DSGMM: Spectrum adapted ECM algorithm by DSGMM

Description Usage Arguments Details Value References Examples

Description

Perform a peak fitting based on the spectrum adapted ECM algorithm by Doniach-Sunjic-Gauss mixture model.

Usage

1
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

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#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-6,
                                 maxit = 100)

#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))

EMpeaksR documentation built on Dec. 20, 2021, 5:08 p.m.