Conducting the Peak Fitting Based on the EM Algorithm.

EMpeaksR

The goal of EMpeaks is to efficiently perform the peak fitting on a large number of spectral data. The EMpeaks can support the investigation of peak fitting 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.

In version 0.2.0, (1) Lorentz mixture model, (2) Pseudo-Voigt mixture model, and (3) Doniach-Sunjic-Gauss mixture model are available for peak fitting. As these models are generally used in spectroscopy, applicability of the EMpeaksR package is expanded.

In version 0.3.0, the pseudo-Voigt mixture model with a linear background model is available for peak fitting. This model enables background subtraction and peak fitting in the one-shot calculation. As the linear background is generally used in spectroscopy, the applicability of EMpeaksR packages is expanded.

In version 0.3.1, we have fixed a bug in that unintended plots were output in show_pvmm_lback_curve().

Installation

You can install the released version of EMpeaksR from CRAN with:

install.packages("EMpeaksR")

Example

This is a basic example which shows you how to solve a common problem:

library(EMpeaksR)
#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-8, maxit = 100000)

#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))

Moreover, this is an example which shows you how to solve a problem using Lorentz mixture model:

#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-8, maxit = 100000)

#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))