Description Usage Arguments Details Value Note Author(s) References See Also Examples
Generate a random set parameters for the Gaussian mixture
model (GMM) and Gaussian mixture copula model (GMCM). Primarily, it provides
an easy prototype of the theta
-format used in GMCM.
1 2 3 4 5 6 |
m |
The number of components in the mixture. |
d |
The dimension of the mixture distribution. |
method |
The method by which the theta should be generated.
See details. Defaults to |
Depending on the method
argument the parameters are generated as
follows. The new behavior is inspired by the simulation scenarios in
Friedman (1989) but not exactly the same.
pie
is generated by m draws of a chi-squared distribution with
3m degrees of freedom divided by their sum. If
method = "old"
the uniform distribution is used instead.
mu
is generated by m i.i.d. d-dimensional zero-mean
normal vectors with covariance matrix 100I
.
(unchanged from the old behavior)
sigma
is dependent on method
. The covariance matrices for each
component are generated as follows. If the method
is
"EqualSpherical"
, then the covariance matrices are the
identity matrix and thus are all equal and spherical.
"UnequalSpherical"
, then the covariance matrices are
scaled identity matrices. In component h, the covariance
matrix is hI
"EqualEllipsoidal"
, then highly elliptical covariance
matrices which equal for all components are used.
The square root of the d eigenvalues are chosen
equidistantly on
the interval 10 to 1 and a randomly (uniformly)
oriented orthonormal basis is chosen and used for all
components.
"UnqualEllipsoidal"
, then highly elliptical covariance
matrices different for all components are used.
The eigenvalues of the covariance matrices equal as in all
components as in "EqualEllipsoidal"
. However, they are all
randomly (uniformly) oriented (unlike as described in
Friedman (1989)).
"old"
, then the old behavior is used.
The old behavior differs from "EqualEllipsoidal"
by using
the absolute value of d zero-mean i.i.d. normal
eigenvalues with a standard deviation of 8.
In all cases, the orientation is selected uniformly.
A named list of parameters with the 4 elements:
|
An integer giving the number of components in the mixture. Default is 3. |
|
An integer giving the dimension of the mixture distribution. Default is 2. |
|
A numeric vector of length |
|
A |
|
A |
The function is.theta
checks whether or not theta
is in the correct format.
Anders Ellern Bilgrau <anders.ellern.bilgrau@gmail.com>
Friedman, Jerome H. "Regularized discriminant analysis." Journal of the American statistical association 84.405 (1989): 165-175.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | rtheta()
rtheta(d = 5, m = 2)
rtheta(d = 3, m = 2, method = "EqualEllipsoidal")
test <- rtheta()
is.theta(test)
summary(test)
print(test)
plot(test)
## Not run:
A <- SimulateGMMData(n = 100, rtheta(d = 2, method = "EqualSpherical"))
plot(A$z, col = A$K, pch = A$K, asp = 1)
B <- SimulateGMMData(n = 100, rtheta(d = 2, method = "UnequalSpherical"))
plot(B$z, col = B$K, pch = B$K, asp = 1)
C <- SimulateGMMData(n = 100, rtheta(d = 2, method = "EqualEllipsoidal"))
plot(C$z, col = C$K, pch = C$K, asp = 1)
D <- SimulateGMMData(n = 100, rtheta(d = 2, method = "UnequalEllipsoidal"))
plot(D$z, col = D$K, pch = D$K, asp = 1)
## End(Not run)
|
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