pca

README

pca

This performs principal component's analysis and associated covariance matrix computations, operating on table.Table or tensor.Tensor data, using the gonum matrix interface.

There is support for the SVD version, which is much faster and produces the same results, with options for how much information to compute trading off with compute time.

Documentation

Overview

Package pca performs principal component's analysis and associated covariance matrix computations, operating on table.Table or tensor.Tensor data.

Index

• func CovarTableColumn(cmat tensor.Tensor, ix *table.IndexView, column string, mfun metric.Func64) error
• func CovarTableColumnStd(cmat tensor.Tensor, ix *table.IndexView, column string, met metric.StdMetrics) error
• func CovarTensor(cmat tensor.Tensor, tsr tensor.Tensor, mfun metric.Func64) error
• func CovarTensorStd(cmat tensor.Tensor, tsr tensor.Tensor, met metric.StdMetrics) error
• func TableColumnRowsVec(vec []float64, ix *table.IndexView, col tensor.Tensor, cidx int)
• func TensorRowsVec(vec []float64, tsr tensor.Tensor, cidx int)
• type PCA
  • func (pa *PCA) Init()
  • func (pa *PCA) PCA() error
  • func (pa *PCA) ProjectColumn(vals *[]float64, ix *table.IndexView, column string, idx int) error
  • func (pa *PCA) ProjectColumnToTable(projections *table.Table, ix *table.IndexView, column, labNm string, ...) error
  • func (pa *PCA) TableColumn(ix *table.IndexView, column string, mfun metric.Func64) error
  • func (pa *PCA) TableColumnStd(ix *table.IndexView, column string, met metric.StdMetrics) error
  • func (pa *PCA) Tensor(tsr tensor.Tensor, mfun metric.Func64) error
  • func (pa *PCA) TensorStd(tsr tensor.Tensor, met metric.StdMetrics) error
• type SVD
  • func (svd *SVD) Init()
  • func (svd *SVD) ProjectColumn(vals *[]float64, ix *table.IndexView, column string, idx int) error
  • func (svd *SVD) ProjectColumnToTable(projections *table.Table, ix *table.IndexView, column, labNm string, ...) error
  • func (svd *SVD) SVD() error
  • func (svd *SVD) TableColumn(ix *table.IndexView, column string, mfun metric.Func64) error
  • func (svd *SVD) TableColumnStd(ix *table.IndexView, column string, met metric.StdMetrics) error
  • func (svd *SVD) Tensor(tsr tensor.Tensor, mfun metric.Func64) error
  • func (svd *SVD) TensorStd(tsr tensor.Tensor, met metric.StdMetrics) error

Functions

func CovarTableColumn

func CovarTableColumn(cmat tensor.Tensor, ix *table.IndexView, column string, mfun metric.Func64) error

CovarTableColumn generates a covariance matrix from given column name in given IndexView of an table.Table, and given metric function (typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the PCA eigenvalue decomposition of the resulting covariance matrix.

func CovarTableColumnStd

func CovarTableColumnStd(cmat tensor.Tensor, ix *table.IndexView, column string, met metric.StdMetrics) error

CovarTableColumnStd generates a covariance matrix from given column name in given IndexView of an table.Table, and given metric function (typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the PCA eigenvalue decomposition of the resulting covariance matrix. This Std version is usable e.g., in Python where the func cannot be passed.

func CovarTensor

func CovarTensor(cmat tensor.Tensor, tsr tensor.Tensor, mfun metric.Func64) error

CovarTensor generates a covariance matrix from given tensor.Tensor, where the outer-most dimension is rows, and all other dimensions within that are covaried against each other, using given metric function (typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the PCA eigenvalue decomposition of the resulting covariance matrix.

func CovarTensorStd

func CovarTensorStd(cmat tensor.Tensor, tsr tensor.Tensor, met metric.StdMetrics) error

CovarTensorStd generates a covariance matrix from given tensor.Tensor, where the outer-most dimension is rows, and all other dimensions within that are covaried against each other, using given metric function (typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the PCA eigenvalue decomposition of the resulting covariance matrix. This Std version is usable e.g., in Python where the func cannot be passed.

func TableColumnRowsVec

func TableColumnRowsVec(vec []float64, ix *table.IndexView, col tensor.Tensor, cidx int)

TableColumnRowsVec extracts row-wise vector from given cell index into vec. vec must be of size ix.Len() -- number of rows

func TensorRowsVec

func TensorRowsVec(vec []float64, tsr tensor.Tensor, cidx int)

TensorRowsVec extracts row-wise vector from given cell index into vec. vec must be of size tsr.DimSize(0) -- number of rows

Types

type PCA

type PCA struct {

	// the covariance matrix computed on original data, which is then eigen-factored
	Covar tensor.Tensor `display:"no-inline"`

	// the eigenvectors, in same size as Covar - each eigenvector is a column in this 2D square matrix, ordered *lowest* to *highest* across the columns -- i.e., maximum eigenvector is the last column
	Vectors tensor.Tensor `display:"no-inline"`

	// the eigenvalues, ordered *lowest* to *highest*
	Values []float64 `display:"no-inline"`
}

PCA computes the eigenvalue decomposition of a square similarity matrix, typically generated using the correlation metric.

func (*PCA) Init

func (pa *PCA) Init()

func (*PCA) PCA

func (pa *PCA) PCA() error

PCA performs the eigen decomposition of the existing Covar matrix. Vectors and Values fields contain the results.

func (*PCA) ProjectColumn

func (pa *PCA) ProjectColumn(vals *[]float64, ix *table.IndexView, column string, idx int) error

ProjectColumn projects values from the given column of given table (via IndexView) onto the idx'th eigenvector (0 = largest eigenvalue, 1 = next, etc). Must have already called PCA() method.

func (*PCA) ProjectColumnToTable

func (pa *PCA) ProjectColumnToTable(projections *table.Table, ix *table.IndexView, column, labNm string, idxs []int) error

ProjectColumnToTable projects values from the given column of given table (via IndexView) onto the given set of eigenvectors (idxs, 0 = largest eigenvalue, 1 = next, etc), and stores results along with labels from column labNm into results table. Must have already called PCA() method.

func (*PCA) TableColumn

func (pa *PCA) TableColumn(ix *table.IndexView, column string, mfun metric.Func64) error

TableColumn is a convenience method that computes a covariance matrix on given column of table and then performs the PCA on the resulting matrix. If no error occurs, the results can be read out from Vectors and Values or used in Projection methods. mfun is metric function, typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the PCA eigenvalue decomposition of the resulting covariance matrix, which extracts the eigenvectors as directions with maximal variance in this matrix.

func (*PCA) TableColumnStd

func (pa *PCA) TableColumnStd(ix *table.IndexView, column string, met metric.StdMetrics) error

TableColumnStd is a convenience method that computes a covariance matrix on given column of table and then performs the PCA on the resulting matrix. If no error occurs, the results can be read out from Vectors and Values or used in Projection methods. mfun is a Std metric function, typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the PCA eigenvalue decomposition of the resulting covariance matrix, which extracts the eigenvectors as directions with maximal variance in this matrix. This Std version is usable e.g., in Python where the func cannot be passed.

func (*PCA) Tensor

func (pa *PCA) Tensor(tsr tensor.Tensor, mfun metric.Func64) error

Tensor is a convenience method that computes a covariance matrix on given tensor and then performs the PCA on the resulting matrix. If no error occurs, the results can be read out from Vectors and Values or used in Projection methods. mfun is metric function, typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the PCA eigenvalue decomposition of the resulting covariance matrix, which extracts the eigenvectors as directions with maximal variance in this matrix.

func (*PCA) TensorStd

func (pa *PCA) TensorStd(tsr tensor.Tensor, met metric.StdMetrics) error

TensorStd is a convenience method that computes a covariance matrix on given tensor and then performs the PCA on the resulting matrix. If no error occurs, the results can be read out from Vectors and Values or used in Projection methods. mfun is Std metric function, typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the PCA eigenvalue decomposition of the resulting covariance matrix, which extracts the eigenvectors as directions with maximal variance in this matrix. This Std version is usable e.g., in Python where the func cannot be passed.

type SVD

type SVD struct {

	// type of SVD to run: SVDNone is the most efficient if you only need the values which are always computed.  Otherwise, SVDThin is the next most efficient for getting approximate vectors
	Kind mat.SVDKind

	// condition value -- minimum normalized eigenvalue to return in values
	Cond float64 `default:"0.01"`

	// the rank (count) of singular values greater than Cond
	Rank int

	// the covariance matrix computed on original data, which is then eigen-factored
	Covar tensor.Tensor `display:"no-inline"`

	// the eigenvectors, in same size as Covar - each eigenvector is a column in this 2D square matrix, ordered *lowest* to *highest* across the columns -- i.e., maximum eigenvector is the last column
	Vectors tensor.Tensor `display:"no-inline"`

	// the eigenvalues, ordered *lowest* to *highest*
	Values []float64 `display:"no-inline"`
}

SVD computes the eigenvalue decomposition of a square similarity matrix, typically generated using the correlation metric.

func (*SVD) Init

func (svd *SVD) Init()

func (*SVD) ProjectColumn

func (svd *SVD) ProjectColumn(vals *[]float64, ix *table.IndexView, column string, idx int) error

ProjectColumn projects values from the given column of given table (via IndexView) onto the idx'th eigenvector (0 = largest eigenvalue, 1 = next, etc). Must have already called SVD() method.

func (*SVD) ProjectColumnToTable

func (svd *SVD) ProjectColumnToTable(projections *table.Table, ix *table.IndexView, column, labNm string, idxs []int) error

ProjectColumnToTable projects values from the given column of given table (via IndexView) onto the given set of eigenvectors (idxs, 0 = largest eigenvalue, 1 = next, etc), and stores results along with labels from column labNm into results table. Must have already called SVD() method.

func (*SVD) SVD

func (svd *SVD) SVD() error

SVD performs the eigen decomposition of the existing Covar matrix. Vectors and Values fields contain the results.

func (*SVD) TableColumn

func (svd *SVD) TableColumn(ix *table.IndexView, column string, mfun metric.Func64) error

TableColumn is a convenience method that computes a covariance matrix on given column of table and then performs the SVD on the resulting matrix. If no error occurs, the results can be read out from Vectors and Values or used in Projection methods. mfun is metric function, typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the SVD eigenvalue decomposition of the resulting covariance matrix, which extracts the eigenvectors as directions with maximal variance in this matrix.

func (*SVD) TableColumnStd

func (svd *SVD) TableColumnStd(ix *table.IndexView, column string, met metric.StdMetrics) error

TableColumnStd is a convenience method that computes a covariance matrix on given column of table and then performs the SVD on the resulting matrix. If no error occurs, the results can be read out from Vectors and Values or used in Projection methods. mfun is a Std metric function, typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the SVD eigenvalue decomposition of the resulting covariance matrix, which extracts the eigenvectors as directions with maximal variance in this matrix. This Std version is usable e.g., in Python where the func cannot be passed.

func (*SVD) Tensor

func (svd *SVD) Tensor(tsr tensor.Tensor, mfun metric.Func64) error

Tensor is a convenience method that computes a covariance matrix on given tensor and then performs the SVD on the resulting matrix. If no error occurs, the results can be read out from Vectors and Values or used in Projection methods. mfun is metric function, typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the SVD eigenvalue decomposition of the resulting covariance matrix, which extracts the eigenvectors as directions with maximal variance in this matrix.

func (*SVD) TensorStd

func (svd *SVD) TensorStd(tsr tensor.Tensor, met metric.StdMetrics) error

TensorStd is a convenience method that computes a covariance matrix on given tensor and then performs the SVD on the resulting matrix. If no error occurs, the results can be read out from Vectors and Values or used in Projection methods. mfun is Std metric function, typically Covariance or Correlation -- use Covar if vars have similar overall scaling, which is typical in neural network models, and use Correl if they are on very different scales -- Correl effectively rescales). A Covariance matrix computes the *row-wise* vector similarities for each pairwise combination of column cells -- i.e., the extent to which each cell co-varies in its value with each other cell across the rows of the table. This is the input to the SVD eigenvalue decomposition of the resulting covariance matrix, which extracts the eigenvectors as directions with maximal variance in this matrix. This Std version is usable e.g., in Python where the func cannot be passed.