1_TSNE_Bh_3D_liveStreaming.js

let DesiredPerplexity = 7;
let numberOfIterations = 5;
let LearningRatio = 3;
let Momentum = 0.3;
let TradeOff = 0.5;
let p = [];
let y = [];
let oldy = [];
let numberOfSamplesInX;
let InversenumberOfSamplesInX;
let BiggestY = 2;
let shouldIStartAllOverAgain = true;
let shouldIStartReInitializeY = true;
let Canvas = {
    Canvas:undefined,
    Size:[700,700],
    Position:[100, 425],
    HalfSize:undefined
}
let ColorMode;
let EarlyExaggeration ={
    DidIFinish : false,
    Counter : 0,
    Iterations : 250,
    Factor : 4,
}
let angle = 0;
let rotationZ = [
    [0, 0, 0],
    [0, 0, 0],
    [0, 0, 1],
];
let rotationX = [
    [1, 0, 0],
    [0, 0, 0],
    [0, 0, 0],
];
let rotationY = [
    [0, 0, 0],
    [0, 1, 0],
    [0, 0, 0],
];
let projection = [
    [1, 0, 0],
    [0, 1, 0],
];
function setup() {
    LoadX(Math.floor(Math.random()*3));
    CreateTheInputsBoxes();
    CreateTheInputs();
    Canvas.HalfSize = [Canvas.Size[0]*0.5,Canvas.Size[1]*0.5];
    Canvas.Canvas = createCanvas(Canvas.Size[0], Canvas.Size[1]);
    Canvas.Canvas.position(Canvas.Position[0], Canvas.Position[1]);
}
function draw(){
    background(0);
    if (shouldIStartAllOverAgain == true){
        LearningRatio *= 4; //By definition of dydt ... It doesn't make sense having it inside the loop.
        TradeOff *= 1.73; //sqrt of 3. Relationship between de side lenght and the diagonal of the octtree ... It doesn't make sense having it inside the loop.
        numberOfSamplesInX = X.length;
        InversenumberOfSamplesInX = 1/numberOfSamplesInX;
        let numberOfDimentions = X[1].length;
        let top1 = Array(numberOfSamplesInX).fill(0);
        let top2 = Array(numberOfSamplesInX).fill(0);
        let middle1 = Array(numberOfSamplesInX).fill(0);
        let middle2 = Array(numberOfSamplesInX).fill(0);
        let bottom1 = Array(numberOfSamplesInX).fill(0);
        let bottom2 = Array(numberOfSamplesInX).fill(0);
        p = []; //pj|i upper
        let p2 = [];
        let aux;
        //
        let IndexElements=[];for(let i = 0; i < X.length; i++){IndexElements[i] = i}
        let VantagePoint = new VantagePointElement();
        VantagePoint.SelectASeedAndFindMu(X, IndexElements);
        VantagePoint.SearchKNeighbors(X, numberOfSamplesInX, DesiredPerplexity);
        delete VantagePoint;
        //
        for(let i = 0; i < numberOfSamplesInX; i++){
            top1[i] = -0.0001;
            bottom1[i] = -0.0001;
        }
        let IShouldStay;
        aux = getMeThePairWiseAffinities1(X, numberOfSamplesInX, numberOfDimentions);
        for(let iter = 0; iter <= 100; iter++){
            IShouldStay = true;
            p = getMeThePairWiseAffinities2(aux, numberOfSamplesInX, top1);
            top2 = GetMeThePerplexity(p, numberOfSamplesInX);
            for(let i = 0; i < numberOfSamplesInX; i++){
                if(top2[i] < DesiredPerplexity){
                    IShouldStay = false;
                    bottom1[i] = top1[i];
                    top1[i] = (top1[i] - 1) * 2;
                }
            }
            if(IShouldStay){iter = 101};
        }
        for(let i = 0; i < numberOfSamplesInX; i++){
            middle1[i] = (top1[i] + bottom1[i]) * 0.5;
        }
        p = getMeThePairWiseAffinities2(aux, numberOfSamplesInX, middle1);
        middle2 = GetMeThePerplexity(p, numberOfSamplesInX);
        for(let iter = 0; iter <= 100; iter++){
        //Decision Maker (you can do better than this, see it later)
            for(let i = 0; i < numberOfSamplesInX; i++){
                if(Math.abs(middle2[i] - DesiredPerplexity) < 0.01){
                }else if(middle2[i] > DesiredPerplexity){
                    top1[i] = middle1[i];
                    top2[i] = middle2[i];
                    middle1[i] = (top1[i] + bottom1[i])*0.5;
                }else{
                    bottom1[i] = middle1[i];
                    bottom2[i] = middle2[i];
                    middle1[i] = (top1[i] + bottom1[i])*0.5;
                }
            }
            p = getMeThePairWiseAffinities2(aux, numberOfSamplesInX, middle1);
            middle2 = GetMeThePerplexity(p, numberOfSamplesInX);
        }
        //Set pij= ( pj|i + pi|j ) / 2 * n
        p2 = Array(numberOfSamplesInX).fill(0);
        for(let i = 0; i < numberOfSamplesInX; i++){
            p2[i] = Array(VantagePointQueryArray[i].length).fill(0);
            for(let z = 0; z < VantagePointQueryArray[i].length; z++){
                j = VantagePointQueryArray[i][z];
                if(j != i){
                    for(let k = 0; k < VantagePointQueryArray[j].length; k++){
                        if(VantagePointQueryArray[j][k]==i){
                            p2[i][z] = (p[i][z] + p[j][k])*InversenumberOfSamplesInX;
                            k = VantagePointQueryArray[j].length;
                        }
                    }
                }
            }
        }
        p = p2;
        delete p2;
        //Sample Initial Solution Y
        if(shouldIStartReInitializeY){
            oldy=zeros(numberOfSamplesInX,3);
            y = CreateAGaussianRandomMatrix(numberOfSamplesInX, 3);
        }
        shouldIStartReInitializeY = false;
        shouldIStartAllOverAgain = false;
    }
    YUpload(p, y, oldy, numberOfSamplesInX, numberOfIterations, Momentum, LearningRatio, VantagePointQueryArray, TradeOff);
    rotationZ[0][0]=cos(angle);
    rotationZ[1][0]=sin(angle);
    rotationZ[0][1]=-rotationZ[1][0];
    rotationZ[1][1]=rotationZ[0][0];
    rotationX[1][1]=rotationZ[0][0];
    rotationX[1][2]=rotationZ[0][1];
    rotationX[2][1]=rotationZ[1][0];
    rotationX[2][2]=rotationZ[0][0];
    rotationY[0][0]=rotationZ[0][0];
    rotationY[0][2]=rotationZ[1][0];
    rotationY[2][0]=rotationZ[0][1];
    rotationY[2][2]=rotationZ[0][0];
    strokeWeight(5);
    noFill();
    let projected = [];
    let compensation;
    if(Canvas.HalfSize[0] > Canvas.HalfSize[1]){
        compensation = Canvas.HalfSize[1] / BiggestY;
    }else{
        compensation = Canvas.HalfSize[0] / BiggestY;    
    }
    if (ColorMode == 0){
        stroke(255);
        for (let i = 0; i < y.length; i++){
            let rotated = matmul(rotationY, y[i]);
            rotated = matmul(rotationX, rotated);
            rotated = matmul(rotationZ, rotated);
            let projected2d = matmul(projection, rotated);
            projected[i] = [];
            projected[i][0] = projected2d[0] * compensation + Canvas.HalfSize[0];
            projected[i][1] = projected2d[1] * compensation + Canvas.HalfSize[1];
            point((projected[i][0]), (projected[i][1]));
        }
    }else if(ColorMode == 1){
        for (let i = 0; i < y.length; i++) {
            let rotated = matmul(rotationY, y[i]);
            rotated = matmul(rotationX, rotated);
            rotated = matmul(rotationZ, rotated);
            let projected2d = matmul(projection, rotated);
            projected[i] = [];
            projected[i][0] = projected2d[0] * compensation + Canvas.HalfSize[0];
            projected[i][1] = projected2d[1] * compensation + Canvas.HalfSize[1];
            stroke(Colors[i]);
            point((projected[i][0]), (projected[i][1]));
        }
    }else{
        for (let i = 0; i < y.length; i++) {
            let rotated = matmul(rotationY, y[i]);
            rotated = matmul(rotationX, rotated);
            rotated = matmul(rotationZ, rotated);
            let projected2d = matmul(projection, rotated);
            projected[i] = [];
            projected[i][0] = projected2d[0] * compensation + Canvas.HalfSize[0];
            projected[i][1] = projected2d[1] * compensation + Canvas.HalfSize[1];
            stroke(Colors[i][0],Colors[i][1],Colors[i][2]);
            point((projected[i][0]), (projected[i][1]));
        }
    }
    if (mouseX > 0 && mouseX < Canvas.Size[0] && mouseY > 0 && mouseY < Canvas.Size[1]){
        let iPressed = null;
        for (let i = 0; i < projected.length; i++) {
            if(Math.abs(projected[i][0] - mouseX) < 5 && Math.abs(projected[i][1] - mouseY) < 5){
                iPressed = i;
                i = projected.length;
            }
        }
        if (iPressed != null){
            //push();
            stroke(255,0,90);
            strokeWeight(10);
            point(projected[iPressed][0], projected[iPressed][1]);
            //pop();
            textSize(30);
            strokeWeight(1);
            stroke(255);
            if (typeof Labels != 'undefined'){
                text(Labels[iPressed], 50, 50, 50, 50);
            }else{text(iPressed,50, 50, 50, 50)}
            pop();
        }
        angle += 0.0005;
    }else{angle += 0.005;}
}
function getMeThePairWiseAffinities1(X, numberOfSamplesInX, numberOfDimentions){
    //This is the part of the code that is independant of minusTwoSigmaSquared.
    //I can play this part of the code only once during the sigma search.
    let p = Array(numberOfSamplesInX).fill(0); //pj|i
    let aux = 0;
    let i = 0;
    let z = 0;
    let n = 0;
    for(i = 0; i < numberOfSamplesInX; i++){
        p[i] = Array(VantagePointQueryArray[i].length).fill(0);
        for(z = 0; z < VantagePointQueryArray[i].length; z++){
            j = VantagePointQueryArray[i][z];
            if(j != i){
                for(n = 0; n < numberOfDimentions; n++){
                    aux = X[i][n] - X[j][n];
                    p[i][z] += aux * aux;
                }
            }
        }
    }
    return p;
}
function getMeThePairWiseAffinities2(auxiliar, numberOfSamplesInX, minusTwoSigmaSquared){
    // get the sum of pair wise affinities and the non normilized pair wise affinities
    let sumOfPairWiseAffinities = Array(numberOfSamplesInX).fill(0);
    let p = Array(numberOfSamplesInX).fill(0); //pj|i upper
    for(let i = 0; i < numberOfSamplesInX; i++){
        p[i] = Array(VantagePointQueryArray[i].length).fill(0);
        for(let z = 0; z < VantagePointQueryArray[i].length; z++){
            if(VantagePointQueryArray[i][z] != i){
                p[i][z] = Math.exp(auxiliar[i][z] / (minusTwoSigmaSquared[i] + 0.000001));
                sumOfPairWiseAffinities[i] += p[i][z];
            }
        }
    }
    // get the normilized pair wise affinities
    for(let i = 0; i < numberOfSamplesInX; i++){
        for(let z = 0; z < VantagePointQueryArray[i].length; z++){
            j = VantagePointQueryArray[i][z];
            if(j != i){
                p[i][z] /= sumOfPairWiseAffinities[j] + 0.000001;
            }
        }
    }
    return p;
}
function GetMeThePerplexity(p, numberOfSamplesInX){
    let Perplexities=Array(numberOfSamplesInX).fill(0);
    for(i = 0; i < numberOfSamplesInX; i++){
        for(let z = 0; z < VantagePointQueryArray[i].length; z++){
            if(VantagePointQueryArray[i][z] != i){
                Perplexities[i] += p[i][z] * Math.log2(p[i][z] + 0.00001);
            }
        }
    }
    for(i = 0; i < numberOfSamplesInX; i++){
        Perplexities[i] = Math.pow( 2, -Perplexities[i]);
    }
    return Perplexities;
}
function YUpload(p, y, oldy, numberOfSamplesInX, numberOfIterations, Momentum, LearningRatio, VantagePointQueryArray, TradeOff){
    let aux;
    let aux1;
    let j;
    let IndexElements=[];
    let ResultOT = new OctTreeResults();
    for(let i = 0; i < y.length; i++){
        IndexElements[i] = i;
    }
    for(let iter = 0; iter <= numberOfIterations; iter++){
        let Fattr = zeros(numberOfSamplesInX,3);
        let Frep = zeros(numberOfSamplesInX,3);
        let Sumq = 0;
        OctTree = new OctTreeElement([0,0,0], BiggestY);
        OctTree.InsertInBoxes(y, IndexElements);
        BiggestY = 0;
        if (EarlyExaggeration.DidIFinish){
            for(let i = 0; i < numberOfSamplesInX; i++){
                for(let z = 0; z < VantagePointQueryArray[i].length; z++){
                    j = VantagePointQueryArray[i][z];
                    if(j != i){
                        aux1=p[i][z] * CalculateZQij( i, j);
                        Fattr[i][0] += aux1 * (y[i][0] - y[j][0]);
                        Fattr[i][1] += aux1 * (y[i][1] - y[j][1]);
                        Fattr[i][2] += aux1 * (y[i][2] - y[j][2]);
                    }
                }
            }
        }else{
            for(let i = 0; i < numberOfSamplesInX; i++){
                for(let z = 0; z < VantagePointQueryArray[i].length; z++){
                    j = VantagePointQueryArray[i][z];
                    if(j != i){
                        aux1= EarlyExaggeration.Factor * p[i][z] * CalculateZQij( i, j);
                        Fattr[i][0] += aux1 * (y[i][0] - y[j][0]);
                        Fattr[i][1] += aux1 * (y[i][1] - y[j][1]);
                        Fattr[i][2] += aux1 * (y[i][2] - y[j][2]);
                    }
                }
            }
            //push();
            stroke(150);
            textSize(20);
            strokeWeight(1);
            text('Early Exaggeration Active', 470, 10, 250, 50);
            //pop();
            EarlyExaggeration.Counter += 1;
            if (EarlyExaggeration.Counter > EarlyExaggeration.Iterations){EarlyExaggeration.DidIFinish = true}
        }
        for(let i = 0; i < numberOfSamplesInX; i++){
            OctTree.ListOfEquivalentBodiesOfI(y, i, TradeOff, ResultOT);
            for(let z = 0; z < ResultOT.ResultOfTheQueryOT1.length; z++){
                aux = CalculateZQij2( i, ResultOT.ResultOfTheQueryOT1[z]);
                Sumq += ResultOT.ResultOfTheQueryOT2[z] / aux;
                aux1 = aux * aux;
                Frep[i][0] -= aux1 * (y[i][0] - ResultOT.ResultOfTheQueryOT1[z][0] * ResultOT.ResultOfTheQueryOT2[z]);
                Frep[i][1] -= aux1 * (y[i][1] - ResultOT.ResultOfTheQueryOT1[z][1] * ResultOT.ResultOfTheQueryOT2[z]);
                Frep[i][2] -= aux1 * (y[i][2] - ResultOT.ResultOfTheQueryOT1[z][2] * ResultOT.ResultOfTheQueryOT2[z]);
            }
            for(let z = 0; z < ResultOT.ResultOfTheQueryOT3.length; z++){
                aux = CalculateZQij( i, ResultOT.ResultOfTheQueryOT3[z]);
                Sumq +=  1 / aux;
                aux1 = aux * aux;
                Frep[i][0] -= aux1 * (y[i][0] - y[ResultOT.ResultOfTheQueryOT3[z]][0]);
                Frep[i][1] -= aux1 * (y[i][1] - y[ResultOT.ResultOfTheQueryOT3[z]][1]);
                Frep[i][2] -= aux1 * (y[i][2] - y[ResultOT.ResultOfTheQueryOT3[z]][2]);
            }
        }
        //y adjustment
        for(let i = 0; i < numberOfSamplesInX; i++){
            aux = y[i][0];
            y[i][0] -= LearningRatio * (Fattr[i][0] + Frep[i][0] / Sumq) + Momentum * (y[i][0] - oldy[i][0]);
            oldy[i][0] = aux;
            if(BiggestY < Math.abs(y[i][0])){BiggestY = Math.abs(y[i][0])}
            aux = y[i][1];
            y[i][1] -= LearningRatio * (Fattr[i][1] + Frep[i][1] / Sumq) + Momentum * (y[i][1] - oldy[i][1]);
            oldy[i][1] = aux;
            if(BiggestY < Math.abs(y[i][1])){BiggestY = Math.abs(y[i][1])}
            aux = y[i][2];
            y[i][2] -= LearningRatio * (Fattr[i][2] + Frep[i][2] / Sumq) + Momentum * (y[i][2] - oldy[i][2]);
            oldy[i][2] = aux;
            if(BiggestY < Math.abs(y[i][2])){BiggestY = Math.abs(y[i][2])}
        }
    }
    function CalculateZQij( i, j){
        let aux1 = y[i][0] - y[j][0];
        let aux = aux1 * aux1;
        aux1 = y[i][1] - y[j][1];
        aux += aux1 * aux1;
        aux1 = y[i][2] - y[j][2];
        aux += aux1 * aux1;
        return 1 / (1 + aux);
    }
    function CalculateZQij2( i, CenterOfMass){
        let aux1 = y[i][0] - CenterOfMass[0];
        let aux = aux1 * aux1;
        aux1 = y[i][1] - CenterOfMass[1];
        aux += aux1 * aux1;
        aux1 = y[i][2] - CenterOfMass[2];
        aux += aux1 * aux1;
        return 1 / (1 + aux);
    }
}
function zeros( DimensionA, DimensionB){
    let array = Array(DimensionA);
    for (let i = 0; i < DimensionA; ++i){
        array[i] = Array(DimensionB).fill(0);
    }
    return array;
}
function matmul(a, b) {
    let rowsA = a.length;
    result = [];
    for (let j = 0; j < rowsA; j++){
      result[j] = [];
      for (let i = 0; i < 1; i++){
        result[j][i] = 0;
        for (let n = 0; n < 3; n++){
            result[j][i] += a[j][n] * b[n];
        }
      }
    }
    return result;
}
function CreateAGaussianRandomMatrix(DimensionA, DimensionB){
    let INVNORM = 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    let Result = Array(DimensionA);
    for (let i = 0; i < DimensionA; ++i) {
        Result[i] = Array(DimensionB);
        for (let j = 0; j < DimensionB; j ++){
            Result[i][j]=INVNORM[Math.floor(Math.random()*999,0)];
        }
    }
    return Result;
}