7 of Cooley et al. (2012).

heatB1_40_69

Projected average number of days where the daily maximum temperature exceeds the high-heat threshold (see above) over period 2040-2069. Projections are based on the B1 scenario and are averaged for four downscaled climate models. The source was Table 7 of Cooley et al. (2012).

heatB1_70_99

Projected average number of days where the daily maximum temperature exceeds the high-heat threshold (see above) over period 2070-2099. Projections are based on the B1 scenario and are averaged for four downscaled climate models. The source was Table 7 of Cooley et al. (2012).

degFA2

County average 95th percentile daily maximum temperature in Fahrenheit from May 1 to September 30 over the historical period (1971-2000) under the climate scenario A2. These are averaged values for 4 different climate models. The source was Table 7 of Cooley et al. (2012).

heatA2_71_00

Projected average number of days where the daily maximum temperature exceeds the high-heat threshold (see above) over period 1971-2000. Projections are based on the A2 scenario and are averaged for four downscaled climate models. The source was Table 7 of Cooley et al. (2012).

heatA2_10_39

Projected average number of days where the daily maximum temperature exceeds the high-heat threshold (see above) over period 2010-2039. Projections are based on the A2 scenario and are averaged for four downscaled climate models. The source was Table 7 of Cooley et al. (2012).

heatA2_40_69

Projected average number of days where the daily maximum temperature exceeds the high-heat threshold (see above) over period 2040-2069. Projections are based on the A2 scenario and are averaged for four downscaled climate models. The source was Table 7 of Cooley et al. (2012).

heatA2_70_99

Projected average number of days where the daily maximum temperature exceeds the high-heat threshold (see above) over period 2070-2099. Projections are based on the A2 scenario and are averaged for four downscaled climate models. The source was Table 7 of Cooley et al. (2012).

flood_2000

The percentage of a county's census block area vulnerable to unimpeded coastal flooding under baseline conditions (2000). The raw data were obtained from Heberger et al. (2009). From the census block areas we computed an area-weighted percentage for each county.

flood_2100

The projected percentage of a county's census block area vulnerable to unimpeded coastal flooding with a 1.4-meter (55-inch) sea-level rise (projected for 2100). The raw data were obtained from Heberger et al (2009). From the census block areas we computed an area-weighted percentage for each county.

basfA2_2000

The median aggregated CCSM3 observed or projected annual baseflow for year 2000 under scenario A2 by county (past years are observed, future years are projected). The source of the raw data was California Energy Commission (2008).

basfA2_2039

The median aggregated CCSM3 observed or projected annual baseflow for year 2039 under scenario A2 by county (past years are observed, future years are projected). The source of the raw data was California Energy Commission (2008).

basfA2_2069

The median aggregated CCSM3 observed or projected annual baseflow for year 2069 under scenario A2 by county (past years are observed, future years are projected). The source of the raw data was California Energy Commission (2008).

basfA2_2099

The median aggregated CCSM3 observed or projected annual baseflow for year 2099 under scenario A2 by county (past years are observed, future years are projected). The source of the raw data was California Energy Commission (2008).

basfB1_2000

The median aggregated CCSM3 observed or projected annual baseflow for year 2000 under scenario B1 by county (past years are observed, future years are projected). The source of the raw data was California Energy Commission (2008).

basfB1_2039

The median aggregated CCSM3 observed or projected annual baseflow for year 2039 under scenario B1 by county (past years are observed, future years are projected). The source of the raw data was California Energy Commission (2008).

basfB1_2069

The median aggregated CCSM3 observed or projected annual baseflow for year 2069 under scenario B1 by county (past years are observed, future years are projected). The source of the raw data was California Energy Commission (2008).

basfB1_2099

The median aggregated CCSM3 observed or projected annual baseflow for year 2099 under scenario B1 by county (past years are observed, future years are projected). The source of the raw data was California Energy Commission (2008).

evapA2_2000

The median aggregated Community Climate System Model v.3 (CCSM3) projected annual actual evapotranspiration for year 2000 under scenarios A2 by county. The source of the raw data was California Energy Commission (2008).

evapA2_2039

The median aggregated Community Climate System Model v.3 (CCSM3) projected annual actual evapotranspiration for year 2039 under scenarios A2 by county. The source of the raw data was California Energy Commission (2008).

evapA2_2069

The median aggregated Community Climate System Model v.3 (CCSM3) projected annual actual evapotranspiration for year 2069 under scenarios A2 by county. The source of the raw data was California Energy Commission (2008).

evapA2_2099

The median aggregated Community Climate System Model v.3 (CCSM3) projected annual actual evapotranspiration for year 2099 under scenarios A2 by county. The source of the raw data was California Energy Commission (2008).

evapB1_2000

The median aggregated Community Climate System Model v.3 (CCSM3) projected annual actual evapotranspiration for year 2000 under scenarios B1 by county. The source of the raw data was California Energy Commission (2008).

evapB1_2039

The median aggregated Community Climate System Model v.3 (CCSM3) projected annual actual evapotranspiration for year 2039 under scenarios B1 by county. The source of the raw data was California Energy Commission (2008).

evapB1_2069

The median aggregated Community Climate System Model v.3 (CCSM3) projected annual actual evapotranspiration for year 2069 under scenarios B1 by county. The source of the raw data was California Energy Commission (2008).

evapB1_2099

The median aggregated Community Climate System Model v.3 (CCSM3) projected annual actual evapotranspiration for year 2099 under scenarios B1 by county. The source of the raw data was California Energy Commission (2008).

prcpA2_2000

The median aggregated CCSM3 projected annual precipitation for year 2000 under scenario A2 by county. The source of the raw data was California Energy Commission (2008).

prcpA2_2039

The median aggregated CCSM3 projected annual precipitation for year 2000 under scenario A2 by county. The source of the raw data was California Energy Commission (2008).

prcpA2_2069

The median aggregated CCSM3 projected annual precipitation for year 2000 under scenario A2 by county. The source of the raw data was California Energy Commission (2008).

prcpA2_2099

The median aggregated CCSM3 projected annual precipitation for year 2000 under scenario A2 by county. The source of the raw data was California Energy Commission (2008).

prcpB1_2000

The median aggregated CCSM3 projected annual precipitation for year 2000 under scenario B1 by county. The source of the raw data was California Energy Commission (2008).

prcpB1_2039

The median aggregated CCSM3 projected annual precipitation for year 2000 under scenario B1 by county. The source of the raw data was California Energy Commission (2008).

prcpB1_2069

The median aggregated CCSM3 projected annual precipitation for year 2000 under scenario B1 by county. The source of the raw data was California Energy Commission (2008).

prcpB1_2099

The median aggregated CCSM3 projected annual precipitation for year 2000 under scenario B1 by county. The source of the raw data was California Energy Commission (2008).

smclA2_2000

The median aggregated CCSM3 projected annual fractional moisture in the entire soil column for year 2000 under scenario A2 by county. The source of the raw data was California Energy Commission (2008).

smclA2_2039

The median aggregated CCSM3 projected annual fractional moisture in the entire soil column for year 2039 under scenario A2 by county. The source of the raw data was California Energy Commission (2008).

smclA2_2069

The median aggregated CCSM3 projected annual fractional moisture in the entire soil column for year 2069 under scenario A2 by county. The source of the raw data was California Energy Commission (2008).

smclA2_2099

The median aggregated CCSM3 projected annual fractional moisture in the entire soil column for year 2099 under scenario A2 by county. The source of the raw data was California Energy Commission (2008).

smclB1_2000

The median aggregated CCSM3 projected annual fractional moisture in the entire soil column for year 2000 under scenario B1 by county. The source of the raw data was California Energy Commission (2008).

smclB1_2039

The median aggregated CCSM3 projected annual fractional moisture in the entire soil column for year 2039 under scenario B1 by county. The source of the raw data was California Energy Commission (2008).

smclB1_2069

The median aggregated CCSM3 projected annual fractional moisture in the entire soil column for year 2069 under scenario B1 by county. The source of the raw data was California Energy Commission (2008).

smclB1_2099

The median aggregated CCSM3 projected annual fractional moisture in the entire soil column for year 2099 under scenario B1 by county. The source of the raw data was California Energy Commission (2008).

fireA2_2020

The median aggregated Centre National de Recherches Meteorologiques (CNRM) projected annual wildfire risk (observing 1 or more fires in the next 30 years) for each county in year 2020 under scenarios A2. The source of the raw data was California Energy Commission (2008).

fireA2_2050

The median aggregated Centre National de Recherches Meteorologiques (CNRM) projected annual wildfire risk (observing 1 or more fires in the next 30 years) for each county in year 2050 under scenarios A2. The source of the raw data was California Energy Commission (2008).

fireA2_2085

The median aggregated Centre National de Recherches Meteorologiques (CNRM) projected annual wildfire risk (observing 1 or more fires in the next 30 years) for each county in year 2085 under scenarios A2. The source of the raw data was California Energy Commission (2008).

fireB1_2020

The median aggregated Centre National de Recherches Meteorologiques (CNRM) projected annual wildfire risk (observing 1 or more fires in the next 30 years) for each county in year 2020 under scenarios B1. The source of the raw data was California Energy Commission (2008).

fireB1_2050

The median aggregated Centre National de Recherches Meteorologiques (CNRM) projected annual wildfire risk (observing 1 or more fires in the next 30 years) for each county in year 2050 under scenarios B1. The source of the raw data was California Energy Commission (2008).

fireB1_2085

The median aggregated Centre National de Recherches Meteorologiques (CNRM) projected annual wildfire risk (observing 1 or more fires in the next 30 years) for each county in year 2085 under scenarios B1. The source of the raw data was California Energy Commission (2008).

Details

Overall there are 50 indicators of natural hazard, one indicator of social vulnerability and 1 identifier of the county which were:

Source

Cooley, H., Moore, E., Heberger, M. and Allen, L. (2012) Social Vulnerability to Climate Change. California Energy Commission. Publication Number: CEC-500-2012-013 , Heberger, M., Cooley, C., Herrera, P., Gleick, P. and Moore, E. (2009) The impacts of sea-level rise on the Californian coast. California Energy Commission. Publication Number: CEC-500-2009-024-F and California Energy Comission (2008) https://cal-adapt.org/data/download/

The OPTICS Cordillera

Description

Calculates the OPTICS Cordillera as described in Rusch et al. (2017). Based on optics in dbscan package.

Usage

cordillera(
  X,
  q = 2,
  minpts = 2,
  epsilon,
  distmeth = "euclidean",
  dmax = NULL,
  rang,
  digits = 10,
  scale = FALSE,
  ...
)

Arguments

X

numeric matrix or data frame representing coordinates of points, or a symmetric matrix of distance of points or an object of class dist. Passed to optics, see also there.

q

The norm used for the Cordillera. Defaults to 2.

minpts

The minimum number of points that must make up a cluster in OPTICS (corresponds to k in the paper). It is passed to optics where it is called minPts. Defaults to 2.

epsilon

The epsilon parameter for OPTICS (called epsilon_max in the paper). Defaults to 2 times the maximum distance between any two points.

distmeth

The distance to be computed if X is not a symmetric matrix (those from dist are available) or a dist object (otherwise ignored). Defaults to Euclidean distance.

dmax

The winsorization value for the highest allowed reachability. If used for comparisons this should be supplied. If no value is supplied, it is NULL (default), then dmax is taken from the data as minimum of epsilon or the largest reachability.

rang

A range of values for making up dmax. If supplied it overrules the dmax parameter and rang[2]-rang[1] is returned as dmax in the object. If no value is supplied rang is taken to be (0, dmax) taken from the data. Only use this when you know what you're doing, which would mean you're me (and even then we should be cautious).

digits

The precision to round the raw Cordillera and the norm factor. Defaults to 10.

scale

Should X be scaled if it is an asymmetric matrix or data frame? Can take values TRUE or FALSE or a numeric value. If TRUE or 1, standardisation is to mean=0 and sd=1. If 2, no centering is applied and scaling of each column is done with the root mean square of each column. If 3, no centering is applied and scaling of all columns is done as X/max(standard deviation(allcolumns)). If 4, no centering is applied and scaling of all columns is done as X/max(rmsq(allcolumns)). If FALSE, 0 or any other numeric value, no standardisation is applied. Defaults to FALSE.

...

Additional arguments to be passed to optics

Value

A list with the elements

Warning

It may happen that the (normed) cordillera cannot be calculated properly (e.g. division by zero, infinite raw cordillera, q value to high etc.). A warning will be printed and the normed Cordillera is either 0, 1 (if infinity is involved) or NA. In that case one needs to check one or more of the following: reachability values returned from optics, minpts, eps, the raw cordillera, dmax and the normalization factor normfac.

Examples

data(iris)
res<-princomp(iris[,1:4])
#2 dim goodness-of-clusteredness with clusters of at least 2 points
#With a matrix of points
cres2<-cordillera(res$scores[,1:2])
cres2
summary(cres2)
plot(cres2)

#with a dist object 
dl0 <- dist(res$scores[,1:2],"maximum") #maximum distance
cres0<-cordillera(dl0)
cres0
summary(cres0)
plot(cres0)

#with any symmetric distance/dissimilarity matrix 
dl1 <- cluster::daisy(res$scores[,1:2],"manhattan") 
cres1<-cordillera(dl1)
cres1
summary(cres1)
plot(cres1)

#4 dim goodness-of-clusteredness with clusters of at least 20
#points for PCA
cres4<-cordillera(res$scores[,1:4],minpts=20,epsilon=13,scale=3) 
#4 dim goodness-of-clusteredness with clusters of at least 20 points for original
#data
cres<-cordillera(iris[,1:4],minpts=20,epsilon=13,dmax=cres4$dmaxe,scale=3)
#There is more clusteredness for the original result
summary(cres4) 
summary(cres) 
plot(cres4) #cluster structure only a bit intelligible
plot(cres) #clearly two well separated clusters

###############################################################################
# Example from Rusch et al. (2018) with original data, PCA and Sammon mapping #
###############################################################################

#data preparation
data(CAClimateIndicatorsCountyMedian)
sovisel <- CAClimateIndicatorsCountyMedian[,-c(1,2,4,9)]
#normalize to [0,1]
sovisel <- apply(sovisel,2,function(x) (x-min(x))/(max(x)-min(x))) 
rownames(sovisel)  <- CAClimateIndicatorsCountyMedian[,1]
dis <- dist(sovisel)

#hyper parameters
dmax=1.22
q=2
minpts=3

#original data directly
cdat <- cordillera(sovisel,distmeth="euclidean",minpts=minpts,epsilon=10,q=q,
                   scale=0)
#equivalently
#dis2=dist(sovisel)
#cdat2 <- cordillera(dis2,minpts=minpts,epsilon=10,q=q,scale=FALSE) 

#PCA in 2-dim
pca1 <- princomp(sovisel)
pcas <- scale(pca1$scores[,1:2])
cpca <- cordillera(pcas,minpts=minpts,epsilon=10,q=q,dmax=dmax,scale=FALSE)

#Sammon mapping in 2-dim
sam <- MASS::sammon(dis)
samp <- scale(sam$points)
csam <- cordillera(samp,epsilon=10,minpts=minpts,q=q,dmax=dmax,scale=FALSE)

#results
cdat
cpca
csam

par(mfrow=c(3,1))
plot(cdat)
plot(cpca)
plot(csam)
par(mfrow=c(1,1))

Plot method for OPTICS Cordilleras

Description

Plots the reachability plot and adds the cordillera to it (as a line). In this plot the cordillera is proportional to the real value.

Usage

## S3 method for class 'cordillera'
plot(
  x,
  colbp = "lightgrey",
  coll = "black",
  liwd = 1.5,
  legend = FALSE,
  ylim,
  ...
)

Arguments

x

an object of class "cordillera"

colbp

color of the barplot.

coll

color of the cordillera line

liwd

width of the cordillera line

legend

draw legend

ylim

ylim for the barplots

...

additional arguments passed to barplot or lines

Print method for the OPTICS Cordillera

Description

Prints the raw and normalized OPTICS Cordillera

Usage

## S3 method for class 'cordillera'
print(x, ...)

Arguments

x

an object of class optics

...

additional arguments passed to print