List of usage examples for org.apache.mahout.math Matrix determinant
double determinant();
From source file:edu.snu.dolphin.bsp.examples.ml.algorithms.clustering.em.EMMainCmpTask.java
License:Apache License
@Override public void run(final int iteration) { clusterToStats = new HashMap<>(); final int numClusters = clusterSummaries.size(); // Compute the partial statistics of each cluster for (final Vector vector : points) { final int dimension = vector.size(); Matrix outProd = null;/*from ww w. j av a 2 s.c o m*/ if (isCovarianceDiagonal) { outProd = new SparseMatrix(dimension, dimension); for (int j = 0; j < dimension; j++) { outProd.set(j, j, vector.get(j) * vector.get(j)); } } else { outProd = vector.cross(vector); } double denominator = 0; final double[] numerators = new double[numClusters]; for (int i = 0; i < numClusters; i++) { final ClusterSummary clusterSummary = clusterSummaries.get(i); final Vector centroid = clusterSummary.getCentroid(); final Matrix covariance = clusterSummary.getCovariance(); final Double prior = clusterSummary.getPrior(); final Vector differ = vector.minus(centroid); numerators[i] = prior / Math.sqrt(covariance.determinant()) * Math.exp(differ.dot(inverse(covariance).times(differ)) / (-2)); denominator += numerators[i]; } for (int i = 0; i < numClusters; i++) { final double posterior = denominator == 0 ? 1.0 / numerators.length : numerators[i] / denominator; if (!clusterToStats.containsKey(i)) { clusterToStats.put(i, new ClusterStats(times(outProd, posterior), vector.times(posterior), posterior, false)); } else { clusterToStats.get(i).add( new ClusterStats(times(outProd, posterior), vector.times(posterior), posterior, false)); } } } }
From source file:org.qcri.pca.SPCADriver.java
/** * Run PPCA sequentially given the small input Y which fit into memory This * could be used also on sampled data from a distributed matrix * /* w ww . ja v a 2 s. c o m*/ * Note: this implementation ignore NaN values by replacing them with 0 * * @param conf * the configuration * @param centralY * the input matrix * @param initVal * the initial values for C and ss * @param MAX_ROUNDS * maximum number of iterations * @return the error * @throws Exception */ double runSequential_JacobVersion(Configuration conf, Matrix centralY, InitialValues initVal, final int MAX_ROUNDS) { Matrix centralC = initVal.C;// the current implementation doesn't use initial ss of // initVal final int nRows = centralY.numRows(); final int nCols = centralY.numCols(); final int nPCs = centralC.numCols(); final float threshold = 0.00001f; log.info("tracec= " + PCACommon.trace(centralC)); // Y = Y - mean(Ye) // Also normalize the matrix for (int r = 0; r < nRows; r++) for (int c = 0; c < nCols; c++) if (new Double(centralY.getQuick(r, c)).isNaN()) { centralY.setQuick(r, c, 0); } Vector mean = centralY.aggregateColumns(new VectorFunction() { @Override public double apply(Vector v) { return v.zSum() / nRows; } }); Vector spanVector = new DenseVector(nCols); for (int c = 0; c < nCols; c++) { Vector col = centralY.viewColumn(c); double max = col.maxValue(); double min = col.minValue(); double span = max - min; spanVector.setQuick(c, span); } for (int r = 0; r < nRows; r++) for (int c = 0; c < nCols; c++) centralY.set(r, c, (centralY.get(r, c) - mean.get(c)) / (spanVector.getQuick(c) != 0 ? spanVector.getQuick(c) : 1)); // -------------------------- initialization // CtC = C'*C; Matrix centralCtC = centralC.transpose().times(centralC); log.info("tracectc= " + PCACommon.trace(centralCtC)); log.info("traceinvctc= " + PCACommon.trace(inv(centralCtC))); log.info("traceye= " + PCACommon.trace(centralY)); // X = Ye * C * inv(CtC); Matrix centralX = centralY.times(centralC).times(inv(centralCtC)); log.info("tracex= " + PCACommon.trace(centralX)); // recon = X * C'; Matrix recon = centralX.times(centralC.transpose()); log.info("tracerec= " + PCACommon.trace(recon)); // ss = sum(sum((recon-Ye).^2)) / (N*D-missing); double ss = recon.minus(centralY).assign(new DoubleFunction() { @Override public double apply(double arg1) { return arg1 * arg1; } }).zSum() / (nRows * nCols); log.info("SSSSSSSSSSSSSSSSSSSSSSSSSSSS " + ss); int count = 1; // old = Inf; double old = Double.MAX_VALUE; // -------------------------- EM Iterations // while count int round = 0; while (round < MAX_ROUNDS && count > 0) { round++; // ------------------ E-step, (co)variances // Sx = inv( eye(d) + CtC/ss ); Matrix centralSx = eye(nPCs).plus(centralCtC.divide(ss)); centralSx = inv(centralSx); // ------------------ E-step expected value // X = Ye*C*(Sx/ss); centralX = centralY.times(centralC).times(centralSx.divide(ss)); // ------------------ M-step // SumXtX = X'*X; Matrix centralSumXtX = centralX.transpose().times(centralX); // C = (Ye'*X) / (SumXtX + N*Sx ); Matrix tmpInv = inv(centralSumXtX.plus(centralSx.times(nRows))); centralC = centralY.transpose().times(centralX).times(tmpInv); // CtC = C'*C; centralCtC = centralC.transpose().times(centralC); // ss = ( sum(sum( (X*C'-Ye).^2 )) + N*sum(sum(CtC.*Sx)) + // missing*ss_old ) /(N*D); recon = centralX.times(centralC.transpose()); double error = recon.minus(centralY).assign(new DoubleFunction() { @Override public double apply(double arg1) { return arg1 * arg1; } }).zSum(); ss = error + nRows * dot(centralCtC.clone(), centralSx).zSum(); ss /= (nRows * nCols); log.info("SSSSSSSSSSSSSSSSSSSSSSSSSSSS " + ss); double traceSx = PCACommon.trace(centralSx); double traceX = PCACommon.trace(centralX); double traceSumXtX = PCACommon.trace(centralSumXtX); double traceC = PCACommon.trace(centralC); double traceCtC = PCACommon.trace(centralCtC); log.info("TTTTTTTTTTTTTTTTT " + traceSx + " " + traceX + " " + traceSumXtX + " " + traceC + " " + traceCtC + " " + 0); // objective = N*D + N*(D*log(ss) +PCACommon.trace(Sx)-log(det(Sx)) ) // +PCACommon.trace(SumXtX) -missing*log(ss_old); double objective = nRows * nCols + nRows * (nCols * Math.log(ss) + PCACommon.trace(centralSx) - Math.log(centralSx.determinant())) + PCACommon.trace(centralSumXtX); double rel_ch = Math.abs(1 - objective / old); old = objective; count++; if (rel_ch < threshold && count > 5) count = 0; System.out.printf("Objective: %.6f relative change: %.6f \n", objective, rel_ch); } double norm1Y = centralY.aggregateColumns(new VectorNorm1()).maxValue(); log.info("Norm1 of Y is: " + norm1Y); Matrix newYerror = centralY.minus(centralX.times(centralC.transpose())); double norm1Err = newYerror.aggregateColumns(new VectorNorm1()).maxValue(); log.info("Norm1 of the reconstruction error is: " + norm1Err); initVal.C = centralC; initVal.ss = ss; return norm1Err / norm1Y; }