@Test
public void testInclinedPlane() throws IOException {
DoubleMatrix1D normal = new DenseDoubleMatrix1D(3);
normal.assign(new double[] {.0, .0, 1.0});
InclinedPlane3D inclinedPlane = new InclinedPlane3D();
inclinedPlane.setRandomGenerator(new MersenneTwister(123456789));
inclinedPlane.setNormal(normal);
inclinedPlane.setBounds(new Rectangle(-5, -5, 10, 10));
inclinedPlane.setNoiseStd(0.5);
DoubleMatrix2D data = inclinedPlane.generate(10);
SVDPCA pca = new SVDPCA(data);
System.out.println("Eigenvalues:");
System.out.println(pca.getEigenvalues());
System.out.println("Eigenvectors:");
System.out.println(pca.getEigenvectors());
System.out.println("Meanvector:");
System.out.println(pca.getMean());
// Recalculate the input from a truncated SVD, first calculate the mean
DoubleMatrix1D mean = new SparseDoubleMatrix1D(3);
for (int i = 0; i < data.rows(); ++i) {
mean.assign(data.viewRow(i), Functions.plus);
}
mean.assign(Functions.div(data.rows()));
// Truncate the SVD and calculate the coefficient matrix
DenseDoubleMatrix2D coefficients = new DenseDoubleMatrix2D(data.rows(), 2);
DoubleMatrix2D centeredInput = data.copy();
for (int i = 0; i < data.rows(); ++i) {
centeredInput.viewRow(i).assign(mean, Functions.minus);
}
centeredInput.zMult(
pca.getEigenvectors().viewPart(0, 0, 2, 3), coefficients, 1, 0, false, true);
// Reconstruct the data from the lower dimensional information
DoubleMatrix2D reconstruction = data.copy();
for (int i = 0; i < reconstruction.rows(); ++i) {
reconstruction.viewRow(i).assign(mean);
}
coefficients.zMult(
pca.getEigenvectors().viewPart(0, 0, 2, 3), reconstruction, 1, 1, false, false);
// Output to file (can be read by GNU Plot)
String fileName = "inclined-plane-svd-pca.dat";
String packagePath = this.getClass().getPackage().getName().replaceAll("\\.", "/");
File outputFile = new File("src/test/resources/" + packagePath + "/" + fileName);
PrintWriter writer = new PrintWriter(outputFile);
writer.write(data.toString());
writer.close();
}
private double multiLL(DoubleMatrix2D coeffs, Node dep, List<Node> indep) {
DoubleMatrix2D indepData =
factory2D.make(internalData.subsetColumns(indep).getDoubleData().toArray());
List<Node> depList = new ArrayList<>();
depList.add(dep);
DoubleMatrix2D depData =
factory2D.make(internalData.subsetColumns(depList).getDoubleData().toArray());
int N = indepData.rows();
DoubleMatrix2D probs =
Algebra.DEFAULT.mult(factory2D.appendColumns(factory2D.make(N, 1, 1.0), indepData), coeffs);
probs =
factory2D
.appendColumns(factory2D.make(indepData.rows(), 1, 1.0), probs)
.assign(Functions.exp);
double ll = 0;
for (int i = 0; i < N; i++) {
DoubleMatrix1D curRow = probs.viewRow(i);
curRow.assign(Functions.div(curRow.zSum()));
ll += Math.log(curRow.get((int) depData.get(i, 0)));
}
return ll;
}
static boolean computeLogMi(
FeatureGenerator featureGen,
double lambda[],
DoubleMatrix2D Mi_YY,
DoubleMatrix1D Ri_Y,
boolean takeExp,
boolean reuseM,
boolean initMDone) {
if (reuseM && initMDone) {
Mi_YY = null;
} else initMDone = false;
if (Mi_YY != null) Mi_YY.assign(0);
Ri_Y.assign(0);
while (featureGen.hasNext()) {
Feature feature = featureGen.next();
int f = feature.index();
int yp = feature.y();
int yprev = feature.yprev();
float val = feature.value();
// System.out.println(feature.toString());
if (yprev < 0) {
// this is a single state feature.
double oldVal = Ri_Y.getQuick(yp);
Ri_Y.setQuick(yp, oldVal + lambda[f] * val);
} else if (Mi_YY != null) {
Mi_YY.setQuick(yprev, yp, Mi_YY.getQuick(yprev, yp) + lambda[f] * val);
initMDone = true;
}
}
if (takeExp) {
for (int r = Ri_Y.size() - 1; r >= 0; r--) {
Ri_Y.setQuick(r, expE(Ri_Y.getQuick(r)));
if (Mi_YY != null)
for (int c = Mi_YY.columns() - 1; c >= 0; c--) {
Mi_YY.setQuick(r, c, expE(Mi_YY.getQuick(r, c)));
}
}
}
return initMDone;
}
/**
* Predict the value of an instance.
*
* @param x instance
* @return value of prediction
*/
public double prediction(I x) {
double pred = b;
DoubleMatrix1D xm = new DenseDoubleMatrix1D(m.columns());
pred +=
x.operate(
(i, xi) -> {
double wi = w.getQuick(i);
DoubleMatrix1D mi = m.viewRow(i);
xm.assign(mi, (r, s) -> r + xi * s);
return xi * wi - 0.5 * xi * xi * mi.zDotProduct(mi);
},
(v1, v2) -> v1 + v2);
pred += 0.5 * xm.zDotProduct(xm);
return pred;
}
/**
* Returns the best cut of a graph w.r.t. the degree of dissimilarity between points of different
* partitions and the degree of similarity between points of the same partition.
*
* @param W the weight matrix of the graph
* @return an array of two elements, each of these contains the points of a partition
*/
protected static int[][] bestCut(DoubleMatrix2D W) {
int n = W.columns();
// Builds the diagonal matrices D and D^(-1/2) (represented as their diagonals)
DoubleMatrix1D d = DoubleFactory1D.dense.make(n);
DoubleMatrix1D d_minus_1_2 = DoubleFactory1D.dense.make(n);
for (int i = 0; i < n; i++) {
double d_i = W.viewRow(i).zSum();
d.set(i, d_i);
d_minus_1_2.set(i, 1 / Math.sqrt(d_i));
}
DoubleMatrix2D D = DoubleFactory2D.sparse.diagonal(d);
// System.out.println("DoubleMatrix2D :\n"+D.toString());
DoubleMatrix2D X = D.copy();
// System.out.println("DoubleMatrix2D copy :\n"+X.toString());
// X = D^(-1/2) * (D - W) * D^(-1/2)
X.assign(W, Functions.minus);
// System.out.println("DoubleMatrix2D X: (D-W) :\n"+X.toString());
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
X.set(i, j, X.get(i, j) * d_minus_1_2.get(i) * d_minus_1_2.get(j));
// Computes the eigenvalues and the eigenvectors of X
EigenvalueDecomposition e = new EigenvalueDecomposition(X);
DoubleMatrix1D lambda = e.getRealEigenvalues();
// Selects the eigenvector z_2 associated with the second smallest eigenvalue
// Creates a map that contains the pairs <index, eigenvalue>
AbstractIntDoubleMap map = new OpenIntDoubleHashMap(n);
for (int i = 0; i < n; i++) map.put(i, Math.abs(lambda.get(i)));
IntArrayList list = new IntArrayList();
// Sorts the map on the value
map.keysSortedByValue(list);
// Gets the index of the second smallest element
int i_2 = list.get(1);
// y_2 = D^(-1/2) * z_2
DoubleMatrix1D y_2 = e.getV().viewColumn(i_2).copy();
y_2.assign(d_minus_1_2, Functions.mult);
// Creates a map that contains the pairs <i, y_2[i]>
map.clear();
for (int i = 0; i < n; i++) map.put(i, y_2.get(i));
// Sorts the map on the value
map.keysSortedByValue(list);
// Search the element in the map previuosly ordered that minimizes the cut
// of the partition
double best_cut = Double.POSITIVE_INFINITY;
int[][] partition = new int[2][];
// The array v contains all the elements of the graph ordered by their
// projection on vector y_2
int[] v = list.elements();
// For each admissible splitting point i
for (int i = 1; i < n; i++) {
// The array a contains all the elements that have a projection on vector
// y_2 less or equal to the one of i-th element
// The array b contains the remaining elements
int[] a = new int[i];
int[] b = new int[n - i];
System.arraycopy(v, 0, a, 0, i);
System.arraycopy(v, i, b, 0, n - i);
double cut = Ncut(W, a, b, v);
if (cut < best_cut) {
best_cut = cut;
partition[0] = a;
partition[1] = b;
}
}
// System.out.println("Partition:");
// UtilsJS.printMatrix(partition);
return partition;
}
/**
* Returns the Euclidean distance between two points. It is used to compute the similarity degree
* of these ones.
*
* @param x the first point
* @param y the second point
* @return the Euclidean distance between the points
*/
protected static double distnorm2(DoubleMatrix1D x, DoubleMatrix1D y) {
DoubleMatrix1D z = x.copy();
z.assign(y, Functions.minus);
return z.zDotProduct(z);
}
public void compute() {
alpha_Y.assign(1);
initMDone = false;
boolean doScaling = params.doScaling;
if ((beta_Y == null) || (beta_Y.length < dataSeq.length())) {
beta_Y = new DenseDoubleMatrix1D[2 * dataSeq.length()];
for (int i = 0; i < beta_Y.length; i++) beta_Y[i] = new DenseDoubleMatrix1D(numY);
scale = new double[2 * dataSeq.length()];
scale[dataSeq.length() - 1] = (doScaling) ? numY : 1;
beta_Y[dataSeq.length() - 1].assign(1.0 / scale[dataSeq.length() - 1]);
}
beta.add(beta_Y[dataSeq.length() - 1]);
// System.out.println("Beta "+beta_Y[3].toString());
for (int i = dataSeq.length() - 1; i > 0; i--) {
if (params.debugLvl > 2) {
Util.printDbg("Features fired");
// featureGenerator.startScanFeaturesAt(dataSeq, i);
// while (featureGenerator.hasNext()) {
// Feature feature = featureGenerator.next();
// Util.printDbg(feature.toString());
// }
}
// compute the Mi matrix
// System.out.println("MI previous" +Mi_YY.toString());
initMDone =
Trainer.computeLogMi(
featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, true, reuseM, initMDone);
// System.out.println("MI "+Mi_YY.toString());
tmp_Y.assign(beta_Y[i]);
tmp_Y.assign(Ri_Y, multFunc);
RobustMath.Mult(Mi_YY, tmp_Y, beta_Y[i - 1], 1, 0, false, edgeGen);
// need to scale the beta-s to avoid overflow
scale[i - 1] = doScaling ? beta_Y[i - 1].zSum() : 1;
if ((scale[i - 1] < 1) && (scale[i - 1] > -1)) scale[i - 1] = 1;
constMultiplier.multiplicator = 1.0 / scale[i - 1];
beta_Y[i - 1].assign(constMultiplier);
// System.out.println("Beta "+beta_Y[i - 1].toString() + " ");
beta.add(beta_Y[i - 1]);
}
double thisSeqLogli = 0;
System.out.println("\n");
// Mi_YY.assign(0);
alpha_temp = new DenseDoubleMatrix1D[2 * dataSeq.length()];
for (int i = 0; i < dataSeq.length(); i++) alpha_temp[i] = new DenseDoubleMatrix1D(numY);
for (int i = 0; i < dataSeq.length(); i++) {
// compute the Mi matrix
//
initMDone =
Trainer.computeLogMi(
featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, true, reuseM, initMDone);
// System.out.println("MI: " + Mi_YY.toString());
// find features that fire at this position..
featureGenerator.startScanFeaturesAt(dataSeq, i);
if (i > 0) {
tmp_Y.assign(alpha_Y);
RobustMath.Mult(Mi_YY, tmp_Y, newAlpha_Y, 1, 0, true, edgeGen);
// Mi_YY.zMult(tmp_Y, newAlpha_Y,1,0,true);
newAlpha_Y.assign(Ri_Y, multFunc);
} else {
newAlpha_Y.assign(Ri_Y);
}
while (featureGenerator.hasNext()) {
Feature feature = featureGenerator.next();
int f = feature.index();
int yp = feature.y();
int yprev = feature.yprev();
float val = feature.value();
if ((dataSeq.y(i) == yp)
&& (((i - 1 >= 0) && (yprev == dataSeq.y(i - 1))) || (yprev < 0))) {
thisSeqLogli += val * lambda[f];
}
}
alpha_Y.assign(newAlpha_Y);
// now scale the alpha-s to avoid overflow problems.
constMultiplier.multiplicator = 1.0 / scale[i];
alpha_Y.assign(constMultiplier);
alpha_temp[i].assign(newAlpha_Y);
alpha_temp[i].assign(constMultiplier);
// System.out.println("ALpha "+alpha_Y.toString());
alpha.add(alpha_temp[i]);
if (params.debugLvl > 2) {
System.out.println("Alpha-i " + alpha_Y.toString());
System.out.println("Ri " + Ri_Y.toString());
System.out.println("Mi " + Mi_YY.toString());
System.out.println("Beta-i " + beta_Y[i].toString());
}
}
Zx = alpha_Y.zSum();
System.out.println("Zx: " + Zx);
} /* end of computeBeta */
protected double computeFunctionGradientLL(double lambda[], double grad[]) {
double logli = 0;
try {
for (int f = 0; f < lambda.length; f++) {
grad[f] = -1 * lambda[f] * params.invSigmaSquare;
logli -= ((lambda[f] * lambda[f]) * params.invSigmaSquare) / 2;
}
diter.startScan();
if (featureGenCache != null) featureGenCache.startDataScan();
for (int numRecord = 0; diter.hasNext(); numRecord++) {
DataSequence dataSeq = (DataSequence) diter.next();
if (featureGenCache != null) featureGenCache.nextDataIndex();
if (params.debugLvl > 1) {
Util.printDbg("Read next seq: " + numRecord + " logli " + logli);
}
alpha_Y.assign(0);
for (int f = 0; f < lambda.length; f++) ExpF[f] = RobustMath.LOG0;
if ((beta_Y == null) || (beta_Y.length < dataSeq.length())) {
beta_Y = new DenseDoubleMatrix1D[2 * dataSeq.length()];
for (int i = 0; i < beta_Y.length; i++) beta_Y[i] = new DenseDoubleMatrix1D(numY);
}
// compute beta values in a backward scan.
// also scale beta-values to 1 to avoid numerical problems.
beta_Y[dataSeq.length() - 1].assign(0);
for (int i = dataSeq.length() - 1; i > 0; i--) {
if (params.debugLvl > 2) {
/* Util.printDbg("Features fired");
featureGenerator.startScanFeaturesAt(dataSeq, i);
while (featureGenerator.hasNext()) {
Feature feature = featureGenerator.next();
Util.printDbg(feature.toString());
}
*/
}
// compute the Mi matrix
initMDone =
computeLogMi(
featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, false, reuseM, initMDone);
tmp_Y.assign(beta_Y[i]);
tmp_Y.assign(Ri_Y, sumFunc);
RobustMath.logMult(Mi_YY, tmp_Y, beta_Y[i - 1], 1, 0, false, edgeGen);
}
double thisSeqLogli = 0;
for (int i = 0; i < dataSeq.length(); i++) {
// compute the Mi matrix
initMDone =
computeLogMi(
featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, false, reuseM, initMDone);
// find features that fire at this position..
featureGenerator.startScanFeaturesAt(dataSeq, i);
if (i > 0) {
tmp_Y.assign(alpha_Y);
RobustMath.logMult(Mi_YY, tmp_Y, newAlpha_Y, 1, 0, true, edgeGen);
newAlpha_Y.assign(Ri_Y, sumFunc);
} else {
newAlpha_Y.assign(Ri_Y);
}
while (featureGenerator.hasNext()) {
Feature feature = featureGenerator.next();
int f = feature.index();
int yp = feature.y();
int yprev = feature.yprev();
float val = feature.value();
if ((dataSeq.y(i) == yp)
&& (((i - 1 >= 0) && (yprev == dataSeq.y(i - 1))) || (yprev < 0))) {
grad[f] += val;
thisSeqLogli += val * lambda[f];
if (params.debugLvl > 2) {
System.out.println("Feature fired " + f + " " + feature);
}
}
if (yprev < 0) {
ExpF[f] =
RobustMath.logSumExp(
ExpF[f], newAlpha_Y.get(yp) + RobustMath.log(val) + beta_Y[i].get(yp));
} else {
ExpF[f] =
RobustMath.logSumExp(
ExpF[f],
alpha_Y.get(yprev)
+ Ri_Y.get(yp)
+ Mi_YY.get(yprev, yp)
+ RobustMath.log(val)
+ beta_Y[i].get(yp));
}
}
alpha_Y.assign(newAlpha_Y);
if (params.debugLvl > 2) {
System.out.println("Alpha-i " + alpha_Y.toString());
System.out.println("Ri " + Ri_Y.toString());
System.out.println("Mi " + Mi_YY.toString());
System.out.println("Beta-i " + beta_Y[i].toString());
}
}
double lZx = RobustMath.logSumExp(alpha_Y);
thisSeqLogli -= lZx;
logli += thisSeqLogli;
// update grad.
for (int f = 0; f < grad.length; f++) {
grad[f] -= RobustMath.exp(ExpF[f] - lZx);
}
if (params.debugLvl > 1) {
System.out.println(
"Sequence "
+ thisSeqLogli
+ " logli "
+ logli
+ " log(Zx) "
+ lZx
+ " Zx "
+ Math.exp(lZx));
}
}
if (params.debugLvl > 2) {
for (int f = 0; f < lambda.length; f++) System.out.print(lambda[f] + " ");
System.out.println(" :x");
for (int f = 0; f < lambda.length; f++) System.out.print(grad[f] + " ");
System.out.println(" :g");
}
if (params.debugLvl > 0)
Util.printDbg(
"Iteration "
+ icall
+ " log-likelihood "
+ logli
+ " norm(grad logli) "
+ norm(grad)
+ " norm(x) "
+ norm(lambda));
} catch (Exception e) {
System.out.println("Alpha-i " + alpha_Y.toString());
System.out.println("Ri " + Ri_Y.toString());
System.out.println("Mi " + Mi_YY.toString());
e.printStackTrace();
System.exit(0);
}
return logli;
}
protected double computeFunctionGradient(double lambda[], double grad[]) {
initMDone = false;
if (params.trainerType.equals("ll")) return computeFunctionGradientLL(lambda, grad);
double logli = 0;
try {
for (int f = 0; f < lambda.length; f++) {
grad[f] = -1 * lambda[f] * params.invSigmaSquare;
logli -= ((lambda[f] * lambda[f]) * params.invSigmaSquare) / 2;
}
boolean doScaling = params.doScaling;
diter.startScan();
if (featureGenCache != null) featureGenCache.startDataScan();
int numRecord = 0;
for (numRecord = 0; diter.hasNext(); numRecord++) {
DataSequence dataSeq = (DataSequence) diter.next();
if (featureGenCache != null) featureGenCache.nextDataIndex();
if (params.debugLvl > 1) {
Util.printDbg("Read next seq: " + numRecord + " logli " + logli);
}
alpha_Y.assign(1);
for (int f = 0; f < lambda.length; f++) ExpF[f] = 0;
if ((beta_Y == null) || (beta_Y.length < dataSeq.length())) {
beta_Y = new DenseDoubleMatrix1D[2 * dataSeq.length()];
for (int i = 0; i < beta_Y.length; i++) beta_Y[i] = new DenseDoubleMatrix1D(numY);
scale = new double[2 * dataSeq.length()];
}
// compute beta values in a backward scan.
// also scale beta-values to 1 to avoid numerical problems.
scale[dataSeq.length() - 1] = (doScaling) ? numY : 1;
beta_Y[dataSeq.length() - 1].assign(1.0 / scale[dataSeq.length() - 1]);
for (int i = dataSeq.length() - 1; i > 0; i--) {
if (params.debugLvl > 2) {
Util.printDbg("Features fired");
// featureGenerator.startScanFeaturesAt(dataSeq, i);
// while (featureGenerator.hasNext()) {
// Feature feature = featureGenerator.next();
// Util.printDbg(feature.toString());
// }
}
// compute the Mi matrix
initMDone =
computeLogMi(
featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, true, reuseM, initMDone);
tmp_Y.assign(beta_Y[i]);
tmp_Y.assign(Ri_Y, multFunc);
RobustMath.Mult(Mi_YY, tmp_Y, beta_Y[i - 1], 1, 0, false, edgeGen);
// Mi_YY.zMult(tmp_Y, beta_Y[i-1]);
// need to scale the beta-s to avoid overflow
scale[i - 1] = doScaling ? beta_Y[i - 1].zSum() : 1;
if ((scale[i - 1] < 1) && (scale[i - 1] > -1)) scale[i - 1] = 1;
constMultiplier.multiplicator = 1.0 / scale[i - 1];
beta_Y[i - 1].assign(constMultiplier);
}
double thisSeqLogli = 0;
for (int i = 0; i < dataSeq.length(); i++) {
// compute the Mi matrix
initMDone =
computeLogMi(
featureGenerator, lambda, dataSeq, i, Mi_YY, Ri_Y, true, reuseM, initMDone);
// find features that fire at this position..
featureGenerator.startScanFeaturesAt(dataSeq, i);
if (i > 0) {
tmp_Y.assign(alpha_Y);
RobustMath.Mult(Mi_YY, tmp_Y, newAlpha_Y, 1, 0, true, edgeGen);
// Mi_YY.zMult(tmp_Y, newAlpha_Y,1,0,true);
newAlpha_Y.assign(Ri_Y, multFunc);
} else {
newAlpha_Y.assign(Ri_Y);
}
while (featureGenerator.hasNext()) {
Feature feature = featureGenerator.next();
int f = feature.index();
int yp = feature.y();
int yprev = feature.yprev();
float val = feature.value();
if ((dataSeq.y(i) == yp)
&& (((i - 1 >= 0) && (yprev == dataSeq.y(i - 1))) || (yprev < 0))) {
grad[f] += val;
thisSeqLogli += val * lambda[f];
}
if (yprev < 0) {
ExpF[f] += newAlpha_Y.get(yp) * val * beta_Y[i].get(yp);
} else {
ExpF[f] +=
alpha_Y.get(yprev)
* Ri_Y.get(yp)
* Mi_YY.get(yprev, yp)
* val
* beta_Y[i].get(yp);
}
}
alpha_Y.assign(newAlpha_Y);
// now scale the alpha-s to avoid overflow problems.
constMultiplier.multiplicator = 1.0 / scale[i];
alpha_Y.assign(constMultiplier);
if (params.debugLvl > 2) {
System.out.println("Alpha-i " + alpha_Y.toString());
System.out.println("Ri " + Ri_Y.toString());
System.out.println("Mi " + Mi_YY.toString());
System.out.println("Beta-i " + beta_Y[i].toString());
}
}
double Zx = alpha_Y.zSum();
thisSeqLogli -= log(Zx);
// correct for the fact that alpha-s were scaled.
for (int i = 0; i < dataSeq.length(); i++) {
thisSeqLogli -= log(scale[i]);
}
logli += thisSeqLogli;
// update grad.
for (int f = 0; f < grad.length; f++) grad[f] -= ExpF[f] / Zx;
if (params.debugLvl > 1) {
System.out.println(
"Sequence "
+ thisSeqLogli
+ " logli "
+ logli
+ " log(Zx) "
+ Math.log(Zx)
+ " Zx "
+ Zx);
}
}
if (params.debugLvl > 2) {
for (int f = 0; f < lambda.length; f++) System.out.print(lambda[f] + " ");
System.out.println(" :x");
for (int f = 0; f < lambda.length; f++)
System.out.println(featureGenerator.featureName(f) + " " + grad[f] + " ");
System.out.println(" :g");
}
if (params.debugLvl > 0)
Util.printDbg(
"Iter "
+ icall
+ " log likelihood "
+ logli
+ " norm(grad logli) "
+ norm(grad)
+ " norm(x) "
+ norm(lambda));
if (icall == 0) {
System.out.println("Number of training records" + numRecord);
}
} catch (Exception e) {
System.out.println("Alpha-i " + alpha_Y.toString());
System.out.println("Ri " + Ri_Y.toString());
System.out.println("Mi " + Mi_YY.toString());
e.printStackTrace();
System.exit(0);
}
return logli;
}