Struct petal_decomposition::RandomizedPca

pub struct RandomizedPca<A, R> where
    A: Scalar,
    R: Rng,  { /* private fields */ }

Principal component analysis using randomized singular value decomposition.

This uses randomized SVD (singular value decomposition) proposed by Halko et al. [1] to reduce the dimensionality of the input data. The data is centered for each feature before applying randomized SVD.

Examples

use petal_decomposition::RandomizedPcaBuilder;

let x = ndarray::arr2(&[[0_f64, 0_f64], [1_f64, 1_f64], [2_f64, 2_f64]]);
let mut pca = RandomizedPcaBuilder::new(1).build();
let y = pca.fit_transform(&x).unwrap();  // [-2_f64.sqrt(), 0_f64, 2_f64.sqrt()]
assert!((y[(0, 0)].abs() - 2_f64.sqrt()).abs() < 1e-8);
assert!(y[(1, 0)].abs() < 1e-8);
assert!((y[(2, 0)].abs() - 2_f64.sqrt()).abs() < 1e-8);

References

1. N. Halko, P. G. Martinsson, and J. A. Tropp. Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions. SIAM Review, 53(2), 217–288, 2011.

Implementations

impl<A> RandomizedPca<A, Pcg> where
    A: Scalar, 

pub fn new(n_components: usize) -> Self

Creates a PCA model based on randomized SVD.

The random matrix for randomized SVD is created from a PCG random number generator (the XSL 128/64 (MCG) variant on a 64-bit CPU and the XSH RR 64/32 (LCG) variant on a 32-bit CPU), initialized with a randomly-generated seed.

pub fn with_seed(n_components: usize, seed: u128) -> Self

Creates a PCA model based on randomized SVD, with a PCG random number generator initialized with the given seed.

It uses a PCG random number generator (the XSL 128/64 (MCG) variant on a 64-bit CPU and the XSH RR 64/32 (LCG) variant on a 32-bit CPU). Use with_rng for a different random number generator.

impl<A, R> RandomizedPca<A, R> where
    A: Scalar,
    R: Rng, 

pub fn with_rng(n_components: usize, rng: R) -> Self

Creates a PCA model with the given number of components and random number generator. The random number generator is used to create a random matrix for randomized SVD.

impl<A, R> RandomizedPca<A, R> where
    A: Scalar + FromPrimitive + Lapack,
    A::Real: ScalarOperand + FromPrimitive,
    R: Rng, 

pub fn components(&self) -> &Array2<A>

Returns the principal axes in feature space.

pub fn mean(&self) -> &Array1<A>

Returns the per-feature empirical mean.

pub fn n_components(&self) -> usize

Returns the number of components.

pub fn singular_values(&self) -> &Array1<A::Real>

Returns sigular values.

pub fn explained_variance_ratio(&self) -> Array1<A::Real>

Returns the ratio of explained variance for each component.

pub fn fit<S>(
    &mut self,
    input: &ArrayBase<S, Ix2>
) -> Result<(), DecompositionError> where
    S: Data<Elem = A>, 

Fits the model with input.

Errors

• DecompositionError::InvalidInput if any of the dimensions of input is less than the number of components, or the layout of input is incompatible with LAPACK.
• DecompositionError::LinalgError if the underlying Singular Vector Decomposition routine fails.

pub fn transform<S>(
    &self,
    input: &ArrayBase<S, Ix2>
) -> Result<Array2<A>, DecompositionError> where
    S: Data<Elem = A>, 

Applies dimensionality reduction to input.

Errors

• DecompositionError::InvalidInput if the number of features in input does not match that of the training data.

pub fn fit_transform<S>(
    &mut self,
    input: &ArrayBase<S, Ix2>
) -> Result<Array2<A>, DecompositionError> where
    S: Data<Elem = A>, 

Fits the model with input and apply the dimensionality reduction on input.

This is equivalent to calling both fit and transform for the same input.

Errors

• DecompositionError::InvalidInput if any of the dimensions of input is less than the number of components, or the layout of input is incompatible with LAPACK.
• DecompositionError::LinalgError if the underlying Singular Vector Decomposition routine fails.

pub fn inverse_transform<S>(
    &self,
    input: &ArrayBase<S, Ix2>
) -> Result<Array2<A>, DecompositionError> where
    S: Data<Elem = A>, 

Transforms data back to its original space.

Errors

Returns DecompositionError::InvalidInput if the number of rows of input is different from that of the training data, or the number of columns of input is different from the number of components.