private static double[] solution(DoubleMatrix2D X, DoubleMatrix2D Y, int k) {
// Solve X * Beta = Y for Beta
// Only the first column of Y is used
// k is number of beta coefficients
QRDecomposition qr = new QRDecomposition(X);
if (qr.hasFullRank()) {
DoubleMatrix2D B = qr.solve(Y);
return B.viewColumn(0).toArray();
} else {
DoubleMatrix1D Y0 = Y.viewColumn(0); // first column of Y
SingularValueDecomposition svd = new SingularValueDecomposition(X);
DoubleMatrix2D S = svd.getS();
DoubleMatrix2D V = svd.getV();
DoubleMatrix2D U = svd.getU();
Algebra alg = new Algebra();
DoubleMatrix2D Ut = alg.transpose(U);
DoubleMatrix1D g = alg.mult(Ut, Y0); // Ut*Y0
for (int j = 0; j < k; j++) {
// solve S*p = g for p; S is a diagonal matrix
double x = S.getQuick(j, j);
if (x > 0.) {
x = g.getQuick(j) / x; // p[j] = g[j]/S[j]
g.setQuick(j, x); // overwrite g by p
} else g.setQuick(j, 0.);
}
DoubleMatrix1D beta = alg.mult(V, g); // V*p
return beta.toArray();
}
}
/**
* Save factorisation machine in a compressed, human readable file.
*
* @param out output
* @throws IOException when I/O error
*/
public void save(OutputStream out) throws IOException {
int N = m.rows();
int K = m.columns();
try (ZipOutputStream zip = new ZipOutputStream(out)) {
zip.putNextEntry(new ZipEntry("info"));
PrintStream ps = new PrintStream(zip);
ps.println(N);
ps.println(K);
ps.flush();
zip.closeEntry();
zip.putNextEntry(new ZipEntry("b"));
ps = new PrintStream(zip);
ps.println(b);
ps.flush();
zip.closeEntry();
zip.putNextEntry(new ZipEntry("w"));
saveDenseDoubleMatrix1D(zip, w);
zip.closeEntry();
zip.putNextEntry(new ZipEntry("m"));
saveDenseDoubleMatrix2D(zip, m);
zip.closeEntry();
}
}
private DoubleMatrix2D newFromTemplate(DoubleMatrix2D template, int rows, int columns) {
if (template != null) {
return template.like(rows, columns);
} else {
return x.like(rows, columns);
}
}
/**
* Computes the regression coefficients using the least squares method. This is a linear
* regression with a polynomial of degree `deg` @f$= k@f$ and @f$k+1@f$ regression
* coefficients @f$\beta_j@f$. The model is
*
* @f[ y = \beta_0 + \sum_{j=1}^k \beta_j x^j.
* @f] Given the @f$n@f$ data points @f$(X_i, Y_i)@f$, @f$i=0,1,…,(n-1)@f$, the method computes
* and returns the array @f$[\beta_0, \beta_1, …, \beta_k]@f$. Restriction: @f$n > k@f$.
* @param X the regressor variables
* @param Y the response
* @return the regression coefficients
*/
public static double[] calcCoefficients(double[] X, double[] Y, int deg) {
final int n = X.length;
if (n != Y.length) throw new IllegalArgumentException("Lengths of X and Y are not equal");
if (n < deg + 1) throw new IllegalArgumentException("Not enough points");
final double[] xSums = new double[2 * deg + 1];
final double[] xySums = new double[deg + 1];
xSums[0] = n;
for (int i = 0; i < n; i++) {
double xv = X[i];
xySums[0] += Y[i];
for (int j = 1; j <= 2 * deg; j++) {
xSums[j] += xv;
if (j <= deg) xySums[j] += xv * Y[i];
xv *= X[i];
}
}
final DoubleMatrix2D A = new DenseDoubleMatrix2D(deg + 1, deg + 1);
final DoubleMatrix2D B = new DenseDoubleMatrix2D(deg + 1, 1);
for (int i = 0; i <= deg; i++) {
for (int j = 0; j <= deg; j++) {
final int d = i + j;
A.setQuick(i, j, xSums[d]);
}
B.setQuick(i, 0, xySums[i]);
}
return solution(A, B, deg + 1);
}
/**
* Computes the density function <SPAN CLASS="MATH"><I>f</I> (<I>x</I>)</SPAN>, with <SPAN
* CLASS="MATH"><I>λ</I><SUB>i</SUB> =</SPAN> <TT>lambda[<SPAN CLASS="MATH"><I>i</I> -
* 1</SPAN>]</TT>, <SPAN CLASS="MATH"><I>i</I> = 1,…, <I>k</I></SPAN>.
*
* @param lambda rates of the hypoexponential distribution
* @param x value at which the density is evaluated
* @return density at <SPAN CLASS="MATH"><I>x</I></SPAN>
*/
public static double density(double[] lambda, double x) {
testLambda(lambda);
if (x < 0) return 0;
DoubleMatrix2D Ax = buildMatrix(lambda, x);
DoubleMatrix2D M = DMatrix.expBidiagonal(Ax);
int k = lambda.length;
return lambda[k - 1] * M.getQuick(0, k - 1);
}
public double apply(int first, int second, double third) {
// System.out.println("checking = " + min_val + " versus " +
// (third/count_matrix.getQuick(first,second)));
if (third / count_matrix.getQuick(first, second) > max_val) {
max_m = first;
max_n = second;
max_val = third / count_matrix.getQuick(first, second);
}
return third;
}
@Override
public DoubleMatrix2D transitionMatrix(double from_time, double to_time) {
double from_time_reminder = from_time % 1.0;
double from_time_div = from_time - from_time_reminder;
double to_time_reminder = to_time - from_time_div;
DoubleMatrix2D cached =
cachedTransitionMatrices.get(
new Pair<Double, Double>(from_time_reminder, to_time_reminder));
if (cached != null) {
return cached;
} else {
double step_start_time = from_time;
double step_end_time = step_start_time;
DoubleMatrix2D result = F.identity(num_states);
while (step_start_time < to_time) {
double step_start_time_reminder = step_start_time % 1.0;
double step_start_time_div = step_start_time - step_start_time_reminder;
if (isInSeason1(step_start_time)) {
step_end_time =
Math.min(
to_time,
step_start_time_div + season1Start + season1Length + infitesimalTimeInterval);
result =
result.zMult(
season1MigrationModel.transitionMatrix(step_start_time, step_end_time), null);
} else { // In Season 2
if (step_start_time_reminder < season1Start) {
step_end_time =
Math.min(to_time, step_start_time_div + season1Start + infitesimalTimeInterval);
} else {
step_end_time =
Math.min(
to_time, step_start_time_div + 1.0 + season1Start + infitesimalTimeInterval);
}
result =
result.zMult(
season2MigrationModel.transitionMatrix(step_start_time, step_end_time), null);
}
step_start_time = step_end_time;
}
// cache result
if (cachedTransitionMatrices.size() >= maxCachedTransitionMatrices) {
for (int i = 0; i < cachedTransitionMatrices.size() / 2; i++) {
cachedTransitionMatrices.remove(cachedTransitionMatrices.keySet().iterator().next());
}
}
cachedTransitionMatrices.put(
new Pair<Double, Double>(from_time_reminder, to_time_reminder), result);
return result;
}
}
public ColtEigenvalueDecomposition(DoubleMatrix dm) {
int nrows = dm.numberOfRows();
int ncols = dm.numberOfColumns();
DoubleMatrix2D matrix = DoubleFactory2D.dense.make(nrows, ncols);
for (int r = 0; r < nrows; r++) {
for (int c = 0; c < ncols; c++) {
matrix.setQuick(r, c, dm.get(r, c));
}
}
myDecomposition = new cern.colt.matrix.linalg.EigenvalueDecomposition(matrix);
}
// Builds the bidiagonal matrix A out of the lambda
private static DoubleMatrix2D buildMatrix(double[] lambda, double x) {
int k = lambda.length;
DoubleFactory2D F2 = DoubleFactory2D.dense;
DoubleMatrix2D A = F2.make(k, k);
for (int j = 0; j < k - 1; j++) {
A.setQuick(j, j, -lambda[j] * x);
A.setQuick(j, j + 1, lambda[j] * x);
}
A.setQuick(k - 1, k - 1, -lambda[k - 1] * x);
return A;
}
/**
* Classifies an instance w.r.t. the partitions found. It applies a naive min-distance algorithm.
*
* @param instance the instance to classify
* @return the cluster that contains the nearest point to the instance
*/
public int clusterInstance(Instance instance) throws java.lang.Exception {
DoubleMatrix1D u = DoubleFactory1D.dense.make(instance.toDoubleArray());
double min_dist = Double.POSITIVE_INFINITY;
int c = -1;
for (int i = 0; i < v.rows(); i++) {
double dist = distnorm2(u, v.viewRow(i));
if (dist < min_dist) {
c = cluster[i];
min_dist = dist;
}
}
return c;
}
/**
* Computes the complementary distribution <SPAN CLASS="MATH">bar(F)(<I>x</I>)</SPAN>, with <SPAN
* CLASS="MATH"><I>λ</I><SUB>i</SUB> =</SPAN> <TT>lambda[<SPAN CLASS="MATH"><I>i</I> -
* 1</SPAN>]</TT>, <SPAN CLASS="MATH"><I>i</I> = 1,…, <I>k</I></SPAN>.
*
* @param lambda rates of the hypoexponential distribution
* @param x value at which the complementary distribution is evaluated
* @return complementary distribution at <SPAN CLASS="MATH"><I>x</I></SPAN>
*/
public static double barF(double[] lambda, double x) {
testLambda(lambda);
if (x <= 0.0) return 1.0;
if (x >= Double.MAX_VALUE) return 0.0;
DoubleMatrix2D M = buildMatrix(lambda, x);
M = DMatrix.expBidiagonal(M);
// prob is first row of final matrix
int k = lambda.length;
double sum = 0;
for (int j = 0; j < k; j++) sum += M.getQuick(0, j);
return sum;
}
/**
* Splits recursively the points of the graph while the value of the best cut found is less of a
* specified limit (the alpha star factor).
*
* @param W the weight matrix of the graph
* @param alpha_star the alpha star factor
* @return an array of sets of points (partitions)
*/
protected int[][] partition(DoubleMatrix2D W, double alpha_star) {
numPartitions++;
// System.out.println("!");
// If the graph contains only one point
if (W.columns() == 1) {
int[][] p = new int[1][1];
p[0][0] = 0;
return p;
// Otherwise
} else {
// Computes the best cut
int[][] cut = bestCut(W);
// Computes the value of the found cut
double cutVal = Ncut(W, cut[0], cut[1], null);
// System.out.println("cutVal = "+cutVal +"\tnumPartitions = "+numPartitions);
// If the value is less than alpha star
if (cutVal < alpha_star && numPartitions < 2) {
// Recursively partitions the first one found ...
DoubleMatrix2D W0 = W.viewSelection(cut[0], cut[0]);
int[][] p0 = partition(W0, alpha_star);
// ... and the second one
DoubleMatrix2D W1 = W.viewSelection(cut[1], cut[1]);
int[][] p1 = partition(W1, alpha_star);
// Merges the partitions found in the previous recursive steps
int[][] p = new int[p0.length + p1.length][];
for (int i = 0; i < p0.length; i++) {
p[i] = new int[p0[i].length];
for (int j = 0; j < p0[i].length; j++) p[i][j] = cut[0][p0[i][j]];
}
for (int i = 0; i < p1.length; i++) {
p[i + p0.length] = new int[p1[i].length];
for (int j = 0; j < p1[i].length; j++) p[i + p0.length][j] = cut[1][p1[i][j]];
}
return p;
} else {
// Otherwise returns the partitions found in current step
// w/o recursive invocation
int[][] p = new int[1][W.columns()];
for (int i = 0; i < p[0].length; i++) p[0][i] = i;
return p;
}
}
}
// assumes m > n
public double apply(int first, int second, double third) {
// System.out.println("m = " + m);
// System.out.println("n = " + n);
// System.out.println("first = " + first);
if (m_col_mode) { // m == 2nd
if (first != m) {
// System.out.println("m = " + m);
// System.out.println("n = " + n);
// System.out.println("first = " + first);
// System.out.println("val = " + m_parent.get(first, n) );
m_parent.set(first, n, m_parent.get(first, n) + third);
} else {
m_parent.set(n, n, m_parent.get(n, n) + third);
}
} else { // m == first
if (second > n) {
// System.out.println("m = " + m);
// System.out.println("n = " + n);
// System.out.println("first = " + first);
// System.out.println("second = " + second);
// System.out.println("val = " + m_parent.get(second, n) );
m_parent.set(second, n, m_parent.get(second, n) + third);
} else if (second < n) {
// System.out.println("m = " + m);
// System.out.println("n = " + n);
// System.out.println("first = " + first);
// System.out.println("second = " + second);
// System.out.println("val = " + m_parent.get(n, second) );
m_parent.set(n, second, m_parent.get(n, second) + third);
}
}
return 0.;
}
@Override
public NativeMatrix inverse() {
if (rows != cols) {
throw new IllegalArgumentException();
}
final DoubleMatrix2D ainv = Algebra.ZERO.inverse(new DenseDoubleMatrix2D(u));
final NativeMatrix r = new NativeMatrix(rows, cols, false);
for (int i = 0; i < rows; ++i) {
for (int j = 0; j < cols; ++j) {
r.u[i][j] = ainv.get(i, j);
}
}
return r;
}
@Override
public DoubleMatrix getEigenvectors() {
DoubleMatrix2D V = myDecomposition.getV();
int nrows = V.rows();
int ncols = V.columns();
DoubleMatrix dm = DoubleMatrixFactory.DEFAULT.make(nrows, ncols);
for (int r = 0; r < nrows; r++) {
for (int c = 0; c < ncols; c++) {
dm.set(r, c, V.getQuick(r, c));
}
}
return dm;
}
/**
* Generates a clusterer by the mean of spectral clustering algorithm.
*
* @param data set of instances serving as training data
* @exception Exception if the clusterer has not been generated successfully
*/
public void buildClusterer(Instances data) throws java.lang.Exception {
m_Sequences = new Instances(data);
int n = data.numInstances();
int k = data.numAttributes();
DoubleMatrix2D w;
if (useSparseMatrix) w = DoubleFactory2D.sparse.make(n, n);
else w = DoubleFactory2D.dense.make(n, n);
double[][] v1 = new double[n][];
for (int i = 0; i < n; i++) v1[i] = data.instance(i).toDoubleArray();
v = DoubleFactory2D.dense.make(v1);
double sigma_sq = sigma * sigma;
// Sets up similarity matrix
for (int i = 0; i < n; i++)
for (int j = i; j < n; j++) {
/*double dist = distnorm2(v.viewRow(i), v.viewRow(j));
if((r == -1) || (dist < r)) {
double sim = Math.exp(- (dist * dist) / (2 * sigma_sq));
w.set(i, j, sim);
w.set(j, i, sim);
}*/
/* String [] key = {data.instance(i).stringValue(0), data.instance(j).stringValue(0)};
System.out.println(key[0]);
System.out.println(key[1]);
System.out.println(simScoreMap.containsKey(key));
Double simValue = simScoreMap.get(key);*/
double sim = sim_matrix[i][j];
w.set(i, j, sim);
w.set(j, i, sim);
}
// Partitions points
int[][] p = partition(w, alpha_star);
// Deploys results
numOfClusters = p.length;
cluster = new int[n];
for (int i = 0; i < p.length; i++) for (int j = 0; j < p[i].length; j++) cluster[p[i][j]] = i;
// System.out.println("Final partition:");
// UtilsJS.printMatrix(p);
// System.out.println("Cluster:\n");
// UtilsJS.printArray(cluster);
this.numOfClusters = cluster[Utils.maxIndex(cluster)] + 1;
// System.out.println("Num clusters:\t"+this.numOfClusters);
}
@Override
public double[] solve(final double[] bIn) {
if (bIn.length != rows()) {
throw new IllegalArgumentException();
}
final DoubleMatrix2D b = new DenseDoubleMatrix2D(rows(), 1);
for (int i = 0; i < rows(); ++i) {
b.set(i, 0, bIn[i]);
}
final DoubleMatrix2D a = new DenseDoubleMatrix2D(u);
final DoubleMatrix2D p = Algebra.ZERO.solve(a, b);
final double[] r = new double[cols()];
for (int i = 0; i < r.length; ++i) {
r[i] = p.get(i, 0);
}
return r;
}
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;
}
/**
* Feature-specific contribution to the prediction of the value of an instance.
*
* @param x instance
* @param i index of the feature of interest
* @param xi value of the feature of interest
* @return value of the contribution of the feature to the prediction
*/
public double prediction(I x, int i, double xi) {
double wi = w.getQuick(i);
DoubleMatrix1D mi = m.viewRow(i);
double pred = 0.0;
pred += xi * wi;
pred +=
x.operate(
(j, xj) -> {
DoubleMatrix1D mj = m.viewRow(j);
return xi * xj * mi.zDotProduct(mj);
},
(v1, v2) -> v1 + v2);
return pred;
}
/**
* Computes the regression coefficients using the least squares method. This is a model for
* multiple linear regression. There are @f$k@f$ regression
* coefficients @f$\beta_j@f$, @f$j=0,1,…,(k-1)@f$ and
*
* @f$k@f$ regressors variables @f$x_j@f$. The model is
* @f[ y = \sum_{j=0}^{k-1} \beta_j x_j.
* @f] There are @f$n@f$ data points @f$Y_i@f$, @f$X_{ij}@f$,
* @f$i=0,1,…,(n-1)@f$, and each @f$X_i@f$ is a @f$k@f$-dimensional point. Given the response
* `Y[i]` and the regressor variables `X[i][j]`, @f$\mathtt{i} =0,1,…,(n-1)@f$, @f$\mathtt{j}
* =0,1,…,(k-1)@f$, the method computes and returns the array
* @f$[\beta_0, \beta_1, …, \beta_{k-1}]@f$. Restriction: @f$n > k@f$.
* @param X the regressor variables
* @param Y the response
* @return the regression coefficients
*/
public static double[] calcCoefficients(double[][] X, double[] Y) {
if (X.length != Y.length)
throw new IllegalArgumentException("Lengths of X and Y are not equal");
if (Y.length <= X[0].length + 1) throw new IllegalArgumentException("Not enough points");
final int n = Y.length;
final int k = X[0].length;
DoubleMatrix2D Xa = new DenseDoubleMatrix2D(n, k);
DoubleMatrix2D Ya = new DenseDoubleMatrix2D(n, 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < k; j++) {
Xa.setQuick(i, j, X[i][j]);
}
Ya.setQuick(i, 0, Y[i]);
}
return solution(Xa, Ya, k);
}
/**
* 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;
}
/**
* Constructs and returns a new eigenvalue decomposition object; The decomposed matrices can be
* retrieved via instance methods of the returned decomposition object. Checks for symmetry, then
* constructs the eigenvalue decomposition.
*
* @param A A square matrix.
* @return A decomposition object to access <tt>D</tt> and <tt>V</tt>.
* @throws IllegalArgumentException if <tt>A</tt> is not square.
*/
public EigenvalueDecomposition(DoubleMatrix2D A) {
Property.DEFAULT.checkSquare(A);
n = A.columns();
V = new double[n][n];
d = new double[n];
e = new double[n];
issymmetric = Property.DEFAULT.isSymmetric(A);
if (issymmetric) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
V[i][j] = A.getQuick(i, j);
}
}
// Tridiagonalize.
tred2();
// Diagonalize.
tql2();
} else {
H = new double[n][n];
ort = new double[n];
for (int j = 0; j < n; j++) {
for (int i = 0; i < n; i++) {
H[i][j] = A.getQuick(i, j);
}
}
// Reduce to Hessenberg form.
orthes();
// Reduce Hessenberg to real Schur form.
hqr2();
}
}
public void random3Partition(DataSet p1, DataSet p2, DataSet p3, double f1, double f2) {
int size1 = (int) (f1 * x.rows());
int size2 = (int) (f2 * x.rows());
int size3 = x.rows() - size1 - size2;
Random random = new Random(new Date().getTime());
p1.x = newFromTemplate(p1.x, size1, x.columns());
p1.y = new double[size1];
p2.x = newFromTemplate(p2.x, size2, x.columns());
p2.y = new double[size2];
p3.x = newFromTemplate(p3.x, size3, x.columns());
p3.y = new double[size3];
// FIXME: Verify the uniformity of the partitioning scheme.
int r1 = 0;
int r2 = 0;
int r3 = 0;
for (int r = 0; r < x.rows(); r++) {
double p = random.nextDouble();
if (p < f1 && r1 < size1) {
p1.copyInstanceTo(r1, this, r);
r1++;
} else if (p < f1 + f2 && r2 < size2) {
p2.copyInstanceTo(r2, this, r);
r2++;
} else if (r3 < size3) {
p3.copyInstanceTo(r3, this, r);
r3++;
} else {
r--;
}
}
}
private static void saveDenseDoubleMatrix2D(OutputStream stream, DoubleMatrix2D matrix)
throws IOException {
BufferedWriter out = new BufferedWriter(new OutputStreamWriter(stream));
double[][] m = matrix.toArray();
for (double[] pu : m) {
for (int j = 0; j < pu.length; j++) {
out.write(Double.toString(pu[j]));
if (j < pu.length - 1) {
out.write('\t');
}
}
out.newLine();
}
out.flush();
}
/**
* Constructs a new time series data contains for the given row-major data array and the given
* list of variables. Each row of the data, data[i], contains a measured for each variable (in
* order) for a particular time. The series of times is in increasing order.
*/
public TimeSeriesData(DoubleMatrix2D matrix, List<String> varNames) {
if (matrix == null) {
throw new NullPointerException("Data must not be null.");
}
if (varNames == null) {
throw new NullPointerException("Variables must not be null.");
}
for (int i = 0; i < varNames.size(); i++) {
if (varNames.get(i) == null) {
throw new NullPointerException("Variable at index " + i + "is null.");
}
}
this.data2 = matrix;
if (varNames.size() != matrix.columns()) {
throw new IllegalArgumentException(
"Number of columns in the data " + "must match the number of variables.");
}
this.varNames = varNames;
this.name = "Time Series Data";
}
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;
}
public void newmanCluster(ItemRegistry registry) {
DoubleMatrix2D distance_matrix =
DoubleFactory2D.sparse.make(
registry.getGraph().getNodeCount(), registry.getGraph().getNodeCount());
DoubleMatrix1D a_matrix = DoubleFactory1D.dense.make(registry.getGraph().getNodeCount(), 0.);
Map<String, Cluster> cluster_map = new HashMap<String, Cluster>();
// construct the leaf node distance matrix
Iterator edge_iter = registry.getGraph().getEdges();
m_total_distances = 0.;
while (edge_iter.hasNext()) {
Edge edge = (Edge) edge_iter.next();
Cluster clust1 = (Cluster) edge.getFirstNode();
Cluster clust2 = (Cluster) edge.getSecondNode();
if (cluster_map.get(clust1.getAttribute("id")) == null) {
cluster_map.put(clust1.getAttribute("id"), clust1);
}
if (cluster_map.get(clust2.getAttribute("id")) == null) {
cluster_map.put(clust2.getAttribute("id"), clust2);
}
int n = Integer.parseInt(clust1.getAttribute("id"));
int m = Integer.parseInt(clust2.getAttribute("id"));
// make reciprocal (big values = good in newman, but not in our case)
double dist = 1 / clust1.getCenter().distance(clust2.getCenter());
distance_matrix.set(Math.max(n, m), Math.min(n, m), dist);
// m_total_distances += dist;
// a_matrix.setQuick( n, a_matrix.getQuick( n ) + dist );
// a_matrix.setQuick( m, a_matrix.getQuick( m ) + dist );
m_total_distances += 1;
a_matrix.setQuick(n, a_matrix.getQuick(n) + 1);
a_matrix.setQuick(m, a_matrix.getQuick(m) + 1);
}
// System.out.println(distance_matrix);
// System.out.println(count_matrix);
// agglomerate nodes until we reach a root node (or nodes)
boolean done = false;
int trash = 0;
QFinder qfinder = new QFinder();
qfinder.a_matrix = a_matrix;
QMerger qmerger = new QMerger();
while (!done) {
// find the minimum cluster distance
qfinder.reset();
distance_matrix.forEachNonZero(qfinder);
// done = true;
// System.out.println(distance_matrix);
// System.out.println(count_matrix);
if (qfinder.getVal() == -Double.MAX_VALUE) {
break;
}
// add a parent cluster to the graph
Cluster clust1 = cluster_map.get("" + qfinder.getM());
Cluster clust2 = cluster_map.get("" + qfinder.getN());
while (clust1.getParent() != null) {
clust1 = clust1.getParent();
}
while (clust2.getParent() != null) {
clust2 = clust2.getParent();
}
trash++;
double dist = Math.max(clust1.getHeight(), clust2.getHeight());
Cluster new_cluster =
new DefaultCluster(
(float) (clust1.getCenter().getX() + clust2.getCenter().getX()) / 2.f,
(float) (clust1.getCenter().getY() + clust2.getCenter().getY()) / 2.f,
(float)
Math.sqrt(
clust1.getRadius() * clust1.getRadius()
+ clust2.getRadius() * clust2.getRadius()),
clust1,
clust2,
dist);
registry.getGraph().addNode(new_cluster);
// merge the clusters distances / counts
int M = Math.max(qfinder.getM(), qfinder.getN());
int N = Math.min(qfinder.getM(), qfinder.getN());
a_matrix.set(N, a_matrix.getQuick(M) + a_matrix.getQuick(N));
a_matrix.set(M, 0);
// System.out.println("M = "+M+" N = "+N + " VAL=" + minfinder.getVal() );
qmerger.setM(M);
qmerger.setN(N);
qmerger.setParent(distance_matrix);
qmerger.setMode(true);
// System.out.println(distance_matrix.viewPart( 0, M, distance_matrix.rows(), 1));
distance_matrix.viewPart(0, M, distance_matrix.rows(), 1).forEachNonZero(qmerger);
qmerger.setMode(false);
// System.out.println(distance_matrix.viewPart( M, 0, 1, M ));
distance_matrix.viewPart(M, 0, 1, M).forEachNonZero(qmerger);
// System.out.println(distance_matrix);
// System.out.println(count_matrix);
// free any superfluous memory randomly ~ (1/20) times
if (Math.random() > 0.95) {
distance_matrix.trimToSize();
}
}
}
@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();
}
/**
* Computes the association degree between two partitions of a graph.<br>
* The association degree is defined as the sum of the weights of all the edges between points of
* the two partitions.
*
* @param W the weight matrix of the graph
* @param a the points of the first partition
* @param b the points of the second partition
* @return the association degree
*/
protected static double asso(DoubleMatrix2D W, int[] a, int[] b) {
return W.viewSelection(a, b).zSum();
}
/**
* 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;
}
