Package Exports

ml-ngmca

This package does not declare an exports field, so the exports above have been automatically detected and optimized by JSPM instead. If any package subpath is missing, it is recommended to post an issue to the original package (ml-ngmca) to support the "exports" field. If that is not possible, create a JSPM override to customize the exports field for this package.

Readme

nGMCA - non-negative Generalized Morphological Component Analysis

NMReDATA

A tool for non-negative matrix factorization.

Instalation

$ npm install ml-ngmca

Usage

import { nGMCA } from 'ml-ngmca';

const result = nGMCA(dataMatrix, options);

As a CommonJS module

const { nGMCA } = require('ml-ngmca');

const result = nGMCA(dataMatrix, options);

API Documentation

This algorithm is based on the article Jérémy Rapin, Jérôme Bobin, Anthony Larue, Jean-Luc Starck. Sparse and Non-negative BSS for Noisy Data, IEEE Transactions on Signal Processing, 2013.IEEE Transactions on Signal Processing, vol. 61, issue 22, p. 5620-5632, 2013.

In order to get a general idea of the problem you could also check the Wikipedia article.

Examples

You will be able to separate the components of a mixture if you have a series of measurements correlated by a composition profile e.g NMR or mass spectra coming from a chromatographic coupled technique of two or more close retention times. So you will have a matrix with a number of rows equal or greater than the number of pure components of the mixture.

import { Matrix } from 'ml-matrix';
import { nGMCA } from 'ml-ngmca';

let pureSpectra = new Matrix([[1, 0, 1, 0]]);
let composition = new Matrix([[1, 2, 3, 2, 1]]);

// matrix = composition.transpose().mmul(pureSpectra)
let matrix = new Matrix([
  [1, 0, 1, 0],
  [2, 0, 2, 0],
  [3, 0, 3, 0],
  [2, 0, 2, 0],
  [1, 0, 1, 0],
]);

const options = {
  maximumIteration: 200,
  phaseRatio: 0.4,
};
const result = nGMCA(matrix, 1, options);
const { A, S } = result;
console.log(`A = ${A.to2DArray()} S =${S.to2DArray()}`);
/**
A = [
    [ 0.22941573387056177 ],
    [ 0.45883146774112354 ],
    [ 0.6882472016116853 ],
    [ 0.45883146774112354 ],
    [ 0.22941573387056177 ]
  ]
S = [ [ 4.358898943540674, 0, 4.358898943540674, 0 ] ]

if you reescale both S maxS and A with 1/maxS.
*/

let maxByRow = [];
for (let i = 0; i < S.rows; i++) {
  maxByRow.push(S.maxRow(i));
}

S.scale('row', { scale: maxByRow });
A.scale('column', {
  scale: maxByRow.map((e) => 1 / e),
});

/**
S = [ [ 1, 0, 1, 0 ] ]
A = [
  [1.0000000000000002],
  [2.0000000000000004],
  [3.0000000000000004],
  [2.0000000000000004],
  [1.0000000000000002]
  ]
*/

const estimatedMatrix = A.mmul(S);
const diff = Matrix.sub(matrix, estimatedMatrix);

Here is a second example:

let matrix = new Matrix([
  [0, 0, 1, 1, 1],
  [0, 0, 1, 1, 1],
  [2, 2, 2, 0, 0],
  [2, 2, 2, 0, 0],
]);

const options = {
  maximumIteration: 200,
  phaseRatio: 0.4,
};
const result = nGMCA(matrix, 1, options);
const { A, S } = result;
console.log(`A = ${A} S =${S}`);
/**
 A = [
  [
    0.707107 0       
    0.707107 0       
    2.26e-17 0.707107
    2.26e-17 0.707107
  ]
]
S = [
  [
    9.86e-32 9.86e-32 1.41421 1.41421 1.41421
    2.82843  2.82843  2.82843 0       0       
  ]
]
note: 9.86e-32 and 2.26e-17 is practically zero
so if you reescale both S maxS and A with 1/maxS.
*/

let maxByRow = [];
for (let i = 0; i < S.rows; i++) {
  maxByRow.push(S.maxRow(i));
}

S.scale('row', { scale: maxByRow });
A.scale('column', {
  scale: maxByRow.map((e) => 1 / e),
});

console.log(`A = ${A} S =${S}`);
/**
 A = [
  [
    1 0       
    1 0       
    0 1
    0 1
  ]
]
S = [
  [
    0 0 1 1 1
    2 2 2 0 0       
  ]
]
*/

The result has the matrices A and S, the estimated matrices of compositions and pureSpectra respectively. It's possible that the matrices A and S have not the same scale than pureSpectra and composition matrices because of AS has an infinity of combination to get the target matrix.

License

MIT