void permuteVector(const arma::Col<ValueType> &original,
arma::Col<ValueType> &permuted) const {
const int dim = original.n_elem;
permuted.set_size(dim);
for (int i = 0; i < dim; ++i)
permuted(m_permutedIndices[i]) = original(i);
}
void unpermuteVector(const arma::Col<ValueType> &permuted,
arma::Col<ValueType> &original) const {
const int dim = permuted.n_elem;
original.set_size(dim);
for (int i = 0; i < dim; ++i)
original(i) = permuted(m_permutedIndices[i]);
}
inline void HRectBound<MetricType, ElemType>::Center(
arma::Col<ElemType>& center) const
{
// Set size correctly if necessary.
if (!(center.n_elem == dim))
center.set_size(dim);
for (size_t i = 0; i < dim; i++)
center(i) = bounds[i].Mid();
}
double HMM<Distribution>::Predict(const arma::mat& dataSeq,
arma::Col<size_t>& stateSeq) const
{
// This is an implementation of the Viterbi algorithm for finding the most
// probable sequence of states to produce the observed data sequence. We
// don't use log-likelihoods to save that little bit of time, but we'll
// calculate the log-likelihood at the end of it all.
stateSeq.set_size(dataSeq.n_cols);
arma::mat logStateProb(transition.n_rows, dataSeq.n_cols);
arma::mat stateSeqBack(transition.n_rows, dataSeq.n_cols);
// Store the logs of the transposed transition matrix. This is because we
// will be using the rows of the transition matrix.
arma::mat logTrans(log(trans(transition)));
// The calculation of the first state is slightly different; the probability
// of the first state being state j is the maximum probability that the state
// came to be j from another state.
logStateProb.col(0).zeros();
for (size_t state = 0; state < transition.n_rows; state++)
{
logStateProb(state, 0) = log(initial[state] *
emission[state].Probability(dataSeq.unsafe_col(0)));
stateSeqBack(state, 0) = state;
}
// Store the best first state.
arma::uword index;
for (size_t t = 1; t < dataSeq.n_cols; t++)
{
// Assemble the state probability for this element.
// Given that we are in state j, we use state with the highest probability
// of being the previous state.
for (size_t j = 0; j < transition.n_rows; j++)
{
arma::vec prob = logStateProb.col(t - 1) + logTrans.col(j);
logStateProb(j, t) = prob.max(index) +
log(emission[j].Probability(dataSeq.unsafe_col(t)));
stateSeqBack(j, t) = index;
}
}
// Backtrack to find the most probable state sequence.
logStateProb.unsafe_col(dataSeq.n_cols - 1).max(index);
stateSeq[dataSeq.n_cols - 1] = index;
for (size_t t = 2; t <= dataSeq.n_cols; t++)
stateSeq[dataSeq.n_cols - t] =
stateSeqBack(stateSeq[dataSeq.n_cols - t + 1], dataSeq.n_cols - t + 1);
return logStateProb(stateSeq(dataSeq.n_cols - 1), dataSeq.n_cols - 1);
}
void NaiveBayesClassifier<MatType>::Classify(const MatType& data,
arma::Col<size_t>& results)
{
// Check that the number of features in the test data is same as in the
// training data.
Log::Assert(data.n_rows == means.n_rows);
arma::vec probs = arma::log(probabilities);
arma::mat invVar = 1.0 / variances;
arma::mat testProbs = arma::repmat(probs.t(), data.n_cols, 1);
results.set_size(data.n_cols); // No need to fill with anything yet.
Log::Info << "Running Naive Bayes classifier on " << data.n_cols
<< " data points with " << data.n_rows << " features each." << std::endl;
// Calculate the joint probability for each of the data points for each of the
// means.n_cols.
// Loop over every class.
for (size_t i = 0; i < means.n_cols; i++)
{
// This is an adaptation of gmm::phi() for the case where the covariance is
// a diagonal matrix.
arma::mat diffs = data - arma::repmat(means.col(i), 1, data.n_cols);
arma::mat rhs = -0.5 * arma::diagmat(invVar.col(i)) * diffs;
arma::vec exponents(diffs.n_cols);
for (size_t j = 0; j < diffs.n_cols; ++j)
exponents(j) = std::exp(arma::accu(diffs.col(j) % rhs.unsafe_col(j)));
testProbs.col(i) += log(pow(2 * M_PI, (double) data.n_rows / -2.0) *
pow(det(arma::diagmat(invVar.col(i))), -0.5) * exponents);
}
// Now calculate the label.
for (size_t i = 0; i < data.n_cols; ++i)
{
// Find the index of the class with maximum probability for this point.
arma::uword maxIndex = 0;
arma::vec pointProbs = testProbs.row(i).t();
pointProbs.max(maxIndex);
results[i] = maxIndex;
}
return;
}
void HMM<Distribution>::Generate(const size_t length,
arma::mat& dataSequence,
arma::Col<size_t>& stateSequence,
const size_t startState) const
{
// Set vectors to the right size.
stateSequence.set_size(length);
dataSequence.set_size(dimensionality, length);
// Set start state (default is 0).
stateSequence[0] = startState;
// Choose first emission state.
double randValue = math::Random();
// We just have to find where our random value sits in the probability
// distribution of emissions for our starting state.
dataSequence.col(0) = emission[startState].Random();
// Now choose the states and emissions for the rest of the sequence.
for (size_t t = 1; t < length; t++)
{
// First choose the hidden state.
randValue = math::Random();
// Now find where our random value sits in the probability distribution of
// state changes.
double probSum = 0;
for (size_t st = 0; st < transition.n_rows; st++)
{
probSum += transition(st, stateSequence[t - 1]);
if (randValue <= probSum)
{
stateSequence[t] = st;
break;
}
}
// Now choose the emission.
dataSequence.col(t) = emission[stateSequence[t]].Random();
}
}
void GMM<FittingType>::Classify(const arma::mat& observations,
arma::Col<size_t>& labels) const
{
// This is not the best way to do this!
// We should not have to fill this with values, because each one should be
// overwritten.
labels.set_size(observations.n_cols);
for (size_t i = 0; i < observations.n_cols; ++i)
{
// Find maximum probability component.
double probability = 0;
for (size_t j = 0; j < gaussians; ++j)
{
double newProb = Probability(observations.unsafe_col(i), j);
if (newProb >= probability)
{
probability = newProb;
labels[i] = j;
}
}
}
}
inline void MeanShift<UseKernel, KernelType, MatType>::Cluster(
const MatType& data,
arma::Col<size_t>& assignments,
arma::mat& centroids,
bool useSeeds)
{
if (radius <= 0)
{
// An invalid radius is given; an estimation is needed.
Radius(EstimateRadius(data));
}
MatType seeds;
const MatType* pSeeds = &data;
if (useSeeds)
{
GenSeeds(data, radius, 1, seeds);
pSeeds = &seeds;
}
// Holds all centroids before removing duplicate ones.
arma::mat allCentroids(pSeeds->n_rows, pSeeds->n_cols);
assignments.set_size(data.n_cols);
range::RangeSearch<> rangeSearcher(data);
math::Range validRadius(0, radius);
std::vector<std::vector<size_t> > neighbors;
std::vector<std::vector<double> > distances;
// For each seed, perform mean shift algorithm.
for (size_t i = 0; i < pSeeds->n_cols; ++i)
{
// Initial centroid is the seed itself.
allCentroids.col(i) = pSeeds->unsafe_col(i);
for (size_t completedIterations = 0; completedIterations < maxIterations;
completedIterations++)
{
// Store new centroid in this.
arma::colvec newCentroid = arma::zeros<arma::colvec>(pSeeds->n_rows);
rangeSearcher.Search(allCentroids.unsafe_col(i), validRadius,
neighbors, distances);
if (neighbors[0].size() <= 1)
break;
// Calculate new centroid.
if (!CalculateCentroid(data, neighbors[0], distances[0], newCentroid))
newCentroid = allCentroids.unsafe_col(i);
// If the mean shift vector is small enough, it has converged.
if (metric::EuclideanDistance::Evaluate(newCentroid,
allCentroids.unsafe_col(i)) < 1e-3 * radius)
{
// Determine if the new centroid is duplicate with old ones.
bool isDuplicated = false;
for (size_t k = 0; k < centroids.n_cols; ++k)
{
const double distance = metric::EuclideanDistance::Evaluate(
allCentroids.unsafe_col(i), centroids.unsafe_col(k));
if (distance < radius)
{
isDuplicated = true;
break;
}
}
if (!isDuplicated)
centroids.insert_cols(centroids.n_cols, allCentroids.unsafe_col(i));
// Get out of the loop.
break;
}
// Update the centroid.
allCentroids.col(i) = newCentroid;
}
}
// Assign centroids to each point.
neighbor::KNN neighborSearcher(centroids);
arma::mat neighborDistances;
arma::Mat<size_t> resultingNeighbors;
neighborSearcher.Search(data, 1, resultingNeighbors, neighborDistances);
assignments = resultingNeighbors.t();
}
void RefinedStart::Cluster(const MatType& data,
const size_t clusters,
arma::Col<size_t>& assignments) const
{
math::RandomSeed(std::time(NULL));
// This will hold the sampled datasets.
const size_t numPoints = size_t(percentage * data.n_cols);
MatType sampledData(data.n_rows, numPoints);
// vector<bool> is packed so each bool is 1 bit.
std::vector<bool> pointsUsed(data.n_cols, false);
arma::mat sampledCentroids(data.n_rows, samplings * clusters);
// We will use these objects repeatedly for clustering.
arma::Col<size_t> sampledAssignments;
arma::mat centroids;
KMeans<> kmeans;
for (size_t i = 0; i < samplings; ++i)
{
// First, assemble the sampled dataset.
size_t curSample = 0;
while (curSample < numPoints)
{
// Pick a random point in [0, numPoints).
size_t sample = (size_t) math::RandInt(data.n_cols);
if (!pointsUsed[sample])
{
// This point isn't used yet. So we'll put it in our sample.
pointsUsed[sample] = true;
sampledData.col(curSample) = data.col(sample);
++curSample;
}
}
// Now, using the sampled dataset, run k-means. In the case of an empty
// cluster, we re-initialize that cluster as the point furthest away from
// the cluster with maximum variance. This is not *exactly* what the paper
// implements, but it is quite similar, and we'll call it "good enough".
kmeans.Cluster(sampledData, clusters, sampledAssignments, centroids);
// Store the sampled centroids.
sampledCentroids.cols(i * clusters, (i + 1) * clusters - 1) = centroids;
pointsUsed.assign(data.n_cols, false);
}
// Now, we run k-means on the sampled centroids to get our final clusters.
kmeans.Cluster(sampledCentroids, clusters, sampledAssignments, centroids);
// Turn the final centroids into assignments.
assignments.set_size(data.n_cols);
for (size_t i = 0; i < data.n_cols; ++i)
{
// Find the closest centroid to this point.
double minDistance = std::numeric_limits<double>::infinity();
size_t closestCluster = clusters;
for (size_t j = 0; j < clusters; ++j)
{
const double distance = kmeans.Metric().Evaluate(data.col(i),
centroids.col(j));
if (distance < minDistance)
{
minDistance = distance;
closestCluster = j;
}
}
// Assign the point to its closest cluster.
assignments[i] = closestCluster;
}
}