/** Why buildingModel2 that follows the paper instructions does not work? */
protected void buildModel2() {
for (int iter = 1; iter <= numIters; iter++) {
// Step 1: update W by fixing H
DenseMatrix trH = H.transpose();
// V * trH
DenseMatrix V_trH = DenseMatrix.mult(V, trH);
// W * H * trH
DenseMatrix W_H_trH = W.mult(H.mult(trH));
// update: W_ij = W_ij * (V_trH)_ij / (W_H_trH)_ij
for (int i = 0; i < W.numRows(); i++)
for (int j = 0; j < W.numColumns(); j++) {
double denorm = W_H_trH.get(i, j) + 1e-9;
W.set(i, j, W.get(i, j) * (V_trH.get(i, j) / denorm));
}
// Step 2: update H by fixing W
DenseMatrix trW = W.transpose();
// trW * V
DenseMatrix trW_V = trW.mult(V);
// trW * W * H
DenseMatrix trW_W_H = trW.mult(W).mult(H);
// update: H_ij = H_ij * (trW_V)_ij / (trW_W_H)_ij
for (int i = 0; i < H.numRows(); i++)
for (int j = 0; j < H.numColumns(); j++) {
double denorm = trW_W_H.get(i, j) + 1e-9;
H.set(i, j, H.get(i, j) * (trW_V.get(i, j) / denorm));
}
// compute errors
loss = 0;
errs = 0;
for (MatrixEntry me : V) {
int u = me.row();
int j = me.column();
double ruj = me.get();
if (ruj > 0) {
double pred = predict(u, j);
double euj = pred - ruj;
errs += euj * euj;
loss += euj * euj;
}
}
errs *= 0.5;
loss *= 0.5;
if (isConverged(iter)) break;
}
}
/**
* Randomly sample a matrix from Wishart Distribution with the given parameters.
*
* @param scale scale parameter for Wishart Distribution.
* @param df degree of freedom for Wishart Distribution.
* @return the sample randomly drawn from the given distribution.
*/
protected DenseMatrix wishart(DenseMatrix scale, double df) {
DenseMatrix A = scale.cholesky();
if (A == null) return null;
int p = scale.numRows();
DenseMatrix z = new DenseMatrix(p, p);
for (int i = 0; i < p; i++) {
for (int j = 0; j < p; j++) {
z.set(i, j, Randoms.gaussian(0, 1));
}
}
SparseVector y = new SparseVector(p);
for (int i = 0; i < p; i++) y.set(i, Randoms.gamma((df - (i + 1)) / 2, 2));
DenseMatrix B = new DenseMatrix(p, p);
B.set(0, 0, y.get(0));
if (p > 1) {
// rest of diagonal:
for (int j = 1; j < p; j++) {
SparseVector zz = new SparseVector(j);
for (int k = 0; k < j; k++) zz.set(k, z.get(k, j));
B.set(j, j, y.get(j) + zz.inner(zz));
}
// first row and column:
for (int j = 1; j < p; j++) {
B.set(0, j, z.get(0, j) * Math.sqrt(y.get(0)));
B.set(j, 0, B.get(0, j)); // mirror
}
}
if (p > 2) {
for (int j = 2; j < p; j++) {
for (int i = 1; i <= j - 1; i++) {
SparseVector zki = new SparseVector(i);
SparseVector zkj = new SparseVector(i);
for (int k = 0; k <= i - 1; k++) {
zki.set(k, z.get(k, i));
zkj.set(k, z.get(k, j));
}
B.set(i, j, z.get(i, j) * Math.sqrt(y.get(i)) + zki.inner(zkj));
B.set(j, i, B.get(i, j)); // mirror
}
}
}
return A.transpose().mult(B).mult(A);
}
@Override
protected void buildModel() throws Exception {
for (int iter = 1; iter <= numIters; iter++) {
// update W by fixing H
for (int u = 0; u < W.numRows(); u++) {
SparseVector uv = V.row(u);
if (uv.getCount() > 0) {
SparseVector euv = new SparseVector(V.numColumns());
for (int j : uv.getIndex()) euv.set(j, predict(u, j));
for (int f = 0; f < W.numColumns(); f++) {
DenseVector fv = H.row(f, false);
double real = fv.inner(uv);
double estm = fv.inner(euv) + 1e-9;
W.set(u, f, W.get(u, f) * (real / estm));
}
}
}
// update H by fixing W
DenseMatrix trW = W.transpose();
for (int j = 0; j < H.numColumns(); j++) {
SparseVector jv = V.column(j);
if (jv.getCount() > 0) {
SparseVector ejv = new SparseVector(V.numRows());
for (int u : jv.getIndex()) ejv.set(u, predict(u, j));
for (int f = 0; f < H.numRows(); f++) {
DenseVector fv = trW.row(f, false);
double real = fv.inner(jv);
double estm = fv.inner(ejv) + 1e-9;
H.set(f, j, H.get(f, j) * (real / estm));
}
}
}
// compute errors
loss = 0;
errs = 0;
for (MatrixEntry me : V) {
int u = me.row();
int j = me.column();
double ruj = me.get();
if (ruj > 0) {
double euj = predict(u, j) - ruj;
errs += euj * euj;
loss += euj * euj;
}
}
errs *= 0.5;
loss *= 0.5;
if (isConverged(iter)) break;
}
}
