MCRLLM: Multivariate Curve Resolution by Log-Likelihood Maximization

## Project description

MCRLLM: Multivariate Curve Resolution by Log-Likelihood Maximization.

X = CS
where
X(nxk): Spectroscopic data where n spectra acquired over k energy levels
C(nxa): Composition map based on a MCRLLM components
S(axk): Spectra of the a components as computed by MCRLLM

# Method first presented in

Lavoie F.B., Braidy N. and Gosselin R. (2016) Including Noise Characteristics in MCR to improve Mapping and Component Extraction from Spectral Images, Chemometrics and Intelligent Laboratory Systems, 153, 40-50.

# Input data

Algorithm is designed to treat 2D data X(nxk) where n spectra acquired over k energy levels.
A 3D spectral image X(n1,n2,k) can be reshaped to a 2D matrix X(n1xn2,k) prior to MCRLLM analysis. Composition maps can then be obtained by reshaping C(n1xn2,a) into 2D chemical maps C(n1,n2,a).

# Input and output arguments

MCRLLM requires 2 inputs : X data and number of MCRLLM components to compute (a).
decomposition = mcr.mcrllm(X,a)
S = decomposition.S
C = decomposition.C

# Example

#Compute MCRLLM on X using 7 components.

#First obtain X data. Spectroscopic data is available in the zip file of this Pypi module (data_EELS.txt). It represents EELS (Electron Energy Loss Spectroscopy). This data consists of 100 spectra acquired over 2048 energy levels.

import MCRLLM as mcr
import matplotlib.pyplot as plt
import numpy as np

decomposition = mcr.mcrllm(X,7)
#Iterate each component 10 times
decomposition.iterate(10)
S = decomposition.S
C = decomposition.C
plt.figure();plt.plot(S.T)
plt.figure();plt.plot(C)

# Compatibility

MCRLLM tested on Python 3.7 using the following modules:
Numpy 1.17.2
Scipy 1.3.1
Sklearn 0.21.3
Pysptools 0.15.0
Tqdm 4.36.1