// InnerProduct computes a Eucledian inner product.
func (e *Euclidean) InnerProduct(vectorX *mat64.Dense, vectorY *mat64.Dense) float64 {
subVector := mat64.NewDense(0, 0, nil)
subVector.MulElem(vectorX, vectorY)
result := mat64.Sum(subVector)
return result
}
func vectorDistance(vec1, vec2 *mat.Vector) (v float64) {
result := mat.NewVector(vec1.Len(), nil)
result.SubVec(vec1, vec2)
result.MulElemVec(result, result)
v = mat.Sum(result)
return
}
func rowSum(M mat.Matrix) mat.Matrix {
rows, _ := M.Dims()
floatRes := make([]float64, rows)
for i := 0; i < rows; i++ {
floatRes[i] = mat.Sum(getRowVector(i, M))
}
return mat.NewDense(rows, 1, floatRes)
}
func columnSum(M mat.Matrix) mat.Matrix {
_, cols := M.Dims()
floatRes := make([]float64, cols)
for i := 0; i < cols; i++ {
floatRes[i] = mat.Sum(getColumnVector(i, M))
}
return mat.NewDense(1, cols, floatRes)
}
func Cost(x *mat64.Dense, y, theta *mat64.Vector) float64 {
//initialize receivers
m, _ := x.Dims()
h := mat64.NewDense(m, 1, make([]float64, m))
squaredErrors := mat64.NewDense(m, 1, make([]float64, m))
//actual calculus
h.Mul(x, theta)
squaredErrors.Apply(func(r, c int, v float64) float64 {
return math.Pow(h.At(r, c)-y.At(r, c), 2)
}, h)
j := mat64.Sum(squaredErrors) * 1.0 / (2.0 * float64(m))
return j
}
func nnlsSubproblem(V, W, Ho *mat64.Dense, tol float64, outer, inner int) (H, G *mat64.Dense, i int, ok bool) {
H = new(mat64.Dense)
H.Clone(Ho)
var WtV, WtW mat64.Dense
WtV.Mul(W.T(), V)
WtW.Mul(W.T(), W)
alpha, beta := 1., 0.1
decFilt := func(r, c int, v float64) float64 {
// decFilt is applied to G, so v = G.At(r, c).
if v < 0 || H.At(r, c) > 0 {
return v
}
return 0
}
G = new(mat64.Dense)
for i = 0; i < outer; i++ {
G.Mul(&WtW, H)
G.Sub(G, &WtV)
G.Apply(decFilt, G)
if mat64.Norm(G, 2) < tol {
break
}
var (
reduce bool
Hp *mat64.Dense
d, dQ mat64.Dense
)
for j := 0; j < inner; j++ {
var Hn mat64.Dense
Hn.Scale(alpha, G)
Hn.Sub(H, &Hn)
Hn.Apply(posFilt, &Hn)
d.Sub(&Hn, H)
dQ.Mul(&WtW, &d)
dQ.MulElem(&dQ, &d)
d.MulElem(G, &d)
sufficient := 0.99*mat64.Sum(&d)+0.5*mat64.Sum(&dQ) < 0
if j == 0 {
reduce = !sufficient
Hp = H
}
if reduce {
if sufficient {
H = &Hn
ok = true
break
} else {
alpha *= beta
}
} else {
if !sufficient || mat64.Equal(Hp, &Hn) {
H = Hp
break
} else {
alpha /= beta
Hp = &Hn
}
}
}
}
return H, G, i, ok
}
// Fit trains the neural network on the given fixed datagrid.
//
// Training stops when the mean-squared error acheived is less
// than the Convergence value, or when back-propagation has occured
// more times than the value set by MaxIterations.
func (m *MultiLayerNet) Fit(X base.FixedDataGrid) {
// Make sure everything's a FloatAttribute
insts := m.convertToFloatInsts(X)
// The size of the first layer is the number of things
// in the revised instances which aren't class Attributes
inputAttrsVec := base.NonClassAttributes(insts)
// The size of the output layer is the number of things
// in the revised instances which are class Attributes
classAttrsVec := insts.AllClassAttributes()
// The total number of layers is input layer + output layer
// plus number of layers specified
totalLayers := 2 + len(m.layers)
// The size is then augmented by the number of nodes
// in the centre
size := len(inputAttrsVec)
size += len(classAttrsVec)
hiddenSize := 0
for _, a := range m.layers {
size += a
hiddenSize += a
}
// Enumerate the Attributes
trainingAttrs := make(map[base.Attribute]int)
classAttrs := make(map[base.Attribute]int)
attrCounter := 0
for i, a := range inputAttrsVec {
attrCounter = i
m.attrs[a] = attrCounter
trainingAttrs[a] = attrCounter
}
m.classAttrOffset = attrCounter + 1
for _, a := range classAttrsVec {
attrCounter++
m.attrs[a] = attrCounter + hiddenSize
classAttrs[a] = attrCounter + hiddenSize
m.classAttrCount++
}
// Create the underlying Network
m.network = NewNetwork(size, len(inputAttrsVec), Sigmoid)
// Initialise inter-hidden layer weights and biases to small random values
layerOffset := len(inputAttrsVec)
for i := 0; i < len(m.layers)-1; i++ {
// Get the size of this layer
thisLayerSize := m.layers[i]
// Next layer size
nextLayerSize := m.layers[i+1]
// For every node in this layer
for j := 1; j <= thisLayerSize; j++ {
// Compute the offset
nodeOffset1 := layerOffset + j
// For every node in the next layer
for k := 1; k <= nextLayerSize; k++ {
// Compute offset
nodeOffset2 := layerOffset + thisLayerSize + k
// Set weight randomly
m.network.SetWeight(nodeOffset1, nodeOffset2, rand.NormFloat64()*0.1)
}
}
layerOffset += thisLayerSize
}
// Initialise biases with each hidden layer
layerOffset = len(inputAttrsVec)
for _, l := range m.layers {
for j := 1; j <= l; j++ {
nodeOffset := layerOffset + j
m.network.SetBias(nodeOffset, rand.NormFloat64()*0.1)
}
layerOffset += l
}
// Initialise biases for output layer
for i := 0; i < len(classAttrsVec); i++ {
nodeOffset := layerOffset + i
m.network.SetBias(nodeOffset, rand.NormFloat64()*0.1)
}
// Connect final hidden layer with the output layer
layerOffset = len(inputAttrsVec)
for i, l := range m.layers {
if i == len(m.layers)-1 {
for j := 1; j <= l; j++ {
nodeOffset1 := layerOffset + j
for k := 1; k <= len(classAttrsVec); k++ {
nodeOffset2 := layerOffset + l + k
m.network.SetWeight(nodeOffset1, nodeOffset2, rand.NormFloat64()*0.1)
}
}
}
layerOffset += l
}
// Connect input layer with first hidden layer (or output layer
for i := 1; i <= len(inputAttrsVec); i++ {
nextLayerLen := 0
if len(m.layers) > 0 {
nextLayerLen = m.layers[0]
} else {
nextLayerLen = len(classAttrsVec)
}
for j := 1; j <= nextLayerLen; j++ {
nodeOffset := len(inputAttrsVec) + j
v := rand.NormFloat64() * 0.1
m.network.SetWeight(i, nodeOffset, v)
}
}
// Create the training activation vector
trainVec := mat64.NewDense(size, 1, make([]float64, size))
// Create the error vector
errVec := mat64.NewDense(size, 1, make([]float64, size))
// Resolve training AttributeSpecs
trainAs := base.ResolveAllAttributes(insts)
// Feed-forward, compute error and update for each training example
// until convergence (what's that)
for iteration := 0; iteration < m.MaxIterations; iteration++ {
totalError := 0.0
maxRow := 0
insts.MapOverRows(trainAs, func(row [][]byte, i int) (bool, error) {
maxRow = i
// Clear vectors
for i := 0; i < size; i++ {
trainVec.Set(i, 0, 0.0)
errVec.Set(i, 0, 0.0)
}
// Build vectors
for i, vb := range row {
v := base.UnpackBytesToFloat(vb)
if attrIndex, ok := trainingAttrs[trainAs[i].GetAttribute()]; ok {
// Add to Activation vector
trainVec.Set(attrIndex, 0, v)
} else if attrIndex, ok := classAttrs[trainAs[i].GetAttribute()]; ok {
// Set to error vector
errVec.Set(attrIndex, 0, v)
} else {
panic("Should be able to find this Attribute!")
}
}
// Activate the network
m.network.Activate(trainVec, totalLayers-1)
// Compute the error
for a := range classAttrs {
cIndex := classAttrs[a]
errVec.Set(cIndex, 0, errVec.At(cIndex, 0)-trainVec.At(cIndex, 0))
}
// Update total error
totalError += math.Abs(mat64.Sum(errVec))
// Back-propagate the error
b := m.network.Error(trainVec, errVec, totalLayers)
// Update the weights
m.network.UpdateWeights(trainVec, b, m.LearningRate)
// Update the biases
m.network.UpdateBias(b, m.LearningRate)
return true, nil
})
totalError /= float64(maxRow)
// If we've converged, no need to carry on
if totalError < m.Convergence {
break
}
}
}