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717
index.html
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@ -1,717 +0,0 @@
<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 = 0.1;
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 = [
[0.7098703863463034, 0.35485944251238033, 0.7642849892333241, 0.03046174288491077],
[-0.30655426258144347, 0.45509633551425077, -0.5013795222004322, -0.3421292736637427]
];
let input = [
[ 0.1, 0.05],
[ 0.0, -0.06],
[ 0.99, 0.85],
[ 1.2, 1.05]
];
let output = [
[1, 0],
[1, 0],
[0, 1],
[0, 1]
];
let nn1 = NN.Network.Create(2, 3, 2);
nn1.Layers[0].Forward.Matrix = matrix1;
nn1.Layers[1].Forward.Matrix = matrix2;
nn1.LearningRate = 0.1;
//let logLayers = inNN => inNN.Layers.forEach(L=>console.log(L.Forward.Matrix));
NN.Network.Batch(nn1, {Input:input, Output:output}, 1000);
console.log(NN.Network.Observe(nn1, input));
</script>

10
m.test.js
View File

@ -98,7 +98,6 @@ Deno.test("Single.Affine", ()=>
assertEquals(t.length, 2, "correct dimensions"); assertEquals(t.length, 2, "correct dimensions");
assertEquals(t[0], 0.5) assertEquals(t[0], 0.5)
assertEquals(t[1], 1.1, "correct placement"); assertEquals(t[1], 1.1, "correct placement");
console.log(t);
}); });
Deno.test("Single.Subtract", ()=> Deno.test("Single.Subtract", ()=>
{ {
@ -137,15 +136,6 @@ Deno.test("Batch.Scale", ()=>
assertEquals(t[0].length, 2, "correct dimensions"); assertEquals(t[0].length, 2, "correct dimensions");
assertEquals(t[1][0], 1.5, "correct placement"); assertEquals(t[1][0], 1.5, "correct placement");
}); });
Deno.test("Batch.Subtract", ()=>
{
const c = [[1, 2], [3, 4]];
const s = [[0.5, 0.5], [0.5, 0.5]];
const t = M.Batch.Subtract(c, s);
assertEquals(t.length, 2, "correct count");
assertEquals(t[0].length, 2, "correct dimensions");
assertEquals(t[1][0], 2.5, "correct placement");
});
Deno.test("Batch.Sigmoid", ()=> Deno.test("Batch.Sigmoid", ()=>
{ {
const m = [[-1000, 1000]]; const m = [[-1000, 1000]];

9
m.ts
View File

@ -38,18 +38,11 @@ const Methods = {
Pad: (inCloud:Cloud.M):Cloud.M=> {inCloud.forEach((row:Cloud.V)=> row.push(1)); return inCloud; }, Pad: (inCloud:Cloud.M):Cloud.M=> {inCloud.forEach((row:Cloud.V)=> row.push(1)); return inCloud; },
Unpad: (inCloud:Cloud.M):Cloud.M=> {inCloud.forEach((row:Cloud.V)=> row.pop()); return inCloud; } Unpad: (inCloud:Cloud.M):Cloud.M=> {inCloud.forEach((row:Cloud.V)=> row.pop()); return inCloud; }
}, },
Test:
{
Dot:(v1:Cloud.V, v2:Cloud.V):number=>
{
return v1.reduce((sum, current, index)=> sum + current*v2[index]);
}
},
Single: Single:
{ {
Subtract: (inV1:Cloud.V, inV2:Cloud.V):Cloud.V=> inV1.map((component, i)=> component-inV2[i]), Subtract: (inV1:Cloud.V, inV2:Cloud.V):Cloud.V=> inV1.map((component, i)=> component-inV2[i]),
Multiply: (inV1:Cloud.V, inV2:Cloud.V):Cloud.V=> inV1.map((component, i)=> component*inV2[i]), Multiply: (inV1:Cloud.V, inV2:Cloud.V):Cloud.V=> inV1.map((component, i)=> component*inV2[i]),
Affine: (inV:Cloud.V, inMatrix:Cloud.M):Cloud.V=> inMatrix.map((row:Cloud.V)=> row.reduce((sum, current, index)=> sum + current*inV[index], 0)) Affine: (inV:Cloud.V, inMatrix:Cloud.M):Cloud.V=> inMatrix.map((row:Cloud.V)=> row.reduce((sum, current, index)=> sum + current*inV[index]))
}, },
Batch: Batch:
{ {

93
nn.test.js
View File

@ -1,52 +1,61 @@
import { assert, assertEquals } from "https://deno.land/std@0.102.0/testing/asserts.ts"; import { assert, assertEquals } from "https://deno.land/std@0.102.0/testing/asserts.ts";
import { Split, Build, Label, Learn, Check } from "./nn.ts"; import { Label, Forward, Backward } from "./nn.ts";
import { default as M } from "./m.ts";
let data = [ const input = [
[ 0.10, 0.05, 0, 1], [ 0.1, 0.05],
[ 0.00, -0.06, 0, 1], [ 0.0, -0.06]
[ 0.99, 0.85, 1, 0], [ 0.99, 0.85],
[ 1.20, 1.05, 1, 0] [ 1.2, 1.05]
]; ];
let columns = [2, 3];
let input, output;
let layers = [];
Deno.test("NN.Split", ()=> const training = [];
{ const stages = [];
[input, output] = Split(data, columns); const layers = [];
assert(input);
assert(output);
assertEquals(input.length, output.length, "data split into equal input and output");
assertEquals(input[0].length, 3, "padded input");
assertEquals(output[0].length, 2, "unpadded output");
});
Deno.test("NN.Build", ()=>
{
layers = Build(2, 5, 2);
assertEquals(layers.length, 2, "correct number of matrices");
assertEquals(layers[0][0].length, input[0].length, "input: padded input");
assertEquals(layers[0].length, 5, "input: unpadded output");
assertEquals(layers[1][0].length, 6, "hidden: padded input");
assertEquals(layers[1].length, output[0].length, "hidden: unpadded output");
});
Deno.test("NN.Label", ()=> Deno.test("NN.Label", ()=>
{ {
let labels = Label(input, layers); Label(training,
assertEquals(labels.length, output.length); [
assertEquals(labels[0].length, output[0].length); [ 0.1, 0.05],
[ 0.0, -0.06]
],
[1]);
Label(training,
[
[ 0.99, 0.85],
[ 1.2, 1.05]
],
[0]);
stages.push(training[0]);
console.log(training);
assertEquals(training.length, 2, "input and output sets created");
assertEquals(training[0].length, training[1].length, "both sets have same length");
assertEquals(training[0][0].length, 3, "padded input component");
assertEquals(training[1][0].length, 1, "unchanged label vector");
}); });
Deno.test("NN.Learn", ()=> Deno.test("NN.Backward", ()=>
{ {
let error = Learn(input, layers, output, 1000, 0.1);
assertEquals(error.length, output.length); layers.push(M.Create.Box([0, 0, 0], [1, 1, 1], 4));
let total = 0; layers.push(M.Create.Box([0, 0, 0, 0, 0], [1, 1, 1, 1, 1], 1));
let count = error.length*error[0].length;
error.forEach(row=> row.forEach(component=> total+=Math.abs(component))); let copy1 = M.Create.Clone(layers[0]);
assert(total/count < 0.3); let copy2 = M.Create.Clone(layers[1]);
});
for(let i=0; i<1000; i++)
{
Backward(stages, layers, training[1], 0.1);
}
assert(layers[0][0][0] != copy1[0][0][0], "first matrix has changed");
assert(layers[1][0][0] != copy2[0][0][0], "second matrix has changed");
});
Deno.test("NN.Forward", ()=>
{
console.log(Forward(stages, layers));
console.log(training[1]);
});

101
nn.ts
View File

@ -1,78 +1,53 @@
import { default as M, Cloud } from "./m.ts"; import { default as M, Cloud } from "./m.ts";
export type N = Array<Array<Array<number>>> export type N = Array<Array<Array<number>>>
const Forward = (inData:Cloud.M, inLayers:N):N => const Label = (inSet:any, inData:Cloud.M, inLabel:Cloud.V):N =>
{ {
let i:number; if(!inSet){inSet = [[], []];}
let stages:N = [inData]; if(inSet.length == 0){inSet.push([]);}
let process = (index:number):Cloud.M => M.Batch.Sigmoid(M.Batch.Affine(stages[index], inLayers[index])); if(inSet.length == 1){inSet.push([]);}
for(i=0; i<inLayers.length-1; i++){ stages[i+1] = M.Mutate.Pad(process(i)); } inData.forEach((row:Cloud.V) =>
stages[i+1] = process(i); {
return stages; row.push(1);
inSet[0].push(row);
inSet[1].push(inLabel);
});
return inSet;
}; };
const Backward = (inStages:N, inLayers:N, inGoals:Cloud.M, inRate:number):N =>
const Forward = (inStages:N, inLayers:N):Cloud.M =>
{ {
let i:number; let i:number;
let errorBack:Cloud.M = M.Batch.Subtract(inStages[inStages.length-1], inGoals); let process = (index:number):Cloud.M => M.Batch.Sigmoid(M.Batch.Affine(inStages[index], inLayers[index]));
for(i=0; i<inLayers.length-1; i++)
{
inStages[i+1] = M.Mutate.Pad(process(i));
}
inStages[i+1] = process(i);
return inStages[i+1];
};
const Backward = (inStages:N, inLayers:N, inGoals:Cloud.M, inRate:number):void =>
{
let i:number;
let errorBack:Cloud.M = M.Batch.Subtract(Forward(inStages, inLayers), inGoals);
for(i=inLayers.length-1; i>=0; i--) for(i=inLayers.length-1; i>=0; i--)
{ {
let errorScaled:Cloud.M = M.Batch.Multiply(errorBack, M.Batch.Derivative(inStages[i+1])); let layerMatrix:Cloud.M = inLayers[i];
errorBack = M.Batch.Affine(errorScaled, M.Create.Transpose(inLayers[i])); let layerInput:Cloud.M = inStages[i];
errorScaled.forEach((inScaledError:Cloud.V, inIndex:number)=> let layerOutput:Cloud.M = inStages[i+1];
{
inLayers[i] = M.Batch.Subtract( let errorScaled:Cloud.M = M.Batch.Multiply(errorBack, M.Batch.Derivative(layerOutput));
inLayers[i],
M.Batch.Scale(M.Create.Outer(inStages[i][inIndex], inScaledError), inRate) errorBack = M.Batch.Affine(errorScaled, M.Create.Transpose(layerMatrix));
); errorScaled.forEach((inScaledError:Cloud.V, inIndex:number)=> {
const deltas = M.Batch.Scale(M.Create.Outer(layerInput[inIndex], inScaledError), inRate);
layerMatrix = M.Batch.Subtract(layerMatrix, deltas);
}); });
} }
return inLayers;
}; };
const Split = (inTrainingSet:Cloud.M, inHeaderLabel:Cloud.V, inHeaderKeep:Cloud.V = []):N =>
{
let data:Cloud.M = [];
let label:Cloud.M = [];
if(!inHeaderKeep.length)
{
inTrainingSet[0].forEach( (item:number, index:number)=> inHeaderLabel.includes(index) ? false : inHeaderKeep.push(index) );
}
inTrainingSet.forEach((row:Cloud.V):void =>
{
let vectorData = [ ...inHeaderKeep.map((i:number)=>row[i]), 1];
let vectorLabel = inHeaderLabel.map((i:number)=>row[i])
data.push( vectorData );
label.push( vectorLabel );
});
return [ data, label ];
};
const Build = (...inLayers:Array<number>):N =>
{
let i:number;
let output:N = [];
let rand = (inDimensions:number, inCount:number):Cloud.M => M.Create.Box( new Array(inDimensions).fill(-1), new Array(inDimensions).fill(1), inCount);
for(i=0; i<inLayers.length-1; i++)
{
output.push(rand( inLayers[i]+1, inLayers[i+1]));
}
return output;
};
const Label = (inData:Cloud.M, inLayers:N):Cloud.M =>
{
let stages:N = Forward(inData, inLayers);
return stages[stages.length-1];
};
const Learn = (inData:Cloud.M, inLayers:N, inLabels:Cloud.M, inIterations:number, inRate:number):Cloud.M =>
{
let stages:N = [];
for(let i=0; i<inIterations; i++)
{
stages = Forward(inData, inLayers);
Backward(stages, inLayers, inLabels, inRate);
}
return M.Batch.Subtract(stages[stages.length-1], inLabels);
};
const Check = (inData:Cloud.M, inLayers:N, inLabels:Cloud.M):Cloud.M => Learn(inData, inLayers, inLabels, 1, 0);
export { Split, Build, Label, Learn, Check, Forward, Backward }; export { Label, Forward, Backward };
export type { Cloud };