| Type: | Package |
| Title: | Conducting the Peak Fitting Based on the EM Algorithm |
| Version: | 0.3.1 |
| Description: | The peak fitting of spectral data is performed by using the frame work of EM algorithm. We adapted the EM algorithm for the peak fitting of spectral data set by considering the weight of the intensity corresponding to the measurement energy steps (Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019, 2021 and 2023) <doi:10.1080/14686996.2019.1620123>, <doi:10.1080/27660400.2021.1899449> <doi:10.1080/27660400.2022.2159753>. The package efficiently estimates the parameters of Gaussian mixture model during iterative calculation between E-step and M-step, and the parameters are converged to a local optimal solution. This package can support the investigation of peak shift with two advantages: (1) a large amount of data can be processed at high speed; and (2) stable and automatic calculation can be easily performed. |
| License: | MIT + file LICENSE |
| Language: | en-US |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.1.1 |
| Suggests: | testthat (≥ 3.0.0) |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | no |
| Packaged: | 2023-03-29 12:38:38 UTC; matsumura_tarojiro |
| Author: | Tarojiro Matsumura [aut, cre] |
| Maintainer: | Tarojiro Matsumura <matsumura-tarojiro@aist.go.jp> |
| Repository: | CRAN |
| Date/Publication: | 2023-03-29 13:40:02 UTC |
Visualization of the result of spect_em_dsgmm
Description
Visualization of the result of spect_em_dsgmm().
Usage
show_dsgmm_curve(spect_em_dsgmm_res,
x,
y,
mix_ratio_init,
mu_init,
sigma_init,
alpha_init,
eta_init)
Arguments
spect_em_dsgmm_res |
data set obtained by spect_em_dsgmm() |
x |
measurement steps |
y |
intensity |
mix_ratio_init |
initial values of the mixture ratio of the components |
mu_init |
initial values of the mean of the components |
sigma_init |
initial values of the standard deviation of the components |
alpha_init |
initial values of the asymmetric parameter of the components |
eta_init |
initial values of the mixing ratio of Gauss and Lorentz distribution |
Details
Perform a visualization of fitting curve estimated by Doniach-Sunjic-Gauss mixture model.
Value
Show the fitting curve and variation of the parameters.
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2021). Spectrum adapted expectation-conditional maximization algorithm for extending high–throughput peak separation method in XPS analysis. Science and Technology of Advanced Materials: Methods, 1(1), 45-55.
Examples
#generating the synthetic spectral data based on three component Doniach-Sunjic-Gauss mixture model.
x <- seq(0, 100, by = 0.5)
true_mu <- c(20, 50, 80)
true_sigma <- c(3, 3, 3)
true_alpha <- c(0.1, 0.3, 0.1)
true_eta <- c(0.4, 0.6, 0.1)
true_mix_ratio <- rep(1/3, 3)
degree <- 4
#trancated Doniach-Sunjic-Gauss
truncated_dsg <- function(x, mu, sigma, alpha, eta) {
((eta*(((gamma(1-alpha)) /
((x-mu)^2+(sqrt(2*log(2))*sigma)^2)^((1-alpha)/2)) *
cos((pi*alpha/2)+(1-alpha)*atan((x-mu) /
(sqrt(2*log(2))*sigma))))) + (1-eta)*dnorm(x, mu, sigma)) /
sum( ((eta*(((gamma(1-alpha)) /
((x-mu)^2+(sqrt(2*log(2))*sigma)^2)^((1-alpha)/2)) *
cos((pi*alpha/2)+(1-alpha)*atan((x-mu) /
(sqrt(2*log(2))*sigma))))) + (1-eta)*dnorm(x, mu, sigma)))
}
y <- c(true_mix_ratio[1]*truncated_dsg(x = x,
mu = true_mu[1],
sigma = true_sigma[1],
alpha = true_alpha[1],
eta = true_eta[1])*10^degree +
true_mix_ratio[2]*truncated_dsg(x = x,
mu = true_mu[2],
sigma = true_sigma[2],
alpha = true_alpha[2],
eta = true_eta[2])*10^degree +
true_mix_ratio[3]*truncated_dsg(x = x,
mu = true_mu[3],
sigma = true_sigma[3],
alpha = true_alpha[3],
eta = true_eta[3])*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
K <- 3
mix_ratio_init <- c(0.2, 0.4, 0.4)
mu_init <- c(20, 40, 70)
sigma_init <- c(4, 3, 2)
alpha_init <- c(0.3, 0.2, 0.4)
eta_init <- c(0.5, 0.4, 0.3)
#Coducting calculation
SP_ECM_DSG_res <- spect_em_dsgmm(x = x,
y = y,
mu = mu_init,
sigma = sigma_init,
alpha = alpha_init,
eta = eta_init,
mix_ratio = mix_ratio_init,
conv.cri = 1e-2,
maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_dsgmm_curve(SP_ECM_DSG_res,
x,
y,
mix_ratio_init,
mu_init,
sigma_init,
alpha_init,
eta_init)
#Showing the result of spect_em_dsgmm()
print(cbind(c(mu_init),
c(sigma_init),
c(alpha_init),
c(eta_init),
c(mix_ratio_init)))
print(cbind(SP_ECM_DSG_res$mu,
SP_ECM_DSG_res$sigma,
SP_ECM_DSG_res$alpha,
SP_ECM_DSG_res$eta,
SP_ECM_DSG_res$mix_ratio))
print(cbind(true_mu,
true_sigma,
true_alpha,
true_eta,
true_mix_ratio))
Visualization of the result of spect_em_gmm
Description
Visualization of the result of spect_em_gmm().
Usage
show_gmm_curve(spect_em_gmm_res, x, y, mix_ratio_init, mu_init, sigma_init)
Arguments
spect_em_gmm_res |
data set obtained by spect_em_gmm() |
x |
measurement steps |
y |
intensity |
mix_ratio_init |
initial values of the mixture ratio of the components |
mu_init |
initial values of the mean of the components |
sigma_init |
initial values of the standard deviation of the components |
Details
Perform a visualization of fitting curve estimated by Gaussian mixture model.
Value
Show the fitting curve and variation of the parameters.
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Examples
#generating the synthetic spectral data based on three component Gausian mixture model.
x <- seq(0, 100, by = 0.5)
true_mu <- c(35, 50, 65)
true_sigma <- c(3, 3, 3)
true_mix_ratio <- rep(1/3, 3)
degree <- 4
y <- c(true_mix_ratio[1] * dnorm(x = x, mean = true_mu[1], sd = true_sigma[1])*10^degree +
true_mix_ratio[2] * dnorm(x = x, mean = true_mu[2], sd = true_sigma[2])*10^degree +
true_mix_ratio[3] * dnorm(x = x, mean = true_mu[3], sd = true_sigma[3])*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
K <- 3
mix_ratio_init <- c(0.2, 0.4, 0.4)
mu_init <- c(20, 40, 70)
sigma_init <- c(2, 5, 4)
#Coducting calculation
SP_EM_G_res <- spect_em_gmm(x, y, mu = mu_init, sigma = sigma_init, mix_ratio = mix_ratio_init,
conv.cri = 1e-2, maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_gmm_curve(SP_EM_G_res, x, y, mix_ratio_init, mu_init, sigma_init)
#Showing the result of spect_em_gmm()
print(cbind(c(mu_init), c(sigma_init), c(mix_ratio_init)))
print(cbind(SP_EM_G_res$mu, SP_EM_G_res$sigma, SP_EM_G_res$mix_ratio))
print(cbind(true_mu, true_sigma, true_mix_ratio))
Visualization of the result of spect_em_lmm
Description
Visualization of the result of spect_em_lmm().
Usage
show_lmm_curve(spect_em_lmm_res, x, y, mix_ratio_init, mu_init, gam_init)
Arguments
spect_em_lmm_res |
data set obtained by spect_em_lmm() |
x |
measurement steps |
y |
intensity |
mix_ratio_init |
initial values of the mixture ratio of the components |
mu_init |
initial values of the mean of the components |
gam_init |
initial values of the scale parameter of the components |
Details
Perform a visualization of fitting curve estimated by Lorentz mixture model.
Value
Show the fitting curve and variation of the parameters.
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2021). Spectrum adapted expectation-conditional maximization algorithm for extending high–throughput peak separation method in XPS analysis. Science and Technology of Advanced Materials: Methods, 1(1), 45-55.
Examples
#generating the synthetic spectral data based on three component Lorentz mixture model.
x <- seq(0, 100, by = 0.5)
true_mu <- c(35, 50, 65)
true_gam <- c(3, 3, 3)
true_mix_ratio <- rep(1/3, 3)
degree <- 4
#Normalized Lorentz distribution
dCauchy <- function(x, mu, gam) {
(dcauchy(x, mu, gam)) / sum(dcauchy(x, mu, gam))
}
y <- c(true_mix_ratio[1] * dCauchy(x = x, mu = true_mu[1], gam = true_gam[1])*10^degree +
true_mix_ratio[2] * dCauchy(x = x, mu = true_mu[2], gam = true_gam[2])*10^degree +
true_mix_ratio[3] * dCauchy(x = x, mu = true_mu[3], gam = true_gam[3])*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
K <- 3
mix_ratio_init <- c(0.2, 0.4, 0.4)
mu_init <- c(20, 40, 70)
gam_init <- c(2, 5, 4)
#Coducting calculation
SP_ECM_L_res <- spect_em_lmm(x, y, mu = mu_init, gam = gam_init, mix_ratio = mix_ratio_init,
conv.cri = 1e-2, maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_lmm_curve(SP_ECM_L_res, x, y, mix_ratio_init, mu_init, gam_init)
#Showing the result of spect_em_lmm()
print(cbind(c(mu_init), c(gam_init), c(mix_ratio_init)))
print(cbind(SP_ECM_L_res$mu, SP_ECM_L_res$gam, SP_ECM_L_res$mix_ratio))
print(cbind(true_mu, true_gam, true_mix_ratio))
Visualization of the result of spect_em_pvmm
Description
Visualization of the result of spect_em_pvmm().
Usage
show_pvmm_curve(spect_em_pvmm_res, x, y, mix_ratio_init, mu_init, sigma_init, eta_init)
Arguments
spect_em_pvmm_res |
data set obtained by spect_em_pvmm() |
x |
measurement steps |
y |
intensity |
mix_ratio_init |
initial values of the mixture ratio of the components |
mu_init |
initial values of the mean of the components |
sigma_init |
initial values of the standard deviation of the components |
eta_init |
initial values of the mixing ratio of Gauss and Lorentz distribution |
Details
Perform a visualization of fitting curve estimated by Pseudo-Voigt mixture model.
Value
Show the fitting curve and variation of the parameters.
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2021). Spectrum adapted expectation-conditional maximization algorithm for extending high–throughput peak separation method in XPS analysis. Science and Technology of Advanced Materials: Methods, 1(1), 45-55.
Examples
#generating the synthetic spectral data based on three component Pseudo-Voigt mixture model.
x <- seq(0, 100, by = 0.5)
true_mu <- c(35, 50, 65)
true_sigma <- c(3, 3, 3)
true_eta <- c(0.3, 0.8, 0.5)
true_mix_ratio <- rep(1/3, 3)
degree <- 4
#Normalized Pseudo-Voigt distribution
truncated_pv <- function(x, mu, sigma, eta) {
(eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma)) /
sum(eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma))
}
y <- c(true_mix_ratio[1]*truncated_pv(x = x,
mu = true_mu[1],
sigma = true_sigma[1],
eta = true_eta[1])*10^degree +
true_mix_ratio[2]*truncated_pv(x = x,
mu = true_mu[2],
sigma = true_sigma[2],
eta = true_eta[2])*10^degree +
true_mix_ratio[3]*truncated_pv(x = x,
mu = true_mu[3],
sigma = true_sigma[3],
eta = true_eta[3])*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
K <- 3
mix_ratio_init <- c(0.2, 0.4, 0.4)
mu_init <- c(20, 40, 70)
sigma_init <- c(2, 5, 4)
eta_init <- c(0.5, 0.4, 0.3)
#Coducting calculation
SP_ECM_PV_res <- spect_em_pvmm(x = x,
y = y,
mu = mu_init,
sigma = sigma_init,
eta = eta_init,
mix_ratio = mix_ratio_init,
conv.cri = 1e-2,
maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_pvmm_curve(SP_ECM_PV_res, x, y, mix_ratio_init, mu_init, sigma_init, eta_init)
#Showing the result of spect_em_pvmm()
print(cbind(c(mu_init), c(sigma_init), c(eta_init), c(mix_ratio_init)))
print(cbind(SP_ECM_PV_res$mu, SP_ECM_PV_res$sigma, SP_ECM_PV_res$eta, SP_ECM_PV_res$mix_ratio))
print(cbind(true_mu, true_sigma, true_eta, true_mix_ratio))
Visualization of the result of spect_em_pvmm_lback
Description
Visualization of the result of spect_em_pvmm_lback().
Usage
show_pvmm_lback_curve(spect_em_pvmm_lback_res,
x, y,
mix_ratio_init,
mu_init,
sigma_init,
eta_init,
x_lower,
x_upper)
Arguments
spect_em_pvmm_lback_res |
data set obtained by spect_em_pvmm_lback() |
x |
measurement steps |
y |
intensity |
mu_init |
initial values of the mean of the components |
sigma_init |
initial values of the standard deviation of the components |
eta_init |
initial values of the mixing ratio of Gauss and Lorentz distribution |
mix_ratio_init |
initial values of the mixture ratio of the components |
x_lower |
lower limit of the measurement steps. Default is a minimum of x |
x_upper |
upper limit of the measurement steps. Default is a maximum of x |
Details
Perform a visualization of fitting curve estimated by pseudo-Voigt mixture model with a linear background.
Value
Show the fitting curve and variation of the parameters.
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2021). Spectrum adapted expectation-conditional maximization algorithm for extending high–throughput peak separation method in XPS analysis. Science and Technology of Advanced Materials: Methods, 1(1), 45-55.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2023). High-throughput XPS spectrum modeling with autonomous background subtraction for 3 d 5/2 peak mapping of SnS. Science and Technology of Advanced Materials: Methods, 3(1), 2159753.
Examples
#generating the synthetic spectral data based on three component Pseudo-Voigt mixture model.
x <- seq(0, 100, by = 0.5)
K <- 3
true_mu <- c(35, 50, 65)
true_sigma <- c(3, 3, 3)
true_mix_ratio <- c(0.5/3, 0.5/3, 0.5/3, 0.5)
true_eta <- c(0.4, 0.6, 0.1)
degree <- 4
#Normalized Pseudo-Voigt distribution
truncated_pv <- function(x, mu, sigma, eta) {
(eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma)) /
sum(eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma))
}
y <- c(true_mix_ratio[1]*truncated_pv(x = x,
mu = true_mu[1],
sigma = true_sigma[1],
eta = true_eta[1])*10^degree +
true_mix_ratio[2]*truncated_pv(x = x,
mu = true_mu[2],
sigma = true_sigma[2],
eta = true_eta[2])*10^degree +
true_mix_ratio[3]*truncated_pv(x = x,
mu = true_mu[3],
sigma = true_sigma[3],
eta = true_eta[3])*10^degree +
true_mix_ratio[4]*(c(500*x + 15000) / sum(500*x + 15000))*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
mu_init <- c(30, 40, 60)
sigma_init <- c(4, 4, 4)
mix_ratio_init <- rep(1/(length(mu_init)+3), length(mu_init)+3)
eta_init <- c(1, 1, 1)
#Coducting calculation
SP_ECM_PV_LBACK_res <- spect_em_pvmm_lback(x = x,
y = y,
mu = mu_init,
sigma = sigma_init,
eta = eta_init,
mix_ratio = mix_ratio_init,
x_lower = min(x),
x_upper = max(x),
conv.cri = 1e-2,
maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_pvmm_lback_curve(spect_em_pvmm_lback_res = SP_ECM_PV_LBACK_res,
x = x,
y = y,
mix_ratio_init = mix_ratio_init,
mu_init = mu_init,
sigma_init = sigma_init,
eta_init = eta_init,
x_lower = min(x),
x_upper = max(x))
#Showing the result of spect_em_pvmm_lback()
print(cbind(SP_ECM_PV_LBACK_res$mu, SP_ECM_PV_LBACK_res$sigma, SP_ECM_PV_LBACK_res$eta,
SP_ECM_PV_LBACK_res$mix_ratio[1:K]))
print(cbind(true_mu, true_sigma, true_eta, true_mix_ratio[1:K]))
Spectrum adapted ECM algorithm by DSGMM
Description
Perform a peak fitting based on the spectrum adapted ECM algorithm by Doniach-Sunjic-Gauss mixture model.
Usage
spect_em_dsgmm(x, y, mu, sigma, alpha, eta, mix_ratio, conv.cri, maxit)
Arguments
x |
measurement steps |
y |
intensity |
mu |
mean of the components |
sigma |
standard deviation of the components |
alpha |
asymmetric parameter of the component |
eta |
mixing ratio of Gauss and Lorentz distribution |
mix_ratio |
mixture ratio of the components |
conv.cri |
criterion of the convergence |
maxit |
maximum number of the iteration |
Details
Peak fitting is conducted by spectrum adapted ECM algorithm.
Value
mu |
estimated mean of the components |
sigma |
estimated standard deviation of the components |
alpha |
estimated asymmetric parameter of the components |
eta |
estimated mixing ratio of Gauss and Lorentz distribution |
mix_ratio |
estimated mixture ratio of the components |
it |
number of the iteration to reach the convergence |
LL |
variation of the weighted log likelihood values |
MU |
variation of mu |
SIGMA |
variation of sigma |
ALPHA |
variation of alpha |
ETA |
variation of beta |
MIX_RATIO |
variation of mix_ratio |
W_K |
decomposed component of the spectral data |
convergence |
message for the convergence in the calculation |
cal_time |
calculation time to complete the peak fitting. Unit is seconds |
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2021). Spectrum adapted expectation-conditional maximization algorithm for extending high–throughput peak separation method in XPS analysis. Science and Technology of Advanced Materials: Methods, 1(1), 45-55.
Examples
#generating the synthetic spectral data based on three component Doniach-Sunjic-Gauss mixture model.
x <- seq(0, 100, by = 0.5)
true_mu <- c(20, 50, 80)
true_sigma <- c(3, 3, 3)
true_alpha <- c(0.1, 0.3, 0.1)
true_eta <- c(0.4, 0.6, 0.1)
true_mix_ratio <- rep(1/3, 3)
degree <- 4
#trancated Doniach-Sunjic-Gauss
truncated_dsg <- function(x, mu, sigma, alpha, eta) {
((eta*(((gamma(1-alpha)) /
((x-mu)^2+(sqrt(2*log(2))*sigma)^2)^((1-alpha)/2)) *
cos((pi*alpha/2)+(1-alpha)*atan((x-mu) /
(sqrt(2*log(2))*sigma))))) + (1-eta)*dnorm(x, mu, sigma)) /
sum( ((eta*(((gamma(1-alpha)) /
((x-mu)^2+(sqrt(2*log(2))*sigma)^2)^((1-alpha)/2)) *
cos((pi*alpha/2)+(1-alpha)*atan((x-mu) /
(sqrt(2*log(2))*sigma))))) + (1-eta)*dnorm(x, mu, sigma)))
}
y <- c(true_mix_ratio[1]*truncated_dsg(x = x,
mu = true_mu[1],
sigma = true_sigma[1],
alpha = true_alpha[1],
eta = true_eta[1])*10^degree +
true_mix_ratio[2]*truncated_dsg(x = x,
mu = true_mu[2],
sigma = true_sigma[2],
alpha = true_alpha[2],
eta = true_eta[2])*10^degree +
true_mix_ratio[3]*truncated_dsg(x = x,
mu = true_mu[3],
sigma = true_sigma[3],
alpha = true_alpha[3],
eta = true_eta[3])*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
K <- 3
mix_ratio_init <- c(0.2, 0.4, 0.4)
mu_init <- c(20, 40, 70)
sigma_init <- c(4, 3, 2)
alpha_init <- c(0.3, 0.2, 0.4)
eta_init <- c(0.5, 0.4, 0.3)
#Coducting calculation
SP_ECM_DSG_res <- spect_em_dsgmm(x = x,
y = y,
mu = mu_init,
sigma = sigma_init,
alpha = alpha_init,
eta = eta_init,
mix_ratio = mix_ratio_init,
conv.cri = 1e-2,
maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_dsgmm_curve(SP_ECM_DSG_res,
x,
y,
mix_ratio_init,
mu_init,
sigma_init,
alpha_init,
eta_init)
#Showing the result of spect_em_dsgmm()
print(cbind(c(mu_init),
c(sigma_init),
c(alpha_init),
c(eta_init),
c(mix_ratio_init)))
print(cbind(SP_ECM_DSG_res$mu,
SP_ECM_DSG_res$sigma,
SP_ECM_DSG_res$alpha,
SP_ECM_DSG_res$eta,
SP_ECM_DSG_res$mix_ratio))
print(cbind(true_mu,
true_sigma,
true_alpha,
true_eta,
true_mix_ratio))
Spectrum adapted EM algorithm by GMM
Description
Perform a peak fitting based on the spectrum adapted EM algorithm by Gaussian mixture model.
Usage
spect_em_gmm(x, y, mu, sigma, mix_ratio, conv.cri, maxit)
Arguments
x |
measurement steps |
y |
intensity |
mu |
mean of the components |
sigma |
standard deviation of the components |
mix_ratio |
mixture ratio of the components |
conv.cri |
criterion of the convergence |
maxit |
maximum number of the iteration |
Details
Peak fitting is conducted by spectrum adapted EM algorithm.
Value
mu |
estimated mean of the components |
sigma |
estimated standard deviation of the components |
mix_ratio |
estimated mixture ratio of the components |
it |
number of the iteration to reach the convergence |
LL |
variation of the weighted log likelihood values |
MU |
variation of mu |
SIGMA |
variation of sigma |
MIX_RATIO |
variation of mix_ratio |
W_K |
decomposed component of the spectral data |
convergence |
message for the convergence in the calculation |
cal_time |
calculation time to complete the peak fitting. Unit is seconds |
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Examples
#generating the synthetic spectral data based on three component Gausian mixture model.
x <- seq(0, 100, by = 0.5)
true_mu <- c(35, 50, 65)
true_sigma <- c(3, 3, 3)
true_mix_ratio <- rep(1/3, 3)
degree <- 4
y <- c(true_mix_ratio[1] * dnorm(x = x, mean = true_mu[1], sd = true_sigma[1])*10^degree +
true_mix_ratio[2] * dnorm(x = x, mean = true_mu[2], sd = true_sigma[2])*10^degree +
true_mix_ratio[3] * dnorm(x = x, mean = true_mu[3], sd = true_sigma[3])*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
K <- 3
mix_ratio_init <- c(0.2, 0.4, 0.4)
mu_init <- c(20, 40, 70)
sigma_init <- c(2, 5, 4)
#Coducting calculation
SP_EM_G_res <- spect_em_gmm(x, y, mu = mu_init, sigma = sigma_init, mix_ratio = mix_ratio_init,
conv.cri = 1e-2, maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_gmm_curve(SP_EM_G_res, x, y, mix_ratio_init, mu_init, sigma_init)
#Showing the result of spect_em_gmm()
print(cbind(c(mu_init), c(sigma_init), c(mix_ratio_init)))
print(cbind(SP_EM_G_res$mu, SP_EM_G_res$sigma, SP_EM_G_res$mix_ratio))
print(cbind(true_mu, true_sigma, true_mix_ratio))
Spectrum adapted ECM algorithm by LMM
Description
Perform a peak fitting based on the spectrum adapted ECM algorithm by Lorentz mixture model.
Usage
spect_em_lmm(x, y, mu, gam, mix_ratio, conv.cri, maxit)
Arguments
x |
measurement steps |
y |
intensity |
mu |
mean of the components |
gam |
scale parameter of the components |
mix_ratio |
mixture ratio of the components |
conv.cri |
criterion of the convergence |
maxit |
maximum number of the iteration |
Details
Peak fitting is conducted by spectrum adapted ECM algorithm.
Value
mu |
estimated mean of the components |
gam |
estimated scale parameter of the components |
mix_ratio |
estimated mixture ratio of the components |
it |
number of the iteration to reach the convergence |
LL |
variation of the weighted log likelihood values |
MU |
variation of mu |
GAM |
variation of gam |
MIX_RATIO |
variation of mix_ratio |
W_K |
decomposed component of the spectral data |
convergence |
message for the convergence in the calculation |
cal_time |
calculation time to complete the peak fitting. Unit is seconds |
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2021). Spectrum adapted expectation-conditional maximization algorithm for extending high–throughput peak separation method in XPS analysis. Science and Technology of Advanced Materials: Methods, 1(1), 45-55.
Examples
#generating the synthetic spectral data based on three component Lorentz mixture model.
x <- seq(0, 100, by = 0.5)
true_mu <- c(35, 50, 65)
true_gam <- c(3, 3, 3)
true_mix_ratio <- rep(1/3, 3)
degree <- 4
#Normalized Lorentz distribution
dCauchy <- function(x, mu, gam) {
(dcauchy(x, mu, gam)) / sum(dcauchy(x, mu, gam))
}
y <- c(true_mix_ratio[1] * dCauchy(x = x, mu = true_mu[1], gam = true_gam[1])*10^degree +
true_mix_ratio[2] * dCauchy(x = x, mu = true_mu[2], gam = true_gam[2])*10^degree +
true_mix_ratio[3] * dCauchy(x = x, mu = true_mu[3], gam = true_gam[3])*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
K <- 3
mix_ratio_init <- c(0.2, 0.4, 0.4)
mu_init <- c(20, 40, 70)
gam_init <- c(2, 5, 4)
#Coducting calculation
SP_ECM_L_res <- spect_em_lmm(x, y, mu = mu_init, gam = gam_init, mix_ratio = mix_ratio_init,
conv.cri = 1e-2, maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_lmm_curve(SP_ECM_L_res, x, y, mix_ratio_init, mu_init, gam_init)
#Showing the result of spect_em_lmm()
print(cbind(c(mu_init), c(gam_init), c(mix_ratio_init)))
print(cbind(SP_ECM_L_res$mu, SP_ECM_L_res$gam, SP_ECM_L_res$mix_ratio))
print(cbind(true_mu, true_gam, true_mix_ratio))
Spectrum adapted ECM algorithm by PVMM
Description
Perform a peak fitting based on the spectrum adapted ECM algorithm by Pseudo-Voigt mixture model.
Usage
spect_em_pvmm(x, y, mu, sigma, eta, mix_ratio, conv.cri, maxit)
Arguments
x |
measurement steps |
y |
intensity |
mu |
mean of the components |
sigma |
standard deviation of the components |
eta |
mixing ratio of Gauss and Lorentz distribution |
mix_ratio |
mixture ratio of the components |
conv.cri |
criterion of the convergence |
maxit |
maximum number of the iteration |
Details
Peak fitting is conducted by spectrum adapted ECM algorithm.
Value
mu |
estimated mean of the components |
sigma |
estimated standard deviation of the components |
eta |
estimated mixing ratio of Gauss and Lorentz distribution |
mix_ratio |
estimated mixture ratio of the components |
it |
number of the iteration to reach the convergence |
LL |
variation of the weighted log likelihood values |
MU |
variation of mu |
SIGMA |
variation of sigma |
ETA |
variation of beta |
MIX_RATIO |
variation of mix_ratio |
W_K |
decomposed component of the spectral data |
convergence |
message for the convergence in the calculation |
cal_time |
calculation time to complete the peak fitting. Unit is seconds |
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2021). Spectrum adapted expectation-conditional maximization algorithm for extending high–throughput peak separation method in XPS analysis. Science and Technology of Advanced Materials: Methods, 1(1), 45-55.
Examples
#generating the synthetic spectral data based on three component Pseudo-Voigt mixture model.
x <- seq(0, 100, by = 0.5)
true_mu <- c(35, 50, 65)
true_sigma <- c(3, 3, 3)
true_eta <- c(0.3, 0.8, 0.5)
true_mix_ratio <- rep(1/3, 3)
degree <- 4
#Normalized Pseudo-Voigt distribution
truncated_pv <- function(x, mu, sigma, eta) {
(eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma)) /
sum(eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma))
}
y <- c(true_mix_ratio[1]*truncated_pv(x = x,
mu = true_mu[1],
sigma = true_sigma[1],
eta = true_eta[1])*10^degree +
true_mix_ratio[2]*truncated_pv(x = x,
mu = true_mu[2],
sigma = true_sigma[2],
eta = true_eta[2])*10^degree +
true_mix_ratio[3]*truncated_pv(x = x,
mu = true_mu[3],
sigma = true_sigma[3],
eta = true_eta[3])*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
K <- 3
mix_ratio_init <- c(0.2, 0.4, 0.4)
mu_init <- c(20, 40, 70)
sigma_init <- c(2, 5, 4)
eta_init <- c(0.5, 0.4, 0.3)
#Coducting calculation
SP_ECM_PV_res <- spect_em_pvmm(x = x,
y = y,
mu = mu_init,
sigma = sigma_init,
eta = eta_init,
mix_ratio = mix_ratio_init,
conv.cri = 1e-2,
maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_pvmm_curve(SP_ECM_PV_res, x, y, mix_ratio_init, mu_init, sigma_init, eta_init)
#Showing the result of spect_em_pvmm()
print(cbind(c(mu_init), c(sigma_init), c(eta_init), c(mix_ratio_init)))
print(cbind(SP_ECM_PV_res$mu, SP_ECM_PV_res$sigma, SP_ECM_PV_res$eta, SP_ECM_PV_res$mix_ratio))
print(cbind(true_mu, true_sigma, true_eta, true_mix_ratio))
Spectrum adapted ECM algorithm by PVMM with a linear background
Description
Perform a peak fitting based on the spectrum adapted ECM algorithm by pseudo-Voigt mixture model with a linear background.
Usage
spect_em_pvmm_lback(x, y, mu, sigma, eta, mix_ratio, x_lower, x_upper, conv.cri, maxit)
Arguments
x |
measurement steps |
y |
intensity |
mu |
mean of the components |
sigma |
standard deviation of the components |
eta |
mixing ratio of Gauss and Lorentz distribution |
mix_ratio |
mixture ratio of the components |
x_lower |
lower limit of the measurement steps. Default is a minimum of x |
x_upper |
upper limit of the measurement steps. Default is a maximum of x |
conv.cri |
criterion of the convergence |
maxit |
maximum number of the iteration |
Details
Peak fitting is conducted by spectrum adapted ECM algorithm.
Value
mu |
estimated mean of the components |
sigma |
estimated standard deviation of the components |
eta |
estimated mixing ratio of Gauss and Lorentz distribution |
mix_ratio |
estimated mixture ratio of the components |
it |
number of the iteration to reach the convergence |
LL |
variation of the weighted log likelihood values |
MU |
variation of mu |
SIGMA |
variation of sigma |
ETA |
variation of beta |
MIX_RATIO |
variation of mix_ratio |
W_K |
decomposed component of the spectral data |
convergence |
message for the convergence in the calculation |
cal_time |
calculation time to complete the peak fitting. Unit is seconds |
References
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2019). Spectrum adapted expectation-maximization algorithm for high-throughput peak shift analysis. Science and technology of advanced materials, 20(1), 733-745.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2021). Spectrum adapted expectation-conditional maximization algorithm for extending high–throughput peak separation method in XPS analysis. Science and Technology of Advanced Materials: Methods, 1(1), 45-55.
Matsumura, T., Nagamura, N., Akaho, S., Nagata, K., & Ando, Y. (2023). High-throughput XPS spectrum modeling with autonomous background subtraction for 3 d 5/2 peak mapping of SnS. Science and Technology of Advanced Materials: Methods, 3(1), 2159753.
Examples
#generating the synthetic spectral data based on three component Pseudo-Voigt mixture model.
x <- seq(0, 100, by = 0.5)
K <- 3
true_mu <- c(35, 50, 65)
true_sigma <- c(3, 3, 3)
true_mix_ratio <- c(0.5/3, 0.5/3, 0.5/3, 0.5)
true_eta <- c(0.4, 0.6, 0.1)
degree <- 4
#Normalized Pseudo-Voigt distribution
truncated_pv <- function(x, mu, sigma, eta) {
(eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma)) /
sum(eta*dcauchy(x, mu, sqrt(2*log(2))*sigma) + (1-eta)*dnorm(x, mu, sigma))
}
y <- c(true_mix_ratio[1]*truncated_pv(x = x,
mu = true_mu[1],
sigma = true_sigma[1],
eta = true_eta[1])*10^degree +
true_mix_ratio[2]*truncated_pv(x = x,
mu = true_mu[2],
sigma = true_sigma[2],
eta = true_eta[2])*10^degree +
true_mix_ratio[3]*truncated_pv(x = x,
mu = true_mu[3],
sigma = true_sigma[3],
eta = true_eta[3])*10^degree +
true_mix_ratio[4]*(c(500*x + 15000) / sum(500*x + 15000))*10^degree)
plot(y~x, main = "genrated synthetic spectral data")
#Peak fitting by EMpeaksR
#Initial values
mu_init <- c(30, 40, 60)
sigma_init <- c(4, 4, 4)
mix_ratio_init <- rep(1/(length(mu_init)+3), length(mu_init)+3)
eta_init <- c(1, 1, 1)
#Coducting calculation
SP_ECM_PV_LBACK_res <- spect_em_pvmm_lback(x = x,
y = y,
mu = mu_init,
sigma = sigma_init,
eta = eta_init,
mix_ratio = mix_ratio_init,
x_lower = min(x),
x_upper = max(x),
conv.cri = 1e-2,
maxit = 2000)
#Plot fitting curve and trace plot of parameters
show_pvmm_lback_curve(spect_em_pvmm_lback_res = SP_ECM_PV_LBACK_res,
x = x,
y = y,
mix_ratio_init = mix_ratio_init,
mu_init = mu_init,
sigma_init = sigma_init,
eta_init = eta_init,
x_lower = min(x),
x_upper = max(x))
#Showing the result of spect_em_pvmm_lback()
print(cbind(SP_ECM_PV_LBACK_res$mu, SP_ECM_PV_LBACK_res$sigma, SP_ECM_PV_LBACK_res$eta,
SP_ECM_PV_LBACK_res$mix_ratio[1:K]))
print(cbind(true_mu, true_sigma, true_eta, true_mix_ratio[1:K]))