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ml_cca.go
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/
ml_cca.go
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package src
import (
//"fmt"
"github.com/gonum/matrix"
"github.com/gonum/matrix/mat64"
"log"
"math"
//"os"
)
func ccaProjectTwoMatrix(X *mat64.Dense, Y *mat64.Dense) (W_x *mat64.Dense, W_y *mat64.Dense) {
var Xsvd, Ysvd, Bsvd mat64.SVD
var uXFull, vXFull, uYFull, vYFull, pBFull mat64.Dense
//init SVD
ok := Xsvd.Factorize(X.T(), matrix.SVDFull)
if !ok {
log.Fatal("SVD for X factorization failed!")
}
ok = Ysvd.Factorize(Y.T(), matrix.SVDFull)
if !ok {
log.Fatal("SVD for Y factorization failed!")
}
uXFull.UFromSVD(&Xsvd)
vXFull.VFromSVD(&Xsvd)
uYFull.UFromSVD(&Ysvd)
vYFull.VFromSVD(&Ysvd)
//ranks and sigma values
nR, nC := X.Caps()
nsX := int(math.Min(float64(nR), float64(nC)))
nR, nC = Y.Caps()
nsY := int(math.Min(float64(nR), float64(nC)))
sValuesFullX := Xsvd.Values(nil)
sValuesX := make([]float64, 0)
for i := 0; i < nsX; i++ {
//0.000001 is the default cut-off for ranks in matlab
if sValuesFullX[i] > 0.000001 {
sValuesX = append(sValuesX, sValuesFullX[i])
}
}
sValuesFullY := Ysvd.Values(nil)
sValuesY := make([]float64, 0)
for i := 0; i < nsY; i++ {
if sValuesFullY[i] > 0.000001 {
sValuesY = append(sValuesY, sValuesFullY[i])
}
}
Xrank := len(sValuesX)
Yrank := len(sValuesY)
//resize matrix according to ranks
a, _ := uXFull.Caps()
uX := uXFull.Slice(0, a, 0, Xrank)
a, _ = vXFull.Caps()
vX := vXFull.Slice(0, a, 0, Xrank)
a, _ = uYFull.Caps()
uY := uYFull.Slice(0, a, 0, Yrank)
a, _ = vYFull.Caps()
vY := vYFull.Slice(0, a, 0, Yrank)
H := mat64.NewDense(0, 0, nil)
H.Mul(vY, uY.T())
//H is correct
//for i := 0; i < 20; i++ {
// fmt.Println(H.RawRowView(i))
//}
sValues := Ysvd.Values(nil)
Y_Sigma := mat64.NewDense(Yrank, Yrank, nil)
Y_Sigma2 := mat64.NewDense(Yrank, Yrank, nil)
for i := 0; i < Yrank; i++ {
Y_Sigma.Set(i, i, sValues[i])
Y_Sigma2.Set(i, i, 1/sValues[i])
}
sValues = Xsvd.Values(nil)
X_Sigma := mat64.NewDense(Xrank, Xrank, nil)
X_Sigma2 := mat64.NewDense(Xrank, 1, nil)
X_Sigma3 := mat64.NewDense(Xrank, Xrank, nil)
X_SigmaB := mat64.NewDense(Xrank, Xrank, nil)
for i := 0; i < Xrank; i++ {
X_Sigma.Set(i, i, sValues[i])
X_Sigma2.Set(i, 0, 1/sValues[i])
X_Sigma3.Set(i, i, 1/sValues[i])
X_SigmaB.Set(i, i, 1.0)
}
//[W, eigenList] =solve_eigen(X_U,X_Sigma,X_V,H,X_reg)
term1 := mat64.NewDense(0, 0, nil)
B := mat64.NewDense(0, 0, nil)
term1.Mul(X_SigmaB, vX.T())
B.Mul(term1, H)
ok = Bsvd.Factorize(B, matrix.SVDFull)
if !ok {
log.Fatal("SVD for B factorization failed!")
}
pBFull.UFromSVD(&Bsvd)
bValuesFull := Bsvd.Values(nil)
Brank := 0
for i := 0; i < len(bValuesFull); i++ {
if bValuesFull[i] > 0.000001 {
Brank += 1
}
}
a, _ = pBFull.Caps()
pB := pBFull.Slice(0, a, 0, Brank)
term2 := mat64.NewDense(0, 0, nil)
W_x = mat64.NewDense(0, 0, nil)
W_y = mat64.NewDense(0, 0, nil)
term2.Mul(X_Sigma3, pB)
W_x.Mul(uX, term2)
//W_y after solve eigen
term3 := mat64.NewDense(0, 0, nil)
term4 := mat64.NewDense(0, 0, nil)
term5 := mat64.NewDense(0, 0, nil)
term3.Mul(uY, Y_Sigma2)
term4.Mul(term3, vY.T())
//was not Transposed for now
term5.Mul(term4, X)
W_y.Mul(term5, W_x)
//normalize W_y
m, n := W_y.Caps()
nFactor := make([]float64, n)
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
nFactor[j] = nFactor[j] + W_y.At(i, j)*W_y.At(i, j)
}
}
for j := 0; j < n; j++ {
nFactor[j] = math.Sqrt(nFactor[j])
}
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
W_y.Set(i, j, W_y.At(i, j)/nFactor[j])
}
}
return W_x, W_y
}
func ccaProject(X *mat64.Dense, Y *mat64.Dense) (W_y *mat64.Dense) {
var Xsvd, Ysvd, Bsvd mat64.SVD
var uXFull, vXFull, uYFull, vYFull, pBFull mat64.Dense
Yreg := 0.5
//init SVD
ok := Xsvd.Factorize(X.T(), matrix.SVDThin)
if !ok {
log.Fatal("SVD for X factorization failed!")
}
ok = Ysvd.Factorize(Y.T(), matrix.SVDThin)
if !ok {
log.Fatal("SVD for Y factorization failed!")
}
uXFull.UFromSVD(&Xsvd)
vXFull.VFromSVD(&Xsvd)
uYFull.UFromSVD(&Ysvd)
vYFull.VFromSVD(&Ysvd)
//ranks and sigma values
nR, nC := X.Caps()
nsX := int(math.Min(float64(nR), float64(nC)))
nR, nC = Y.Caps()
nsY := int(math.Min(float64(nR), float64(nC)))
sValuesFullX := Xsvd.Values(nil)
sValuesX := make([]float64, 0)
for i := 0; i < nsX; i++ {
//0.000001 is the default cut-off for ranks in matlab
if sValuesFullX[i] > 0.000001 {
sValuesX = append(sValuesX, sValuesFullX[i])
}
}
sValuesFullY := Ysvd.Values(nil)
sValuesY := make([]float64, 0)
for i := 0; i < nsY; i++ {
if sValuesFullY[i] > 0.000001 {
sValuesY = append(sValuesY, sValuesFullY[i])
}
}
Xrank := len(sValuesX)
Yrank := len(sValuesY)
//resize matrix according to ranks
a, _ := uXFull.Caps()
uX := uXFull.Slice(0, a, 0, Xrank)
a, _ = vXFull.Caps()
vX := vXFull.Slice(0, a, 0, Xrank)
a, _ = uYFull.Caps()
uY := uYFull.Slice(0, a, 0, Yrank)
a, _ = vYFull.Caps()
//fmt.Println(a, b, Yrank)
vY := vYFull.Slice(0, a, 0, Yrank)
H := mat64.NewDense(0, 0, nil)
H.Mul(vX, uX.T())
sValues := Ysvd.Values(nil)
Y_Sigma := mat64.NewDense(Yrank, Yrank, nil)
Y_SigmaReg := mat64.NewDense(Yrank, Yrank, nil)
Y_SigmaRegInv := mat64.NewDense(Yrank, Yrank, nil)
Y_SigmaB := mat64.NewDense(Yrank, Yrank, nil)
for i := 0; i < Yrank; i++ {
Y_Sigma.Set(i, i, sValues[i])
Y_SigmaReg.Set(i, i, sValues[i]*sValues[i]+Yreg)
Y_SigmaRegInv.Set(i, i, 1/(sValues[i]*sValues[i]+Yreg))
Y_SigmaB.Set(i, i, sValues[i]/Y_SigmaRegInv.At(i, i))
}
sValues = Xsvd.Values(nil)
X_Sigma := mat64.NewDense(Xrank, Xrank, nil)
X_Sigma2 := mat64.NewDense(Xrank, 1, nil)
for i := 0; i < Xrank; i++ {
X_Sigma.Set(i, i, sValues[i])
X_Sigma2.Set(i, 0, 1/sValues[i])
}
term1 := mat64.NewDense(0, 0, nil)
B := mat64.NewDense(0, 0, nil)
term1.Mul(Y_SigmaB, vY.T())
B.Mul(term1, H)
ok = Bsvd.Factorize(B, matrix.SVDThin)
if !ok {
log.Fatal("SVD for B factorization failed!")
}
pBFull.UFromSVD(&Bsvd)
bValuesFull := Bsvd.Values(nil)
Brank := 0
for i := 0; i < len(bValuesFull); i++ {
if bValuesFull[i] > 0.000001 {
Brank += 1
}
}
a, _ = pBFull.Caps()
pB := pBFull.Slice(0, a, 0, Brank)
term2 := mat64.NewDense(0, 0, nil)
W_y = mat64.NewDense(0, 0, nil)
term2.Mul(Y_SigmaRegInv, pB)
W_y.Mul(uY, term2)
return W_y
}