rself.ref: Generation of Points from Self Correspondence Pattern
In nnspat: Nearest Neighbor Methods for Spatial Patterns
rself.ref R Documentation
Generation of Points from Self Correspondence Pattern
Description
An object of class "SpatPatterns".
Generates n_1 2D points from class 1 and n_2 (denoted as n2 as an argument)
2D points from class 2 in such a way that
self-reflexive pairs are more frequent than expected under CSR independence.
If distribution="uniform", the points from class 1, say X_i are generated as follows:
X_i \stackrel{iid}{\sim} Uniform(S_1) for S_1=(c1r[1],c1r[2])^2 for i=1,2,\ldots,n_{1h}
where n_{1h}=\lfloor n_1/2 \rfloor,
and for k=n_{1h},+1,\ldots,n_1, X_k=X_{k-n_{1h}}+r (\cos(T_k), \sin(T_k)) where r \sim Uniform(0,r_0)
and T_k are iid \sim Uniform(0,2 \pi).
Similarly, the points from class 2, say Y_j are generated as follows:
Y_j \stackrel{iid}{\sim} Uniform(S_2) for S_2=(c2r[1],c2r[2])^2 for j=1,2,\ldots,n_{2h} where n_{2h}=\lfloor n_2/2\rfloor),
and for l=n_{2h},+1,\ldots,n_2, Y_l=Y_{l-n_{2h}}+r (\cos(T_l), \sin(T_l)) where r \sim Uniform(0,r_0) and
T_l \stackrel{iid}{\sim} Uniform(0,2 \pi).
This version is the case IV in the article (\insertCiteceyhan:NNCorrespond2018;textualnnspat).
If distribution="bvnormal", the points from class 1,
say X_i are generated as follows:
X_i \stackrel{iid}{\sim} BVN(CM(S_1),I_{2x})
where CM(S_1) is the center of mass of S_1
and I_{2x} is a 2 \times 2 matrix with diagonals
equal to s_1^2 with s_1=(c1r[2]-c1r[1])/3
and off-diagonals are 0 for i=1,2,\ldots,n_{1h}
where n_{1h}=\lfloor{n_1/2\rfloor},
and for k=n_{1h}+1,\ldots,n_1, X_k = Z_k+r (\cos(T_k), \sin(T_k))
where Z_k \sim BVN(X_{k-n_{1h}}, I_2(r_0))
with I_2(r_0) being the 2 \times 2 matrix
with diagonals r_0/3 and 0 off-diagonals, r \sim Uniform(0,r_0) and
T_k are iid \sim Uniform(0,2 \pi).
Similarly, the points from class 2, say Y_j are generated as follows:
Y_j \stackrel{iid}{\sim} BVN(CM(S_2),I_{2y})
where CM(S_1) is the center of mass of S_1 and
I_{2y} is a 2 \times 2 matrix with diagonals
equal to s_2^2 with s_2=(c2r[2]-c2r[1])/3 and
off-diagonals are 0 for j=1,2,\ldots,n_{2h}
where n_{2h}=\lfloor n_2/2\rfloor),
and for l=n_{2h},+1,\ldots,n_2, Y_l = W_k+r (\cos(T_l), \sin(T_l))
where W_l \sim BVN(Y_{l-n_{2h}}, I_2(r_0))
with I_2(r_0) being the 2 \times 2 matrix
with diagonals r_0/3 and 0 off-diagonals, r \sim Uniform(0,r_0) and
T_l \stackrel{iid}{\sim} Uniform(0,2 \pi).
Notice that the classes will be segregated
if the supports S_1 and S_2 are separated, with more separation
implying stronger segregation. Furthermore, r_0
(denoted as r0 as an argument) determines
the level of self-reflexivity or self correspondence,
i.e., smaller r_0 implies a higher level of self correspondence
and vice versa for higher r_0 .
See also (\insertCiteceyhan:NNCorrespond2018;textualnnspat)
and the references therein.
Usage
rself.ref(n1, n2, c1r, c2r, r0, distribution = c("uniform", "bvnormal"))
Arguments
n1, n2
Positive integers representing the numbers of points to be generated from the two classes
c1r, c2r
Ranges of the squares which constitute the supports of the two classes
r0
The radius of attraction which determines the level of self-reflexivity (or self correspondence) in
both the uniform and bvnormal distributions for the two classes
distribution
The argument determining the distribution of each class. Takes on values "uniform" and
"bvnormal" (see the description for the details).
Value
A list with the elements
pat.type
"2c" for the 2-class pattern of self-correspondence of the two classes
type
The type of the spatial pattern
parameters
The radius of attraction r_0 which determines the level of self-correspondence.
lab
The class labels of the generated points, it is 1 class 1 or X1 points and
2 for class 2 or X_2 points
init.cases
The initial points for class 1 and class 2, one initial point for each class, marked
with a cross in the plot.
gen.points
The output set of generated points from the self-correspondence pattern.
ref.points
The input set of reference points, it is NULL for this function.
desc.pat
Description of the species correspondence pattern
mtitle
The "main" title for the plot of the point pattern
num.points
The number of generated points.
xlimit, ylimit
The possible ranges of the x- and y-coordinates of the generated points
Author(s)
Elvan Ceyhan
See Also
Zself.ref and Xsq.spec.cor
Examples
n1<-50; #try also n1<-50; n1<-1000;
n2<-50; #try also n2<-50; n2<-1000;
c1r<-c(0,1) #try also c(0,5/6), C(0,3/4), c(0,2/3)
c2r<-c(0,1) #try also c(1/6,1), c(1/4,1), c(1/3,1)
r0<-1/9 #try also 1/7, 1/8
#data generation
Xdat<-rself.ref(n1,n2,c1r,c2r,r0)
Xdat
summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)
#data generation (bvnormal)
Xdat<-rself.ref(n1,n2,c1r,c2r,r0,distr="bvnormal")
Xdat
summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)
nnspat documentation built on May 29, 2024, 10:03 a.m.
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| rself.ref | R Documentation |
Generation of Points from Self Correspondence Pattern
Description
An object of class "SpatPatterns".
Generates n_1 2D points from class 1 and n_2 (denoted as n2 as an argument)
2D points from class 2 in such a way that
self-reflexive pairs are more frequent than expected under CSR independence.
If distribution="uniform", the points from class 1, say X_i are generated as follows:
X_i \stackrel{iid}{\sim} Uniform(S_1) for S_1=(c1r[1],c1r[2])^2 for i=1,2,\ldots,n_{1h}
where n_{1h}=\lfloor n_1/2 \rfloor,
and for k=n_{1h},+1,\ldots,n_1, X_k=X_{k-n_{1h}}+r (\cos(T_k), \sin(T_k)) where r \sim Uniform(0,r_0)
and T_k are iid \sim Uniform(0,2 \pi).
Similarly, the points from class 2, say Y_j are generated as follows:
Y_j \stackrel{iid}{\sim} Uniform(S_2) for S_2=(c2r[1],c2r[2])^2 for j=1,2,\ldots,n_{2h} where n_{2h}=\lfloor n_2/2\rfloor),
and for l=n_{2h},+1,\ldots,n_2, Y_l=Y_{l-n_{2h}}+r (\cos(T_l), \sin(T_l)) where r \sim Uniform(0,r_0) and
T_l \stackrel{iid}{\sim} Uniform(0,2 \pi).
This version is the case IV in the article (\insertCiteceyhan:NNCorrespond2018;textualnnspat).
If distribution="bvnormal", the points from class 1,
say X_i are generated as follows:
X_i \stackrel{iid}{\sim} BVN(CM(S_1),I_{2x})
where CM(S_1) is the center of mass of S_1
and I_{2x} is a 2 \times 2 matrix with diagonals
equal to s_1^2 with s_1=(c1r[2]-c1r[1])/3
and off-diagonals are 0 for i=1,2,\ldots,n_{1h}
where n_{1h}=\lfloor{n_1/2\rfloor},
and for k=n_{1h}+1,\ldots,n_1, X_k = Z_k+r (\cos(T_k), \sin(T_k))
where Z_k \sim BVN(X_{k-n_{1h}}, I_2(r_0))
with I_2(r_0) being the 2 \times 2 matrix
with diagonals r_0/3 and 0 off-diagonals, r \sim Uniform(0,r_0) and
T_k are iid \sim Uniform(0,2 \pi).
Similarly, the points from class 2, say Y_j are generated as follows:
Y_j \stackrel{iid}{\sim} BVN(CM(S_2),I_{2y})
where CM(S_1) is the center of mass of S_1 and
I_{2y} is a 2 \times 2 matrix with diagonals
equal to s_2^2 with s_2=(c2r[2]-c2r[1])/3 and
off-diagonals are 0 for j=1,2,\ldots,n_{2h}
where n_{2h}=\lfloor n_2/2\rfloor),
and for l=n_{2h},+1,\ldots,n_2, Y_l = W_k+r (\cos(T_l), \sin(T_l))
where W_l \sim BVN(Y_{l-n_{2h}}, I_2(r_0))
with I_2(r_0) being the 2 \times 2 matrix
with diagonals r_0/3 and 0 off-diagonals, r \sim Uniform(0,r_0) and
T_l \stackrel{iid}{\sim} Uniform(0,2 \pi).
Notice that the classes will be segregated
if the supports S_1 and S_2 are separated, with more separation
implying stronger segregation. Furthermore, r_0
(denoted as r0 as an argument) determines
the level of self-reflexivity or self correspondence,
i.e., smaller r_0 implies a higher level of self correspondence
and vice versa for higher r_0 .
See also (\insertCiteceyhan:NNCorrespond2018;textualnnspat) and the references therein.
Usage
rself.ref(n1, n2, c1r, c2r, r0, distribution = c("uniform", "bvnormal"))
Arguments
n1, n2 |
Positive integers representing the numbers of points to be generated from the two classes |
c1r, c2r |
Ranges of the squares which constitute the supports of the two classes |
r0 |
The radius of attraction which determines the level of self-reflexivity (or self correspondence) in both the uniform and bvnormal distributions for the two classes |
distribution |
The argument determining the distribution of each class. Takes on values |
Value
A list with the elements
pat.type |
|
type |
The type of the spatial pattern |
parameters |
The radius of attraction |
lab |
The class labels of the generated points, it is 1 class 1 or X1 points and
2 for class 2 or |
init.cases |
The initial points for class 1 and class 2, one initial point for each class, marked with a cross in the plot. |
gen.points |
The output set of generated points from the self-correspondence pattern. |
ref.points |
The input set of reference points, it is |
desc.pat |
Description of the species correspondence pattern |
mtitle |
The |
num.points |
The number of generated points. |
xlimit, ylimit |
The possible ranges of the |
Author(s)
Elvan Ceyhan
See Also
Zself.ref and Xsq.spec.cor
Examples
n1<-50; #try also n1<-50; n1<-1000;
n2<-50; #try also n2<-50; n2<-1000;
c1r<-c(0,1) #try also c(0,5/6), C(0,3/4), c(0,2/3)
c2r<-c(0,1) #try also c(1/6,1), c(1/4,1), c(1/3,1)
r0<-1/9 #try also 1/7, 1/8
#data generation
Xdat<-rself.ref(n1,n2,c1r,c2r,r0)
Xdat
summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)
#data generation (bvnormal)
Xdat<-rself.ref(n1,n2,c1r,c2r,r0,distr="bvnormal")
Xdat
summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)
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