afryca.ase.Snippet Library mds

var mds = (typeof exports === "undefined")?(function mds() {}):(exports);
if(typeof global !== "undefined") { global.mds = mds; }

//
// Compute euclidean dissimilarity
//
mds.euclideanDissimilarity = function euclideanDissimilarity(x, y) {
	var result = 0;
	for (var i = 0; i < x.length; i++) {
		if(isNaN(x[i])){
			x[i]=0;
		}
		if(isNaN(y[i])){
			y[i]=0;
		}
		result += Math.pow(x[i] - y[i], 2);
	}
	return Math.sqrt(result);
}

//
// Compute dissimilarity matrix
//
mds.dissimilarityMatrix = function dissimilarityMatrix(preferences) {
	var vectorsArrays = adapters.matrixAsVectorsArray(preferences);
	var vectors = vectorsArrays.length;
	var result = [];
	for (var i = 0; i < vectors; i++) {
		result[i] = [];
		for (var j = 0; j < vectors; j++) {
			result[i][j] = mds.euclideanDissimilarity(vectorsArrays[i], vectorsArrays[j]);
		}
	}
	return result;
}

//
// https://github.com/benfred/mds.js/blob/master/mds.js
//
mds.classicalMDS = function classicalMDS(distances, dimensions) {
	dimensions = dimensions || 2;
    // square distances
	var M = numeric.mul(-0.5, numeric.pow(distances, 2));
	// double centre the rows/columns
	function mean(A) { return numeric.div(numeric.add.apply(null, A), A.length); }
	var rowMeans = mean(M),
		colMeans = mean(numeric.transpose(M)),
		totalMean = mean(rowMeans);
	for (var i = 0; i < M.length; ++i) {
		for (var j =0; j < M[0].length; ++j) {
			M[i][j] += totalMean - rowMeans[i] - colMeans[j];
		}
	}
	// take the SVD of the double centred matrix, and return the
	// points from it
	var ret = numeric.svd(M),
		eigenValues = numeric.sqrt(ret.S);
	return ret.U.map(function(row) {
		return numeric.mul(row, eigenValues).splice(0, dimensions);
	});
}

mds.classicalMDS3D = function classicalMDS3D(distances, dimensions) {
	dimensions = dimensions;
    // square distances
	var M = numeric.mul(-0.5, numeric.pow(distances, 2));
	// double centre the rows/columns
	function mean(A) { return numeric.div(numeric.add.apply(null, A), A.length); }
	var rowMeans = mean(M),
		colMeans = mean(numeric.transpose(M)),
		totalMean = mean(rowMeans);
	for (var i = 0; i < M.length; ++i) {
		for (var j =0; j < M[0].length; ++j) {
			M[i][j] += totalMean - rowMeans[i] - colMeans[j];
		}
	}
	// take the SVD of the double centred matrix, and return the
	// points from it
	var ret = numeric.svd(M),
		eigenValues = numeric.sqrt(ret.S);
	return ret.U.map(function(row) {
		return numeric.mul(row, eigenValues).splice(0, dimensions);
	});
}

//
// Adapt MDS points to AFRYCA input [X -> values, Y -> values]
//
mds.mdsForAFRYCA = function mdsForAFRYCA(points) {	
	var result = [];
	var X = 0;
	var Y = 1;
	result[X] = []; // X values
	result[Y] = []; // Y values
	for (var p = 0; p < points.length; p++) {
		result[X][p] = points[p][X];
		result[Y][p] = points[p][Y];
	}
	return result;
}

//
// Adapt MDS points to AFRYCA input [X -> values, Y -> values, Z -> values]
//
mds.mds3dForAFRYCA = function mds3dForAFRYCA(points) {	
	var result = [];
	var X = 0;
	var Y = 1;
	var Z = 2;
	result[X] = []; // X values
	result[Y] = []; // Y values
	result[Z] = []; // Z values
	for (var p = 0; p < points.length; p++) {
		result[X][p] = points[p][X];
		result[Y][p] = points[p][Y];
		result[Z][p] = points[p][Z];
	}
	return result;
}

//
// Compute MDS
//
mds.MDS = function MDS(preferences) {
	var dissimilarityMatrix = mds.dissimilarityMatrix(preferences);
	var points = mds.classicalMDS(dissimilarityMatrix);
	return mds.mdsForAFRYCA(points);
}

//
// Compute MDS 3D
//
mds.MDS3D = function MDS3D(preferences) {
	var dissimilarityMatrix = mds.dissimilarityMatrix(preferences);
	var points = mds.classicalMDS3D(dissimilarityMatrix, 3);
	return mds.mds3dForAFRYCA(points);
}


mds