spect_em_lmm {EMpeaksR}

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))