void NaiveBayesClassifier<MatType>::Classify(const MatType& data,
arma::Row<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) // log(exp(value)) == value
exponents(j) = arma::accu(diffs.col(j) % rhs.unsafe_col(j));
// Calculate probability as sum of logarithm to decrease floating point
// errors.
testProbs.col(i) += (data.n_rows / -2.0 * log(2 * M_PI) - 0.5 *
log(arma::det(arma::diagmat(variances.col(i)))) + 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;
}
/**
* Calculates the multivariate Gaussian probability density function for each
* data point (column) in the given matrix, with respect to the given mean and
* variance.
*
* @param x List of observations.
* @param mean Mean of multivariate Gaussian.
* @param cov Covariance of multivariate Gaussian.
* @param probabilities Output probabilities for each input observation.
*/
inline void phi(const arma::mat& x,
const arma::vec& mean,
const arma::mat& cov,
arma::vec& probabilities)
{
// Column i of 'diffs' is the difference between x.col(i) and the mean.
arma::mat diffs = x - (mean * arma::ones<arma::rowvec>(x.n_cols));
// Now, we only want to calculate the diagonal elements of (diffs' * cov^-1 *
// diffs). We just don't need any of the other elements. We can calculate
// the right hand part of the equation (instead of the left side) so that
// later we are referencing columns, not rows -- that is faster.
arma::mat rhs = -0.5 * inv(cov) * diffs;
arma::vec exponents(diffs.n_cols); // We will now fill this.
for (size_t i = 0; i < diffs.n_cols; i++)
exponents(i) = exp(accu(diffs.unsafe_col(i) % rhs.unsafe_col(i)));
probabilities = pow(2 * M_PI, (double) mean.n_elem / -2.0) *
pow(det(cov), -0.5) * exponents;
}
Eigen::MatrixXd build_exponents(size_t max_exponent,size_t xdimensions)
{
std::vector<size_t> current_exponent_scratch(xdimensions);
std::vector<std::vector<size_t>> output_list;
size_t maxtop=1;
for(size_t k=0;k<xdimensions;k++)
{
maxtop*=max_exponent;
}
for(size_t ei=0;ei<maxtop;ei++)
{
current_exponent_scratch.resize(xdimensions,0);
size_t cei=ei;
size_t total=0;
for(size_t k=0;k<xdimensions;k++)
{
size_t remainder=cei % max_exponent;
current_exponent_scratch[k]=remainder;
total+=remainder;
cei/=max_exponent;
if(cei == 0) break;
}
if(total <= max_exponent)
{
output_list.emplace_back(current_exponent_scratch);
}
}
Eigen::MatrixXd exponents(xdimensions,output_list.size()); //exponent at dimension R for position col C
for(size_t c=0;c<exponents.cols();c++)
{
const vector<double> srcrows&=output_list[c];
for(size_t r=0;r<exponents.rows();r++)
{
exponents(r,c)=srcrows[r];
}
}
return exponents;
}
void SimultaneousMultiplication(Iterator result, const AbstractGroup<Element> &group, const Element &base, ConstIterator expBegin, ConstIterator expEnd)
{
unsigned int expCount = std::distance(expBegin, expEnd);
std::vector<WindowSlider<Element> > exponents(expCount);
unsigned int i;
bool notDone = false;
for (i=0; i<expCount; i++)
notDone = exponents[i].FindFirstWindow(group, *expBegin++) || notDone;
unsigned int expBitPosition = 0;
Element g = base;
while (notDone)
{
notDone = false;
for (i=0; i<expCount; i++)
{
if (expBitPosition < exponents[i].expLen && expBitPosition == exponents[i].windowBegin)
{
Element &bucket = exponents[i].buckets[exponents[i].nextBucket];
group.Accumulate(bucket, g);
exponents[i].FindNextWindow();
}
notDone = notDone || exponents[i].windowBegin < exponents[i].expLen;
}
if (notDone)
{
g = group.Double(g);
expBitPosition++;
}
}
for (i=0; i<expCount; i++)
{
Element &r = *result++;
std::vector<Element> &buckets = exponents[i].buckets;
r = buckets[buckets.size()-1];
if (buckets.size() > 1)
{
for (int j = buckets.size()-2; j >= 1; j--)
{
group.Accumulate(buckets[j], buckets[j+1]);
group.Accumulate(r, buckets[j]);
}
group.Accumulate(buckets[0], buckets[1]);
r = group.Add(group.Double(r), buckets[0]);
}
}
}