// Batch gradient descent finds the local minimum of a function.
// See http://en.wikipedia.org/wiki/Gradient_descent for more details.
func BatchGradientDescent(x, y, theta *mat64.Dense, alpha float64, epoch int) *mat64.Dense {
m, _ := y.Dims()
for i := 0; i < epoch; i++ {
xFlat := mat64.DenseCopyOf(x)
xFlat.TCopy(xFlat)
temp := mat64.DenseCopyOf(x)
// Calculate our best prediction, given theta
temp.Mul(temp, theta)
// Calculate our error from the real values
temp.Sub(temp, y)
xFlat.Mul(xFlat, temp)
// Temporary hack to get around the fact there is no scalar division in mat64
xFlatRow, _ := xFlat.Dims()
gradient := make([]float64, 0)
for k := 0; k < xFlatRow; k++ {
row := xFlat.RowView(k)
for v := range row {
divd := row[v] / float64(m) * alpha
gradient = append(gradient, divd)
}
}
grows := len(gradient)
grad := mat64.NewDense(grows, 1, gradient)
theta.Sub(theta, grad)
}
return theta
}
func (self *Layer) Update(learningConfiguration LearningConfiguration) {
var deltas mat64.Dense
deltas.Mul(self.Deltas, self.Input)
rows, cols := self.Weight.Dims()
weight := self.Weight.View(0, 0, rows-1, cols).(*mat64.Dense)
if *learningConfiguration.Decay > 0 {
var decay mat64.Dense
decay.Scale(*learningConfiguration.Decay, weight)
deltas.Sub(&deltas, decay.T())
}
deltas.Scale(*learningConfiguration.Rate, &deltas)
weight.Sub(weight, deltas.T())
}
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
}
func (self *Layer) BackwardOutput(values *mat64.Dense,
error_function ErrorFunction) {
// TODO(ariw): ErrorFunction Delta use goes here.
values.Sub(self.Output, values)
self.Deltas.MulElem(values.T(), self.Derivatives)
}