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 sptk::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.