@Override
protected double predict(int u, int j) {
// find a number of similar items
Map<Integer, Double> nns = new HashMap<>();
SparseVector ui = trainMatrix.row(u);
for (int i : ui.getIndex()) {
if (itemCorrsmap.get(j).containsKey(i)) {
nns.put(i, itemCorrsmap.get(j).get(i));
}
}
// for (int i : dv.getIndex()) {
// double sim = dv.get(i);
// //用户u对商品i也购买过
// double rate = trainMatrix.get(u, i);
//
// if (isRankingPred && rate > 0){
// nns.put(i, sim);
// }
// else if (sim > 0 && rate > 0)
// nns.put(i, sim);
// }
// topN similar items
if (knn > 0 && knn < nns.size()) {
List<KeyValPair<Integer>> sorted = Lists.sortMap(nns, true);
List<KeyValPair<Integer>> subset = sorted.subList(0, knn);
nns.clear();
for (KeyValPair<Integer> kv : subset) nns.put(kv.getKey(), kv.getValue());
}
if (nns.size() == 0) return isRankingPred ? 0 : globalMean;
if (isRankingPred) {
// for recommendation task: item ranking
return Stats.sum(nns.values());
} else {
// for recommendation task: rating prediction
double sum = 0, ws = 0;
for (Entry<Integer, Double> en : nns.entrySet()) {
int i = en.getKey();
double sim = en.getValue();
double rate = trainMatrix.get(u, i);
sum += sim * (rate - itemMeans.get(i));
ws += Math.abs(sim);
}
return ws > 0 ? itemMeans.get(j) + sum / ws : globalMean;
}
}
/**
* Do vector operation: {@code a * b^t}
*
* @return the outer product of two vectors
*/
public DenseMatrix outer(DenseVector vec) {
DenseMatrix mat = new DenseMatrix(this.size, vec.size);
for (int i = 0; i < mat.numRows; i++)
for (int j = 0; j < mat.numColumns; j++) mat.set(i, j, get(i) * vec.get(j));
return mat;
}
/**
* Do vector operation: {@code a^t * b}
*
* @return the inner product of two vectors
*/
public double inner(DenseVector vec) {
assert size == vec.size;
double result = 0;
for (int i = 0; i < vec.size; i++) result += get(i) * vec.get(i);
return result;
}
/**
* Given the similarity, it applies the given kernel. This is done either for all users or for all
* items.
*
* @param size The length of user or item vector.
* @param id The identifier of anchor point.
* @param kernelType The type of kernel.
* @param width Kernel width.
* @param isItemFeature return item kernel if yes, return user kernel otherwise.
* @return The kernel-smoothed values for all users or all items.
*/
private DenseVector kernelSmoothing(
int size, int id, int kernelType, double width, boolean isItemFeature) {
DenseVector newFeatureVector = new DenseVector(size);
newFeatureVector.set(id, 1.0);
for (int i = 0; i < size; i++) {
double sim;
if (isItemFeature) {
sim = getItemSimilarity(i, id);
} else {
sim = getUserSimilarity(i, id);
}
newFeatureVector.set(i, KernelSmoothing.kernelize(sim, width, kernelType));
}
return newFeatureVector;
}
/**
* Calculate similarity between two items, based on the global base SVD.
*
* @param idx1 The first item's ID.
* @param idx2 The second item's ID.
* @return The similarity value between two items idx1 and idx2.
*/
private double getItemSimilarity(int idx1, int idx2) {
double sim;
DenseVector i_vec = Q.row(idx1);
DenseVector j_vec = Q.row(idx2);
sim =
1
- 2.0
/ Math.PI
* Math.acos(
i_vec.inner(j_vec)
/ (Math.sqrt(i_vec.inner(i_vec)) * Math.sqrt(j_vec.inner(j_vec))));
if (Double.isNaN(sim)) {
sim = 0.0;
}
return sim;
}
/**
* Calculate similarity between two users, based on the global base SVD.
*
* @param idx1 The first user's ID.
* @param idx2 The second user's ID.
* @return The similarity value between two users idx1 and idx2.
*/
private double getUserSimilarity(int idx1, int idx2) {
double sim;
DenseVector u_vec = P.row(idx1);
DenseVector v_vec = P.row(idx2);
sim =
1
- 2.0
/ Math.PI
* Math.acos(
u_vec.inner(v_vec)
/ (Math.sqrt(u_vec.inner(u_vec)) * Math.sqrt(v_vec.inner(v_vec))));
if (Double.isNaN(sim)) {
sim = 0.0;
}
return sim;
}
@Override
protected void initModel() throws Exception {
itemCorrs = buildCorrs(false);
itemMeans = new DenseVector(numItems);
for (int i = 0; i < numItems; i++) {
SparseVector vs = trainMatrix.column(i);
itemMeans.set(i, vs.getCount() > 0 ? vs.mean() : globalMean);
}
for (int i = 0; i < numItems; i++) {
SparseVector dv = itemCorrs.row(i);
Map<Integer, Double> temp = new HashMap<>();
for (VectorEntry entry : dv) {
temp.put(entry.index(), entry.get());
}
itemCorrsmap.put(i, temp);
}
}
@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;
}
}
@Override
protected void buildModel() throws Exception {
// Initialize hierarchical priors
int beta = 2; // observation noise (precision)
DenseVector mu_u = new DenseVector(numFactors);
DenseVector mu_m = new DenseVector(numFactors);
// parameters of Inv-Whishart distribution
DenseMatrix WI_u = DenseMatrix.eye(numFactors);
int b0_u = 2;
int df_u = numFactors;
DenseVector mu0_u = new DenseVector(numFactors);
DenseMatrix WI_m = DenseMatrix.eye(numFactors);
int b0_m = 2;
int df_m = numFactors;
DenseVector mu0_m = new DenseVector(numFactors);
// initializing Bayesian PMF using MAP solution found by PMF
P = new DenseMatrix(numUsers, numFactors);
Q = new DenseMatrix(numItems, numFactors);
P.init(0, 1);
Q.init(0, 1);
for (int f = 0; f < numFactors; f++) {
mu_u.set(f, P.columnMean(f));
mu_m.set(f, Q.columnMean(f));
}
DenseMatrix alpha_u = P.cov().inv();
DenseMatrix alpha_m = Q.cov().inv();
// Iteration:
DenseVector x_bar = new DenseVector(numFactors);
DenseVector normalRdn = new DenseVector(numFactors);
DenseMatrix S_bar, WI_post, lam;
DenseVector mu_temp;
double df_upost, df_mpost;
int M = numUsers, N = numItems;
for (int iter = 1; iter <= numIters; iter++) {
// Sample from user hyper parameters:
for (int f = 0; f < numFactors; f++) x_bar.set(f, P.columnMean(f));
S_bar = P.cov();
DenseVector mu0_u_x_bar = mu0_u.minus(x_bar);
DenseMatrix e1e2 = mu0_u_x_bar.outer(mu0_u_x_bar).scale(M * b0_u / (b0_u + M + 0.0));
WI_post = WI_u.inv().add(S_bar.scale(M)).add(e1e2);
WI_post = WI_post.inv();
WI_post = WI_post.add(WI_post.transpose()).scale(0.5);
df_upost = df_u + M;
DenseMatrix wishrnd_u = wishart(WI_post, df_upost);
if (wishrnd_u != null) alpha_u = wishrnd_u;
mu_temp = mu0_u.scale(b0_u).add(x_bar.scale(M)).scale(1 / (b0_u + M + 0.0));
lam = alpha_u.scale(b0_u + M).inv().cholesky();
if (lam != null) {
lam = lam.transpose();
for (int f = 0; f < numFactors; f++) normalRdn.set(f, Randoms.gaussian(0, 1));
mu_u = lam.mult(normalRdn).add(mu_temp);
}
// Sample from item hyper parameters:
for (int f = 0; f < numFactors; f++) x_bar.set(f, Q.columnMean(f));
S_bar = Q.cov();
DenseVector mu0_m_x_bar = mu0_m.minus(x_bar);
DenseMatrix e3e4 = mu0_m_x_bar.outer(mu0_m_x_bar).scale(N * b0_m / (b0_m + N + 0.0));
WI_post = WI_m.inv().add(S_bar.scale(N)).add(e3e4);
WI_post = WI_post.inv();
WI_post = WI_post.add(WI_post.transpose()).scale(0.5);
df_mpost = df_m + N;
DenseMatrix wishrnd_m = wishart(WI_post, df_mpost);
if (wishrnd_m != null) alpha_m = wishrnd_m;
mu_temp = mu0_m.scale(b0_m).add(x_bar.scale(N)).scale(1 / (b0_m + N + 0.0));
lam = alpha_m.scale(b0_m + N).inv().cholesky();
if (lam != null) {
lam = lam.transpose();
for (int f = 0; f < numFactors; f++) normalRdn.set(f, Randoms.gaussian(0, 1));
mu_m = lam.mult(normalRdn).add(mu_temp);
}
// Gibbs updates over user and item feature vectors given hyper parameters:
// NOTE: in PREA, only 1 iter for gibbs where in the original Matlab code, 2 iters are used.
for (int gibbs = 0; gibbs < 2; gibbs++) {
// Infer posterior distribution over all user feature vectors
for (int u = 0; u < numUsers; u++) {
// list of items rated by user uu:
SparseVector rv = trainMatrix.row(u);
int count = rv.getCount();
if (count == 0) continue;
// features of items rated by user uu:
DenseMatrix MM = new DenseMatrix(count, numFactors);
DenseVector rr = new DenseVector(count);
int idx = 0;
for (int j : rv.getIndex()) {
rr.set(idx, rv.get(j) - globalMean);
for (int f = 0; f < numFactors; f++) MM.set(idx, f, Q.get(j, f));
idx++;
}
DenseMatrix covar = alpha_u.add((MM.transpose().mult(MM)).scale(beta)).inv();
DenseVector a = MM.transpose().mult(rr).scale(beta);
DenseVector b = alpha_u.mult(mu_u);
DenseVector mean_u = covar.mult(a.add(b));
lam = covar.cholesky();
if (lam != null) {
lam = lam.transpose();
for (int f = 0; f < numFactors; f++) normalRdn.set(f, Randoms.gaussian(0, 1));
DenseVector w1_P1_u = lam.mult(normalRdn).add(mean_u);
for (int f = 0; f < numFactors; f++) P.set(u, f, w1_P1_u.get(f));
}
}
// Infer posterior distribution over all movie feature vectors
for (int j = 0; j < numItems; j++) {
// list of users who rated item ii:
SparseVector jv = trainMatrix.column(j);
int count = jv.getCount();
if (count == 0) continue;
// features of users who rated item ii:
DenseMatrix MM = new DenseMatrix(count, numFactors);
DenseVector rr = new DenseVector(count);
int idx = 0;
for (int u : jv.getIndex()) {
rr.set(idx, jv.get(u) - globalMean);
for (int f = 0; f < numFactors; f++) MM.set(idx, f, P.get(u, f));
idx++;
}
DenseMatrix covar = alpha_m.add((MM.transpose().mult(MM)).scale(beta)).inv();
DenseVector a = MM.transpose().mult(rr).scale(beta);
DenseVector b = alpha_m.mult(mu_m);
DenseVector mean_m = covar.mult(a.add(b));
lam = covar.cholesky();
if (lam != null) {
lam = lam.transpose();
for (int f = 0; f < numFactors; f++) normalRdn.set(f, Randoms.gaussian(0, 1));
DenseVector w1_M1_j = lam.mult(normalRdn).add(mean_m);
for (int f = 0; f < numFactors; f++) Q.set(j, f, w1_M1_j.get(f));
}
}
} // end of gibbs
loss = 0;
for (MatrixEntry me : trainMatrix) {
int u = me.row();
int j = me.column();
double ruj = me.get();
double pred = predict(u, j);
double euj = ruj - pred;
loss += euj * euj;
}
loss *= 0.5;
if (isConverged(iter)) break;
}
}
