Public
Edited
Oct 16, 2023
Importers
1 star
function sammon(X, n, args={}) {
// TODO: Should the input be normalized? Along which dimensions?
const columnFlatten = d => math.flatten(math.transpose(d))
args = Object.assign({
maxIter: 500,
maxHalves: 20,
tolFun:1e-9,
init:null
}, args)
const {maxIter, maxHalves, tolFun, init} = args
let D = cdist(X, X)
const N = X.length
const scale = 0.5 / math.sum(D)
D = math.add(D, eye(N))
const Dinv = math.dotDivide(1, D)
let y = []
if (init) {
y = init
} else if (X[0].length > X.length) {
console.warn("More columns than rows, so initializing using random vectors rather than PCA")
X.forEach(() => y.push(math.random([n])))
} else {
const eigenVectors = PCA.getEigenVectors(X, n)
const adjusted = PCA.computeAdjustedData(X, ...eigenVectors.slice(0,n)).adjustedData
for (let i = 0; i < X.length; i++) {
y.push(Array.from({length: n}, (_,j) => adjusted[j][i]))
}
}
const one = math.ones([X.length, n])
let d = math.add(cdist(y,y), eye(X.length))
let dinv = math.dotDivide(1, d)
let delta = math.subtract(D, d)
let E = math.sum(math.dotMultiply(math.dotPow(delta, 2), Dinv))
let yOld = null
let i = 0
for (i = 0; i < maxIter; i++) {
delta = math.subtract(dinv, Dinv)
const deltaOne = math.multiply(delta, one)
const g = math.subtract(math.multiply(delta,y), math.dotMultiply(y, deltaOne))
const dinv3 = math.dotPow(dinv, 3)
const y2 = math.dotPow(y, 2)
const Ha = math.multiply(dinv3,y2)
const Hb = math.multiply(2,y)
const Hc = math.multiply(dinv3, y)
const Hd = math.dotMultiply(y2, math.multiply(dinv3,one))
const Hbc = math.dotMultiply(Hb,Hc)
const H = math.add(math.subtract(math.subtract(Ha, deltaOne),Hbc),Hd)
let s = math.subtract(0,math.dotDivide(columnFlatten(g.toArray()), math.abs(columnFlatten(H.toArray()))))
yOld = y
let j = 0
let Enew = null
for (j = 0; j < maxHalves; j++) {
const sReshape = math.transpose(math.reshape(s, [n,X.length]))
y = math.add(yOld, sReshape)
d = math.add(cdist(y,y) , eye(X.length))
dinv = math.dotDivide(1,d)
delta = math.subtract(D,d)
Enew = math.sum(math.dotMultiply(math.dotPow(delta,2),Dinv))
if (Enew < E) {
break
} else {
s = math.multiply(s, .5)
}
}
if (j == maxHalves-1) {
console.warn("Warning: maxHalves exceeded. Sammon mapping may not converge...")
}
if (Math.abs((E-Enew)/E) < tolFun) {
break
}
E = Enew
}
if (i == maxIter-1) {
console.warn("Warning: maxiter exceeded. Sammon mapping may not have converged...")
}
E = E * scale
return {vectors:y, E: E}
}
{
const M = [[1,2,3],[4,5,6]]
return [columnFlatten(M), math.flatten(math.transpose(M))]
}
PCA2 = (await import('https://cdn.skypack.dev/ml-pca@4.1.1?min')).PCA
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