// 根据正则化方法计算偏导数向量需要添加正则化项
func ComputeRegularization(weights *util.Matrix, options OptimizerOptions) *util.Matrix {
reg := weights.Populate()
if options.RegularizationScheme == 1 {
// L-1正则化
for iLabel := 0; iLabel < weights.NumLabels(); iLabel++ {
for _, k := range weights.GetValues(iLabel).Keys() {
if weights.Get(iLabel, k) > 0 {
reg.Set(iLabel, k, options.RegularizationFactor)
} else {
reg.Set(iLabel, k, -options.RegularizationFactor)
}
}
}
} else if options.RegularizationScheme == 2 {
// L-2正则化
for iLabel := 0; iLabel < weights.NumLabels(); iLabel++ {
for _, k := range weights.GetValues(iLabel).Keys() {
reg.Set(iLabel, k, options.RegularizationFactor*float64(2)*weights.Get(iLabel, k))
}
}
}
return reg
}
// 计算 z = 1 + sum(exp(sum(w_i * x_i)))
//
// 在temp中保存 exp(sum(w_i * x_i))
func ComputeZ(weights *util.Matrix, features *util.Vector, label int, temp *util.Matrix) float64 {
result := float64(1.0)
numLabels := weights.NumLabels() + 1
for iLabel := 1; iLabel < numLabels; iLabel++ {
exp := math.Exp(util.VecDotProduct(features, weights.GetValues(iLabel-1)))
result += exp
tempVec := temp.GetValues(iLabel - 1)
if tempVec.IsSparse() {
for _, k := range features.Keys() {
tempVec.Set(k, exp)
}
} else {
tempVec.SetAll(exp)
}
}
return result
}
func MaxEntComputeInstanceDerivative(
weights *util.Matrix, instance *data.Instance, instanceDerivative *util.Matrix) {
// 定义偏导和特征向量
features := instance.Features
// 得到维度信息
numLabels := weights.NumLabels() + 1
// 计算 z = 1 + exp(sum(w_i * x_i))
label := instance.Output.Label
z := ComputeZ(weights, features, label, instanceDerivative)
inverseZ := float64(1) / z
for iLabel := 1; iLabel < numLabels; iLabel++ {
vec := instanceDerivative.GetValues(iLabel - 1)
if label == 0 || label != iLabel {
vec.Multiply(inverseZ, 0, features)
} else {
vec.Multiply(inverseZ, -1, features)
}
}
}