/**
* Use PCA for dimensionality reduction on the given dataset. This will save
* as many dimensions as necessary to retain at least the given amount of
* variance (specified by parameter varRetained). The amount should be
* between 0 and 1; if the amount is 0, then only 1 dimension will be
* retained. If the amount is 1, then all dimensions will be retained.
*
* The method returns the actual amount of variance retained, which will
* always be greater than or equal to the varRetained parameter.
*/
double PCA::Apply(arma::mat& data, const double varRetained) const
{
// Parameter validation.
if (varRetained < 0)
Log::Fatal << "PCA::Apply(): varRetained (" << varRetained << ") must be "
<< "greater than or equal to 0." << endl;
if (varRetained > 1)
Log::Fatal << "PCA::Apply(): varRetained (" << varRetained << ") should be "
<< "less than or equal to 1." << endl;
arma::mat coeffs;
arma::vec eigVal;
Apply(data, data, eigVal, coeffs);
// Calculate the dimension we should keep.
size_t newDimension = 0;
double varSum = 0.0;
eigVal /= arma::sum(eigVal); // Normalize eigenvalues.
while ((varSum < varRetained) && (newDimension < eigVal.n_elem))
{
varSum += eigVal[newDimension];
++newDimension;
}
// varSum is the actual variance we will retain.
if (newDimension < eigVal.n_elem)
data.shed_rows(newDimension, data.n_rows - 1);
return varSum;
}
/**
* Apply Dimensionality Reduction using Principal Component Analysis
* to the provided data set.
*
* @param data - M x N Data matrix
* @param newDimension - matrix consisting of N column vectors,
* where each vector is the projection of the corresponding data vector
* from data matrix onto the basis vectors contained in the columns of
* coeff/eigen vector matrix with only newDimension number of columns chosen.
*/
void PCA::Apply(arma::mat& data, const size_t newDimension) const
{
arma::mat coeffs;
arma::vec eigVal;
Apply(data, data, eigVal, coeffs);
if (newDimension < coeffs.n_rows && newDimension > 0)
data.shed_rows(newDimension, data.n_rows - 1);
}
void KernelPCA<KernelType, KernelRule>::Apply(arma::mat& data,
const size_t newDimension)
{
arma::mat coeffs;
arma::vec eigVal;
Apply(data, data, eigVal, coeffs, newDimension);
if (newDimension < coeffs.n_rows && newDimension > 0)
data.shed_rows(newDimension, data.n_rows - 1);
}
/**
* Use PCA for dimensionality reduction on the given dataset. This will save
* the newDimension largest principal components of the data and remove the
* rest. The parameter returned is the amount of variance of the data that is
* retained; this is a value between 0 and 1. For instance, a value of 0.9
* indicates that 90% of the variance present in the data was retained.
*
* @param data Data matrix.
* @param newDimension New dimension of the data.
* @return Amount of the variance of the data retained (between 0 and 1).
*/
double PCA::Apply(arma::mat& data, const size_t newDimension) const
{
// Parameter validation.
if (newDimension == 0)
Log::Fatal << "PCA::Apply(): newDimension (" << newDimension << ") cannot "
<< "be zero!" << endl;
if (newDimension > data.n_rows)
Log::Fatal << "PCA::Apply(): newDimension (" << newDimension << ") cannot "
<< "be greater than the existing dimensionality of the data ("
<< data.n_rows << ")!" << endl;
arma::mat coeffs;
arma::vec eigVal;
Apply(data, data, eigVal, coeffs);
if (newDimension < coeffs.n_rows)
// Drop unnecessary rows.
data.shed_rows(newDimension, data.n_rows - 1);
// Calculate the total amount of variance retained.
return (sum(eigVal.subvec(0, newDimension - 1)) / sum(eigVal));
}