713 lines
15 KiB
HTML
713 lines
15 KiB
HTML
<script>
|
|
/* Vector Library */
|
|
/*
|
|
Works with n-dimensional vectors: represented as arrays of numbers
|
|
*/
|
|
var V = {};
|
|
V.Subtract = function(inV1, inV2)
|
|
{
|
|
var out = [];
|
|
for(var i=0; i<inV1.length; i++)
|
|
{
|
|
out[i] = inV1[i] - inV2[i];
|
|
}
|
|
return out;
|
|
};
|
|
V.Add = function(inV1, inV2)
|
|
{
|
|
var out = [];
|
|
for(var i=0; i<inV1.length; i++)
|
|
{
|
|
out[i] = inV1[i] + inV2[i];
|
|
}
|
|
return out;
|
|
};
|
|
V.Distance = function(inV1, inV2)
|
|
{
|
|
return V.Length(V.Subtract(inV1, inV2))
|
|
};
|
|
V.Dot = function(inV1, inV2)
|
|
{
|
|
var out = 0;
|
|
for(var i=0; i<inV1.length; i++)
|
|
{
|
|
out += inV1[i] * inV2[i];
|
|
}
|
|
return out;
|
|
};
|
|
V.Multiply = function(inV1, inV2)
|
|
{
|
|
var out = [];
|
|
for(var i=0; i<inV1.length; i++)
|
|
{
|
|
out[i] = inV1[i] * inV2[i];
|
|
}
|
|
return out;
|
|
};
|
|
V.Length = function(inV1)
|
|
{
|
|
return Math.sqrt(V.Dot(inV1, inV1));
|
|
};
|
|
V.Scale = function(inV1, inScalar)
|
|
{
|
|
var out = [];
|
|
for(var i=0; i<inV1.length; i++)
|
|
{
|
|
out[i] = inV1[i] * inScalar;
|
|
}
|
|
return out;
|
|
};
|
|
V.Normalize = function(inV1)
|
|
{
|
|
return V.Scale(inV1, 1/V.Length(inV1));
|
|
};
|
|
V.Clone = function(inV1)
|
|
{
|
|
var out = [];
|
|
var i;
|
|
for(i=0; i<inV1.length; i++)
|
|
{
|
|
out[i] = inV1[i];
|
|
}
|
|
return out;
|
|
};
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
var M = {};
|
|
|
|
/**************************
|
|
M A T R I X
|
|
*/
|
|
// transform inC with inM
|
|
// returns the transformed inC
|
|
M.Transform = function(inM, inC)
|
|
{
|
|
var outM = [];
|
|
var outV = [];
|
|
var i, j;
|
|
|
|
for(i=0; i<inC.length; i++)
|
|
{
|
|
outV = [];
|
|
for(j=0; j<inM.length; j++)
|
|
{
|
|
outV[j] = V.Dot(inM[j], inC[i]);
|
|
}
|
|
outM.push(outV);
|
|
}
|
|
return outM;
|
|
};
|
|
|
|
|
|
// flip rows for columns in inM
|
|
// returns the modified Matrix
|
|
M.Transpose = function(inM)
|
|
{
|
|
var dimensions = inM[0].length;
|
|
var i, j;
|
|
var outM = [];
|
|
var outV = [];
|
|
for(i=0; i<dimensions; i++)
|
|
{
|
|
outV = [];
|
|
for(j=0; j<inM.length; j++)
|
|
{
|
|
//the Ith componenth of the Jth member
|
|
outV[j] = inM[j][i];
|
|
}
|
|
outM.push(outV);
|
|
}
|
|
return outM;
|
|
}
|
|
|
|
// returns a matrix that is the result of the outer product of inV1 and inV2
|
|
// where the Nth member of outM is a copy of V1, scaled by the Nth component of V2
|
|
M.Outer = function(inV1, inV2)
|
|
{
|
|
var outM = [];
|
|
|
|
var i;
|
|
for(i=0; i<inV2.length; i++)
|
|
{
|
|
outM.push(V.Scale(inV1, inV2[i]));
|
|
}
|
|
|
|
return outM;
|
|
};
|
|
|
|
|
|
|
|
|
|
|
|
/**************************
|
|
B A T C H
|
|
*/
|
|
//smash the members of inM with a softmax
|
|
M.Sigmoid = function(inM)
|
|
{
|
|
var i, j;
|
|
var outM = [];
|
|
var outV = [];
|
|
for(i=0; i<inM.length; i++)
|
|
{
|
|
outV = [];
|
|
for(j=0; j<inM[i].length; j++)
|
|
{
|
|
outV[j] = 1/(1 + Math.pow(Math.E, -inM[i][j]));
|
|
}
|
|
outM.push(outV);
|
|
}
|
|
return outM;
|
|
};
|
|
// return the derivatives of the members of inM (that have been run through the softmax)
|
|
M.Derivative = function(inM)
|
|
{
|
|
var i, j;
|
|
var component;
|
|
var outM = [];
|
|
var outV = [];
|
|
for(i=0; i<inM.length; i++)
|
|
{
|
|
outV = [];
|
|
for(j=0; j<inM[i].length; j++)
|
|
{
|
|
component = inM[i][j];
|
|
outV[j] = component*(1 - component);
|
|
}
|
|
outM.push(outV);
|
|
}
|
|
return outM;
|
|
};
|
|
// batch multiply these pairs of vectors
|
|
M.Multiply = function(inCloud1, inCloud2)
|
|
{
|
|
var i;
|
|
var outM = [];
|
|
for(i=0; i<inCloud1.length; i++)
|
|
{
|
|
outM.push(V.Multiply(inCloud1[i], inCloud2[i]));
|
|
};
|
|
return outM;
|
|
};
|
|
// batch add
|
|
M.Add = function(inCloud1, inCloud2)
|
|
{
|
|
var outM = [];
|
|
|
|
var i;
|
|
for(i=0; i<inCloud1.length; i++)
|
|
{
|
|
outM.push(V.Add(inCloud1[i], inCloud2[i]));
|
|
}
|
|
return outM;
|
|
};
|
|
M.Subtract = function(inCloud1, inCloud2)
|
|
{
|
|
var outM = [];
|
|
|
|
var i;
|
|
for(i=0; i<inCloud1.length; i++)
|
|
{
|
|
outM.push(V.Subtract(inCloud1[i], inCloud2[i]));
|
|
}
|
|
return outM;
|
|
};
|
|
M.Scale = function(inCloud1, inScalar)
|
|
{
|
|
var outM = [];
|
|
|
|
var i;
|
|
for(i=0; i<inCloud1.length; i++)
|
|
{
|
|
outM.push(V.Scale(inCloud1[i], inScalar));
|
|
}
|
|
return outM;
|
|
};
|
|
M.Clone = function(inM)
|
|
{
|
|
var i;
|
|
var outM;
|
|
var outV;
|
|
|
|
outM =[];
|
|
for(i=0; i<inM.length; i++)
|
|
{
|
|
outM.push(V.Clone(inM[i]));
|
|
}
|
|
return outM;
|
|
};
|
|
|
|
|
|
/**************************
|
|
B O U N D S
|
|
*/
|
|
// return the bounding box of inM as a two-member Matrix
|
|
M.Bounds = function(inM)
|
|
{
|
|
var dimensions = inM[0].length;
|
|
var i, j;
|
|
var min = [];
|
|
var max = [];
|
|
for(i=0; i<dimensions; i++)
|
|
{
|
|
min[i] = 9999999;
|
|
max[i] = -999999;
|
|
}
|
|
for(i=0; i<inM.length; i++)
|
|
{
|
|
for(j=0; j<dimensions; j++)
|
|
{
|
|
if(inM[i][j] < min[j])
|
|
{
|
|
min[j] = inM[i][j];
|
|
}
|
|
if(inM[i][j] > max[j])
|
|
{
|
|
max[j] = inM[i][j];
|
|
}
|
|
}
|
|
}
|
|
return [min, max];
|
|
};
|
|
|
|
// find the local coordinates for all the members of inM, within the bounding box inB
|
|
// returns a new Matrix of relative vectors
|
|
M.GlobalToLocal = function(inM, inB)
|
|
{
|
|
var dimensions = inB[0].length;
|
|
var i, j;
|
|
var outM = [];
|
|
var outV = [];
|
|
var size;
|
|
var min;
|
|
var denominator;
|
|
for(i=0; i<inM.length; i++)
|
|
{
|
|
outV = [];
|
|
for(j=0; j<dimensions; j++)
|
|
{
|
|
denominator = inB[1][j] - inB[0][j];
|
|
if(denominator == 0)
|
|
{
|
|
outV[j] = inB[1][j];// if min and max are the same, just output max
|
|
}
|
|
else
|
|
{
|
|
outV[j] = (inM[i][j] - inB[0][j])/denominator;
|
|
}
|
|
}
|
|
outM.push(outV);
|
|
}
|
|
return outM;
|
|
};
|
|
// find the global coordinates for all the members of inM, within the bounding box inB
|
|
// returns a new Matrix of global vectors
|
|
M.LocalToGlobal = function(inM, inB)
|
|
{
|
|
var dimensions = inB[0].length;
|
|
var i, j;
|
|
var outM = [];
|
|
var outV = [];
|
|
var size;
|
|
var min;
|
|
for(i=0; i<inM.length; i++)
|
|
{
|
|
outV = [];
|
|
for(j=0; j<dimensions; j++)
|
|
{
|
|
outV[j] = inB[0][j] + inM[i][j] * (inB[1][j] - inB[0][j]);
|
|
}
|
|
outM.push(outV);
|
|
}
|
|
return outM;
|
|
};
|
|
|
|
|
|
/**************************
|
|
C L O U D
|
|
*/
|
|
// return some number of points from inM as a new Matrix
|
|
M.Reduce = function(inM, inCount)
|
|
{
|
|
var largeGroupSize;
|
|
var largeGroupCount;
|
|
var smallGroupSize;
|
|
var outM = [];
|
|
|
|
largeGroupSize = Math.floor(inM.length/inM);
|
|
smallGroupSize = inM.length%inCount
|
|
for(i=0; i<inM-1; i++)
|
|
{
|
|
index = i*largeGroupSize + Math.floor(Math.random()*largeGroupSize);
|
|
outM.push( V.Clone(inM[index]) );
|
|
}
|
|
if(smallGroupSize != 0)
|
|
{
|
|
index = i*largeGroupSize + Math.floor(Math.random()*smallGroupSize)
|
|
outM.push( V.Clone(inM[index]) );
|
|
}
|
|
return outM;
|
|
};
|
|
|
|
// return a Matrix of length inCount, where all the members fall within the circle paramemters, including a bias
|
|
M.Circle = function(inCenter, inRadius, inBias, inCount)
|
|
{
|
|
var i, j;
|
|
var vector;
|
|
var length;
|
|
var outM = [];
|
|
|
|
for(i=0; i<inCount; i++)
|
|
{
|
|
//generate a random vector
|
|
vector = [];
|
|
for(j=0; j<inCenter.length; j++)
|
|
{
|
|
vector[j] = (Math.random() - 0.5);
|
|
}
|
|
|
|
//normalize the vector
|
|
vector = V.Scale(vector, 1/V.Length(vector));
|
|
|
|
//set a random length (with a bias)
|
|
length = Math.pow(Math.random(), Math.log(inBias)/Math.log(0.5))*inRadius;
|
|
vector = V.Scale(vector, length);
|
|
|
|
//move the vector to the center
|
|
vector = V.Add(vector, inCenter);
|
|
|
|
outM.push(vector);
|
|
}
|
|
return outM;
|
|
};
|
|
|
|
// return a Matrix of length inCount, where all the members fall within inBounds
|
|
M.Box = function(inBounds, inCount)
|
|
{
|
|
var vector;
|
|
var dimensions = inBounds[0].length;
|
|
var i, j;
|
|
var min, max;
|
|
var outM = [];
|
|
|
|
for(i=0; i<inCount; i++)
|
|
{
|
|
vector = [];
|
|
for(j=0; j<dimensions; j++)
|
|
{
|
|
min = inBounds[0][j];
|
|
max = inBounds[1][j];
|
|
|
|
vector[j] = min + Math.random()*(max - min);
|
|
}
|
|
outM.push(vector);
|
|
}
|
|
return outM;
|
|
};
|
|
|
|
//combine all the matricies in inList into one long Matrix
|
|
M.Combine = function(inList)
|
|
{
|
|
var i, j;
|
|
var outM = [];
|
|
for(i=0; i<inList.length; i++)
|
|
{
|
|
for(j=0; j<inList[i].length; j++)
|
|
{
|
|
outM.push(V.Clone(inList[i][j]));
|
|
}
|
|
}
|
|
return outM;
|
|
};
|
|
|
|
/*
|
|
PLEASE NOTE: These padding routines are unique to this library in that they
|
|
actually modify the input object(s) rather than returning modified copies!
|
|
*/
|
|
// add a new component (set to '1') to each member of inM
|
|
M.Pad = function(inM)
|
|
{
|
|
var i;
|
|
for(i=0; i<inM.length; i++)
|
|
{
|
|
inM[i].push(1);
|
|
}
|
|
return inM;
|
|
};
|
|
// remove the last component of each memeber of inM
|
|
M.Unpad = function(inM)
|
|
{
|
|
var i;
|
|
for(i=0; i<inM.length; i++)
|
|
{
|
|
inM[i].pop();
|
|
}
|
|
return inM;
|
|
};
|
|
// set the last component of each member of inM to 1
|
|
M.Repad = function(inM)
|
|
{
|
|
var i;
|
|
var last = inM[0].length-1;
|
|
for(i=0; i<inM.length; i++)
|
|
{
|
|
inM[i][last] = 1;
|
|
}
|
|
return inM;
|
|
};
|
|
</script>
|
|
|
|
<script>
|
|
var NN = {};
|
|
|
|
NN.TrainingSet = {};
|
|
NN.TrainingSet.Instances = [];
|
|
NN.TrainingSet.Create = function()
|
|
{
|
|
var obj = {};
|
|
|
|
obj.Input = [];
|
|
obj.Output = [];
|
|
obj.Order = [];
|
|
|
|
NN.TrainingSet.Instances.push(obj);
|
|
return obj;
|
|
};
|
|
NN.TrainingSet.AddPoint = function(inTrainingSet, inType, inData)
|
|
{
|
|
inTrainingSet.Input.push(inData);
|
|
inTrainingSet.Output.push(inType);
|
|
inTrainingSet.Order.push(inTrainingSet.Order.length);
|
|
};
|
|
NN.TrainingSet.AddCloud = function(inTrainingSet, inLabel, inCloud)
|
|
{
|
|
var i;
|
|
for(i=0; i<inCloud.length; i++)
|
|
{
|
|
NN.TrainingSet.AddPoint(inTrainingSet, inLabel, inCloud[i]);
|
|
}
|
|
};
|
|
NN.TrainingSet.Randomize = function(inTrainingSet)
|
|
{
|
|
var newOrder = [];
|
|
var selection;
|
|
while(inTrainingSet.Order.length != 0)
|
|
{
|
|
selection = Math.floor(inTrainingSet.Order.length * Math.random());
|
|
inTrainingSet.Order.splice(selection, 1);
|
|
newOrder.push(selection);
|
|
}
|
|
inTrainingSet.Order = newOrder;
|
|
};
|
|
|
|
|
|
NN.Layer = {};
|
|
NN.Layer.Create = function(sizeIn, sizeOut)
|
|
{
|
|
var i;
|
|
var min = [];
|
|
var max = [];
|
|
var obj = {};
|
|
|
|
sizeIn++;
|
|
|
|
obj.Forward = {};
|
|
for(i=0; i<sizeIn; i++)
|
|
{
|
|
min.push(-1);
|
|
max.push(1);
|
|
}
|
|
obj.Forward.Matrix = M.Box([min, max], sizeOut);
|
|
obj.Forward.StageInput = [];
|
|
obj.Forward.StageAffine = [];
|
|
obj.Forward.StageSigmoid = [];
|
|
obj.Forward.StageDerivative = [];
|
|
|
|
obj.Backward = {};
|
|
obj.Backward.Matrix = M.Transpose(obj.Forward.Matrix);
|
|
obj.Backward.StageInput = [];
|
|
obj.Backward.StageDerivative = [];
|
|
obj.Backward.StageAffine = [];
|
|
|
|
return obj;
|
|
};
|
|
NN.Layer.Forward = function(inLayer, inInput)
|
|
{
|
|
inLayer.Forward.StageInput = M.Pad(inInput); // Pad the input
|
|
inLayer.Forward.StageAffine = M.Transform(inLayer.Forward.Matrix, inLayer.Forward.StageInput);
|
|
inLayer.Forward.StageSigmoid = M.Sigmoid(inLayer.Forward.StageAffine);
|
|
|
|
return inLayer.Forward.StageSigmoid;
|
|
};
|
|
NN.Layer.Error = function(inLayer, inTarget)
|
|
{
|
|
return M.Subtract(inLayer.Forward.StageSigmoid, inTarget);
|
|
};
|
|
NN.Layer.Backward = function(inLayer, inInput)
|
|
{
|
|
/* We need the derivative of the forward pass, but only during the backward pass.
|
|
That's why-- even though it "belongs" to the forward pass-- it is being calculated here. */
|
|
inLayer.Forward.StageDerivative = M.Derivative(inLayer.Forward.StageSigmoid);
|
|
|
|
/* This transpose matrix is for sending the error back to a previous layer.
|
|
And again, even though it is derived directly from the forward matrix, it is only needed during the backward pass so we calculate it here.*/
|
|
inLayer.Backward.Matrix = M.Transpose(inLayer.Forward.Matrix);
|
|
|
|
/* When the error vector arrives at a layer, it always needs to be multiplied (read 'supressed') by the derivative of
|
|
what the layer output earlier during the forward pass.
|
|
So despite its name, Backward.StageDerivative contains the result of this *multiplication* and not some new derivative calculation.*/
|
|
inLayer.Backward.StageInput = inInput;
|
|
inLayer.Backward.StageDerivative = M.Multiply(inLayer.Backward.StageInput, inLayer.Forward.StageDerivative);
|
|
inLayer.Backward.StageAffine = M.Transform(inLayer.Backward.Matrix, inLayer.Backward.StageDerivative);
|
|
|
|
return M.Unpad(inLayer.Backward.StageAffine);// Unpad the output
|
|
};
|
|
NN.Layer.Adjust = function(inLayer, inLearningRate)
|
|
{
|
|
var deltas;
|
|
var vector;
|
|
var scalar;
|
|
var i, j;
|
|
|
|
for(i=0; i<inLayer.Forward.StageInput.length; i++)
|
|
{
|
|
deltas = M.Outer(inLayer.Forward.StageInput[i], inLayer.Backward.StageDerivative[i]);
|
|
deltas = M.Scale(deltas, inLearningRate);
|
|
|
|
inLayer.Forward.Matrix = M.Subtract(inLayer.Forward.Matrix, deltas);
|
|
}
|
|
};
|
|
NN.Layer.Stochastic = function(inLayer, inTrainingSet, inIterations)
|
|
{
|
|
/* this method is ONLY for testing individual layers, and does not translate to network-level training */
|
|
var i, j;
|
|
var current;
|
|
var error;
|
|
for(i=0; i<inIterations; i++)
|
|
{
|
|
NN.TrainingSet.Randomize(inTrainingSet);
|
|
for(j=0; j<inTrainingSet.Order.length; j++)
|
|
{
|
|
current = inTrainingSet.Order[j];
|
|
NN.Layer.Forward(inLayer, [inTrainingSet.Input[current]]);
|
|
error = M.Subtract(inLayer.Forward.StageSigmoid, [inTrainingSet.Output[current]]);
|
|
NN.Layer.Backward(inLayer, error);
|
|
NN.Layer.Adjust(inLayer, 0.1);
|
|
}
|
|
}
|
|
};
|
|
|
|
NN.Network = {};
|
|
NN.Network.Instances = [];
|
|
NN.Network.Create = function()
|
|
{
|
|
var obj = {};
|
|
var i;
|
|
|
|
obj.Layers = [];
|
|
obj.LearningRate = 0.8;
|
|
obj.Error = [];
|
|
|
|
for(i=0; i<arguments.length-1; i++)
|
|
{
|
|
obj.Layers.push(NN.Layer.Create(arguments[i], arguments[i+1]));
|
|
}
|
|
|
|
NN.Network.Instances.push(obj);
|
|
return obj;
|
|
};
|
|
NN.Network.Observe = function(inNetwork, inBatch)
|
|
{
|
|
var input = M.Clone(inBatch);
|
|
var i;
|
|
for(i=0; i<inNetwork.Layers.length; i++)
|
|
{
|
|
input = NN.Layer.Forward(inNetwork.Layers[i], input);
|
|
}
|
|
return inNetwork.Layers[inNetwork.Layers.length-1].Forward.StageSigmoid;
|
|
};
|
|
NN.Network.Error = function(inNetwork, inTraining)
|
|
{
|
|
return M.Subtract(inNetwork.Layers[inNetwork.Layers.length-1].Forward.StageSigmoid, inTraining);
|
|
};
|
|
NN.Network.Learn = function(inNetwork, inError)
|
|
{
|
|
var input = inError;
|
|
var i;
|
|
for(i=inNetwork.Layers.length-1; i>=0; i--)
|
|
{
|
|
input = NN.Layer.Backward(inNetwork.Layers[i], input);
|
|
NN.Layer.Adjust(inNetwork.Layers[i], inNetwork.LearningRate);
|
|
}
|
|
};
|
|
|
|
|
|
NN.Network.Batch = function(inNetwork, inTrainingSet, inIterations)
|
|
{
|
|
var i;
|
|
for(i=0; i<inIterations; i++)
|
|
{
|
|
NN.Network.Observe(inNetwork, inTrainingSet.Input);
|
|
inNetwork.Error = NN.Network.Error(inNetwork, inTrainingSet.Output)
|
|
NN.Network.Learn(inNetwork, inNetwork.Error);
|
|
}
|
|
};
|
|
NN.Network.Stochastic = function(inNetwork, inTrainingSet, inIterations)
|
|
{
|
|
var i, j;
|
|
var current;
|
|
|
|
for(i=0; i<inIterations; i++)
|
|
{
|
|
NN.TrainingSet.Randomize(inTrainingSet);
|
|
for(j=0; j<inTrainingSet.Order.length; j++)
|
|
{
|
|
current = inTrainingSet.Order[j];
|
|
NN.Network.Observe(inNetwork, [inTrainingSet.Input[current]]);
|
|
inNetwork.Error = NN.Network.Error(inNetwork, [inTrainingSet.Output[current]]);
|
|
NN.Network.Learn(inNetwork, inNetwork.Error);
|
|
}
|
|
}
|
|
};
|
|
</script>
|
|
|
|
<script>
|
|
let matrix1 = [
|
|
[-0.43662948305036675, -0.368590640707799, -0.23227179558890843],
|
|
[-0.004292653969505622, 0.38670055222186317, -0.2478421495365568],
|
|
[0.738181366836224, 0.3389203747353555, 0.4920200816404332]
|
|
];
|
|
|
|
let matrix2 = [
|
|
[0.5793881115472015, 0.9732593374796092, 0.15207639877016987, -0.5356575655337803]
|
|
];
|
|
|
|
let typeA = [
|
|
[ 0.1, 0.05],
|
|
[ 0.0, -0.06]
|
|
];
|
|
let typeB = [
|
|
[ 0.99, 0.85],
|
|
[ 1.2, 1.05]
|
|
];
|
|
|
|
var layer1 = NN.Layer.Create(1, 1);
|
|
layer1.Forward.Matrix = matrix1;
|
|
|
|
var layer2 = NN.Layer.Create(1, 1);
|
|
layer2.Forward.Matrix = matrix2;
|
|
|
|
let stage1 = NN.Layer.Forward(layer1, typeA);
|
|
|
|
console.log(stage1);
|
|
|
|
</script> |