| parestimate {Rssa} | R Documentation |
Estimate periods from (set of) eigenvectors
Description
Function to estimate the parameters (frequencies and rates) given a set of SSA eigenvectors.
Usage
## S3 method for class '1d.ssa'
parestimate(x, groups, method = c("esprit", "pairs"),
subspace = c("column", "row"),
normalize.roots = NULL,
dimensions = NULL,
solve.method = c("ls", "tls"),
...,
drop = TRUE)
## S3 method for class 'toeplitz.ssa'
parestimate(x, groups, method = c("esprit", "pairs"),
subspace = c("column", "row"),
normalize.roots = NULL,
dimensions = NULL,
solve.method = c("ls", "tls"),
...,
drop = TRUE)
## S3 method for class 'mssa'
parestimate(x, groups, method = c("esprit", "pairs"),
subspace = c("column", "row"),
normalize.roots = NULL,
dimensions = NULL,
solve.method = c("ls", "tls"),
...,
drop = TRUE)
## S3 method for class 'cssa'
parestimate(x, groups, method = c("esprit", "pairs"),
subspace = c("column", "row"),
normalize.roots = NULL,
dimensions = NULL,
solve.method = c("ls", "tls"),
...,
drop = TRUE)
## S3 method for class 'nd.ssa'
parestimate(x, groups,
method = c("esprit"),
subspace = c("column", "row"),
normalize.roots = NULL,
dimensions = NULL,
solve.method = c("ls", "tls"),
pairing.method = c("diag", "memp"),
beta = 8,
...,
drop = TRUE)
Arguments
x |
SSA object |
groups |
list of indices of eigenvectors to estimate from |
... |
further arguments passed to 'decompose' routine, if necessary |
drop |
logical, if 'TRUE' then the result is coerced to lowest
dimension, when possible (length of |
dimensions |
a vector of dimension indices to perform ESPRIT along. 'NULL' means all dimensions. |
method |
For 1D-SSA, Toeplitz SSA, and MSSA: parameter estimation method, 'esprit' for 1D-ESPRIT (Algorithm 3.3 in Golyandina et al (2018)), 'pairs' for rough estimation based on pair of eigenvectors (Algorithm 3.4 in Golyandina et al (2018)). For nD-SSA: parameter estimation method. For now only 'esprit' is supported (Algorithm 5.6 in Golyandina et al (2018)). |
solve.method |
approximate matrix equation solving method, 'ls' for least-squares, 'tls' for total-least-squares. |
pairing.method |
method for esprit roots pairing, 'diag' for ‘2D-ESPRIT diagonalization’, 'memp' for “MEMP with an improved pairing step' |
subspace |
which subspace will be used for parameter estimation |
normalize.roots |
logical vector or 'NULL', force signal roots to lie on unit circle. 'NULL' means automatic selection: normalize iff circular topology OR Toeplitz SSA used |
beta |
In nD-ESPRIT, coefficient(s) in convex linear combination of
shifted matrices. The length of |
Details
See Sections 3.1 and 5.3 in Golyandina et al (2018) for full details.
Briefly, the time series is assumed to satisfy the model
x_n = \sum_k{C_k\mu_k^n}
for complex \mu_k or, alternatively,
x_n = \sum_k{A_k \rho_k^n \sin(2\pi\omega_k n + \phi_k)}.
The return value are the estimated moduli and arguments of complex
\mu_k, more precisely, \rho_k ('moduli') and T_k =
1/\omega_k ('periods').
For images, the model
x_{ij}=\sum_k C_k \lambda_k^i \mu_k^j
is considered.
Also ‘print’ and ‘plot’ methods are implemented for classes ‘fdimpars.1d’ and ‘fdimpars.nd’.
Value
For 1D-SSA (and Toeplitz), a list of objects of S3-class ‘fdimpars.1d’. Each object is a list with 5 components:
- roots
complex roots of minimal LRR characteristic polynomial
- periods
periods of dumped sinusoids
- frequencies
frequencies of dumped sinusoids
- moduli
moduli of roots
- rates
rates of exponential trend (
rates == log(moduli))
For 'method' = 'pairs' all moduli are set equal to 1 and all rates equal to 0.
For nD-SSA, a list of objects of S3-class ‘fdimpars.nd’. Each object
is named list of n ‘fdimpars.1d’ objects, each for corresponding
spatial coordinate.
In all cases elements of the list have the same names as elements of
groups. If group is unnamed, corresponding component gets name
‘Fn’, where ‘n’ is its index in groups list.
If 'drop = TRUE' and length of 'groups' is one, then corresponding list of estimated parameters is returned.
References
Golyandina N., Korobeynikov A., Zhigljavsky A. (2018): Singular Spectrum Analysis with R. Use R!. Springer, Berlin, Heidelberg.
Roy, R., Kailath, T., (1989): ESPRIT: estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. 37, 984–995.
Rouquette, S., Najim, M. (2001): Estimation of frequencies and damping factors by two- dimensional esprit type methods. IEEE Transactions on Signal Processing 49(1), 237–245.
Wang, Y., Chan, J-W., Liu, Zh. (2005): Comments on “estimation of frequencies and damping factors by two-dimensional esprit type methods”. IEEE Transactions on Signal Processing 53(8), 3348–3349.
Shlemov A, Golyandina N (2014) Shaped extensions of Singular Spectrum Analysis. In: 21st international symposium on mathematical theory of networks and systems, July 7–11, 2014. Groningen, The Netherlands, pp 1813–1820.
See Also
Rssa for an overview of the package, as well as,
ssa,
lrr,
Examples
# Decompose 'co2' series with default parameters
s <- ssa(co2, neig = 20)
# Estimate the periods from 2nd and 3rd eigenvectors using 'pairs' method
print(parestimate(s, groups = list(c(2, 3)), method = "pairs"))
# Estimate the peroids from 2nd, 3rd, 5th and 6th eigenvectors using ESPRIT
pe <- parestimate(s, groups = list(c(2, 3, 5, 6)), method = "esprit")
print(pe)
plot(pe)
# Artificial image for 2D SSA
mx <- outer(1:50, 1:50,
function(i, j) sin(2*pi * i/17) * cos(2*pi * j/7) + exp(i/25 - j/20)) +
rnorm(50^2, sd = 0.1)
# Decompose 'mx' with default parameters
s <- ssa(mx, kind = "2d-ssa")
# Estimate parameters
pe <- parestimate(s, groups = list(1:5))
print(pe)
plot(pe, col = c("green", "red", "blue"))
# Real example: Mars photo
data(Mars)
# Decompose only Mars image (without background)
s <- ssa(Mars, mask = Mars != 0, wmask = circle(50), kind = "2d-ssa")
# Reconstruct and plot texture pattern
plot(reconstruct(s, groups = list(c(13,14, 17, 18))))
# Estimate pattern parameters
pe <- parestimate(s, groups = list(c(13,14, 17, 18)))
print(pe)
plot(pe, col = c("green", "red", "blue", "black"))