/**
* 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 static double getItemSimilarity(int idx1, int idx2) {
double sim;
if (idx1 <= idx2) {
sim = itemSimilarity.getValue(idx1, idx2);
} else {
sim = itemSimilarity.getValue(idx2, idx1);
}
if (sim == 0.0) {
SparseVector i_vec = baseline.getV().getColRef(idx1);
SparseVector j_vec = baseline.getV().getColRef(idx2);
sim =
1 - 2.0 / Math.PI * Math.acos(i_vec.innerProduct(j_vec) / (i_vec.norm() * j_vec.norm()));
if (Double.isNaN(sim)) {
sim = 0.0;
}
if (idx1 <= idx2) {
itemSimilarity.setValue(idx1, idx2, sim);
} else {
itemSimilarity.setValue(idx2, idx1, sim);
}
}
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 static double getUserSimilarity(int idx1, int idx2) {
double sim;
if (idx1 <= idx2) {
sim = userSimilarity.getValue(idx1, idx2);
} else {
sim = userSimilarity.getValue(idx2, idx1);
}
if (sim == 0.0) {
SparseVector u_vec = baseline.getU().getRowRef(idx1);
SparseVector v_vec = baseline.getU().getRowRef(idx2);
sim =
1 - 2.0 / Math.PI * Math.acos(u_vec.innerProduct(v_vec) / (u_vec.norm() * v_vec.norm()));
if (Double.isNaN(sim)) {
sim = 0.0;
}
if (idx1 <= idx2) {
userSimilarity.setValue(idx1, idx2, sim);
} else {
userSimilarity.setValue(idx2, idx1, sim);
}
}
return sim;
}
/** Items in validationMatrix are moved to original rateMatrix. */
private void restoreValidationSet(SparseMatrix rateMatrix) {
for (int i = 1; i <= userCount; i++) {
SparseVector row = validationMatrix.getRowRef(i);
int[] itemList = row.indexList();
if (itemList != null) {
for (int j : itemList) {
rateMatrix.setValue(i, j, validationMatrix.getValue(i, j));
}
}
}
}
/**
* Items which will be used for validation purpose are moved from rateMatrix to validationMatrix.
*
* @param validationRatio Proportion of dataset, using for validation purpose.
*/
private void makeValidationSet(SparseMatrix rateMatrix, double validationRatio) {
validationMatrix = new SparseMatrix(userCount + 1, itemCount + 1);
int validationCount = (int) (rateMatrix.itemCount() * validationRatio);
while (validationCount > 0) {
int index = (int) (Math.random() * userCount) + 1;
SparseVector row = rateMatrix.getRowRef(index);
int[] itemList = row.indexList();
if (itemList != null && itemList.length > 5) {
int index2 = (int) (Math.random() * itemList.length);
validationMatrix.setValue(
index, itemList[index2], rateMatrix.getValue(index, itemList[index2]));
rateMatrix.setValue(index, itemList[index2], 0.0);
validationCount--;
}
}
}
/**
* Evaluate the designated algorithm with the given test data.
*
* @param testMatrix The rating matrix with test data.
* @return The result of evaluation, such as MAE, RMSE, and rank-score.
*/
@Override
public EvaluationMetrics evaluate(SparseMatrix testMatrix) {
SparseMatrix predicted = new SparseMatrix(userCount + 1, itemCount + 1);
for (int u = 1; u <= userCount; u++) {
SparseVector items = testMatrix.getRowRef(u);
int[] itemIndexList = items.indexList();
if (itemIndexList != null) {
for (int i : itemIndexList) {
double prediction = 0.0;
for (int l = 0; l < modelMax; l++) {
prediction +=
localUserFeatures[l].getRow(u).innerProduct(localItemFeatures[l].getCol(i))
* KernelSmoothing.kernelize(
getUserSimilarity(anchorUser[l], u), kernelWidth, kernelType)
* KernelSmoothing.kernelize(
getItemSimilarity(anchorItem[l], i), kernelWidth, kernelType)
/ weightSum[u][i];
}
if (Double.isNaN(prediction) || prediction == 0.0) {
prediction = (maxValue + minValue) / 2;
}
if (prediction < minValue) {
prediction = minValue;
} else if (prediction > maxValue) {
prediction = maxValue;
}
predicted.setValue(u, i, prediction);
}
}
}
return new EvaluationMetrics(testMatrix, predicted, maxValue, minValue);
}
/**
* Build a model with given training set.
*
* @param rateMatrix The rating matrix with train data.
*/
@Override
public void buildModel(SparseMatrix rateMatrix) {
makeValidationSet(rateMatrix, validationRatio);
// Preparing data structures:
localUserFeatures = new SparseMatrix[modelMax];
localItemFeatures = new SparseMatrix[modelMax];
anchorUser = new int[modelMax];
anchorItem = new int[modelMax];
for (int l = 0; l < modelMax; l++) {
boolean done = false;
while (!done) {
int u_t = (int) Math.floor(Math.random() * userCount) + 1;
int[] itemList = rateMatrix.getRow(u_t).indexList();
if (itemList != null) {
int idx = (int) Math.floor(Math.random() * itemList.length);
int i_t = itemList[idx];
anchorUser[l] = u_t;
anchorItem[l] = i_t;
done = true;
}
}
}
// Pre-calculating similarity:
userSimilarity = new SparseMatrix(userCount + 1, userCount + 1);
itemSimilarity = new SparseMatrix(itemCount + 1, itemCount + 1);
weightSum = new double[userCount + 1][itemCount + 1];
for (int u = 1; u <= userCount; u++) {
for (int i = 1; i <= itemCount; i++) {
for (int l = 0; l < modelMax; l++) {
weightSum[u][i] +=
KernelSmoothing.kernelize(
getUserSimilarity(anchorUser[l], u), kernelWidth, kernelType)
* KernelSmoothing.kernelize(
getItemSimilarity(anchorItem[l], i), kernelWidth, kernelType);
}
}
}
// Initialize local models:
for (int l = 0; l < modelMax; l++) {
localUserFeatures[l] = new SparseMatrix(userCount + 1, featureCount);
localItemFeatures[l] = new SparseMatrix(featureCount, itemCount + 1);
for (int u = 1; u <= userCount; u++) {
for (int r = 0; r < featureCount; r++) {
double rdm = Math.random();
localUserFeatures[l].setValue(u, r, rdm);
}
}
for (int i = 1; i <= itemCount; i++) {
for (int r = 0; r < featureCount; r++) {
double rdm = Math.random();
localItemFeatures[l].setValue(r, i, rdm);
}
}
}
// Learn by gradient descent:
int round = 0;
double prevErr = 99999;
double currErr = 9999;
while (Math.abs(prevErr - currErr) > 0.001 && round < maxIter) {
for (int u = 1; u <= userCount; u++) {
SparseVector items = rateMatrix.getRowRef(u);
int[] itemIndexList = items.indexList();
if (itemIndexList != null) {
for (int i : itemIndexList) {
// current estimation:
double RuiEst = 0.0;
for (int l = 0; l < modelMax; l++) {
RuiEst +=
localUserFeatures[l].getRow(u).innerProduct(localItemFeatures[l].getCol(i))
* KernelSmoothing.kernelize(
getUserSimilarity(anchorUser[l], u), kernelWidth, kernelType)
* KernelSmoothing.kernelize(
getItemSimilarity(anchorItem[l], i), kernelWidth, kernelType)
/ weightSum[u][i];
}
double RuiReal = rateMatrix.getValue(u, i);
double err = RuiReal - RuiEst;
// parameter update:
for (int l = 0; l < modelMax; l++) {
double weight =
KernelSmoothing.kernelize(
getUserSimilarity(anchorUser[l], u), kernelWidth, kernelType)
* KernelSmoothing.kernelize(
getItemSimilarity(anchorItem[l], i), kernelWidth, kernelType)
/ weightSum[u][i];
for (int r = 0; r < featureCount; r++) {
double Fus = localUserFeatures[l].getValue(u, r);
double Gis = localItemFeatures[l].getValue(r, i);
localUserFeatures[l].setValue(
u, r, Fus + learningRate * (err * Gis * weight - regularizer * Fus));
if (Double.isNaN(Fus + learningRate * (err * Gis * weight - regularizer * Fus))) {
// System.out.println("a");
}
localItemFeatures[l].setValue(
r, i, Gis + learningRate * (err * Fus * weight - regularizer * Gis));
if (Double.isNaN(Gis + learningRate * (err * Fus * weight - regularizer * Gis))) {
// System.out.println("b");
}
}
}
}
}
}
// Intermediate evaluation for trend graphing:
SparseMatrix predicted = new SparseMatrix(userCount + 1, itemCount + 1);
for (int u = 1; u <= userCount; u++) {
SparseVector items = validationMatrix.getRowRef(u);
int[] itemIndexList = items.indexList();
if (itemIndexList != null) {
for (int i : itemIndexList) {
double prediction = 0.0;
for (int l = 0; l < modelMax; l++) {
prediction +=
localUserFeatures[l].getRow(u).innerProduct(localItemFeatures[l].getCol(i))
* KernelSmoothing.kernelize(
getUserSimilarity(anchorUser[l], u), kernelWidth, kernelType)
* KernelSmoothing.kernelize(
getItemSimilarity(anchorItem[l], i), kernelWidth, kernelType)
/ weightSum[u][i];
}
if (Double.isNaN(prediction) || prediction == 0.0) {
prediction = (maxValue + minValue) / 2;
}
if (prediction < minValue) {
prediction = minValue;
} else if (prediction > maxValue) {
prediction = maxValue;
}
predicted.setValue(u, i, prediction);
}
}
}
EvaluationMetrics e = new EvaluationMetrics(validationMatrix, predicted, maxValue, minValue);
prevErr = currErr;
currErr = e.getRMSE();
round++;
// Show progress:
if (showProgress) {
System.out.println(round + "\t" + e.printOneLine());
}
}
restoreValidationSet(rateMatrix);
}