pca

Functions

int main(int argc, char *argv[])

pca [ option ] [ infile ]

• -l int

  • length of vector \((1 \le L)\)

• -m int

  • order of vector \((0 \le M)\)

• -n int

  • number of principal components \((1 \le N \le L)\)

• -i int

  • number of iterations \((1 \le I)\)

• -d double

  • convergence threshold \((0 \le \epsilon)\)

• -u int

  • covariance type

    • 0 sample covariance

    • 1 unbiased covariance

    • 2 correlation

• -v str

  • double-type eigenvalues and proportions

• infile str

  • double-type vector sequence

• stdout

  • double-type mean vector and eigenvectors

In the below example, principal component analysis is applied to the three-dimensional training vectors contained in data.d. The eigenvectors and the eigenvalues are written to eigvec.dat and eigval.dat, repectively.

pca -l 3 -n 2 -v eigval.dat < data.d > eigvec.dat

The eigenvalues are sorted in descending order.

Parameters:

• argc – [in] Number of arguments.

• argv – [in] Argument vector.

Returns:

0 on success, 1 on failure.

See also

pcas

class PrincipalComponentAnalysis

Perform principal component analysis.

The input is the \(M\)-th order vectors:

\[ \begin{array}{cccc} \boldsymbol{x}(0), & \boldsymbol{x}(1), & \ldots, & \boldsymbol{x}(T-1), \end{array} \]

and the outputs are the \(M\)-th order mean vector

\[ \boldsymbol{m} = \frac{1}{T} \sum_{t=0}^{T-1} \boldsymbol{x}(t), \]

the \(M\)-th order eigenvectors

\[ \begin{array}{cccc} \boldsymbol{v}(0), & \boldsymbol{v}(1), & \ldots, & \boldsymbol{v}(M), \end{array} \]

and the corresponding eigenvalues:

\[ \begin{array}{cccc} \lambda(0), & \lambda(1), & \ldots, & \lambda(M). \end{array} \]

The eigenvalue problem is solved by the Jacobi iterative method.

Public Types

enum CovarianceType

Type of covariance.

Values:

enumerator kSampleCovariance

enumerator kUnbiasedCovariance

enumerator kCorrelation

enumerator kNumCovarianceTypes

Public Functions

PrincipalComponentAnalysis(int num_order, int num_iteration, double convergence_threshold, CovarianceType covariance_type)

Parameters:

• num_order – [in] Order of vector, \(M\).

• num_iteration – [in] Number of iterations.

• convergence_threshold – [in] Convergence threshold.

• covariance_type – [in] Type of covariance.

inline int GetNumOrder() const

Returns:

Order of vector.

inline int GetNumIteration() const

Returns:

Number of iterations.

inline double GetConvergenceThreshold() const

Returns:

Convergence threshold.

inline CovarianceType GetCovarianceType() const

Returns:

Type of covariance.

inline bool IsValid() const

Returns:

True if this object is valid.

bool Run(const std::vector<std::vector<double>> &input_vectors, std::vector<double> *mean_vector, std::vector<double> *eigenvalues, Matrix *eigenvectors, PrincipalComponentAnalysis::Buffer *buffer) const

Parameters:

• input_vectors – [in] \(M\)-th order input vectors. The shape is \([T, M+1]\).

• mean_vector – [out] \(M\)-th order mean vector.

• eigenvalues – [out] \(M+1\) eigenvalues.

• eigenvectors – [out] \(M\)-th order eigenvectors. The shape is \([M+1, M+1]\).

• buffer – [out] Buffer.

Returns:

True on success, false on failure.

class Buffer

Buffer for PrincipalComponentAnalysis class.