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Implement PCA for f32 and f64 #234

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Implement PCA for f32 and f64 #234

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95a3ebe
Add float param to PcaParams
YuhanLiin Aug 7, 2022
c3b8006
Generate f32 PCA impl using macros
YuhanLiin Aug 7, 2022
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161 changes: 88 additions & 73 deletions algorithms/linfa-reduction/src/pca.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -21,6 +21,8 @@
//! let dataset = embedding.predict(dataset);
//! ```
//!
use std::marker::PhantomData;

use crate::error::{ReductionError, Result};
#[cfg(not(feature = "blas"))]
use linfa_linalg::{lobpcg::TruncatedSvd, Order};
Expand All @@ -44,12 +46,13 @@ use linfa::{
serde(crate = "serde_crate")
)]
#[derive(Debug, Clone, PartialEq, Eq)]
pub struct PcaParams {
pub struct PcaParams<F> {
embedding_size: usize,
apply_whitening: bool,
_float: PhantomData<F>,
}

impl PcaParams {
impl<F> PcaParams<F> {
/// Apply whitening to the embedding vector
///
/// Whitening will scale the eigenvalues of the transformation such that the covariance will be
Expand All @@ -61,64 +64,6 @@ impl PcaParams {
}
}

/// Fit a PCA model given a dataset
///
/// The Principal Component Analysis takes the records of a dataset and tries to find the best
/// fit in a lower dimensional space such that the maximal variance is retained.
///
/// # Parameters
///
/// * `dataset`: A dataset with records in N dimensions
///
/// # Returns
///
/// A fitted PCA model with origin and hyperplane
impl<T, D: Data<Elem = f64>> Fit<ArrayBase<D, Ix2>, T, ReductionError> for PcaParams {
type Object = Pca<f64>;

fn fit(&self, dataset: &DatasetBase<ArrayBase<D, Ix2>, T>) -> Result<Pca<f64>> {
if dataset.nsamples() == 0 {
return Err(ReductionError::NotEnoughSamples);
} else if dataset.nfeatures() < self.embedding_size || self.embedding_size == 0 {
return Err(ReductionError::EmbeddingTooSmall(self.embedding_size));
}

let x = dataset.records();
// calculate mean of data and subtract it
// safe because of above 0 samples check
let mean = x.mean_axis(Axis(0)).unwrap();
let x = x - &mean;

// estimate Singular Value Decomposition
#[cfg(feature = "blas")]
let result =
TruncatedSvd::new(x, TruncatedOrder::Largest).decompose(self.embedding_size)?;
#[cfg(not(feature = "blas"))]
let result = TruncatedSvd::new_with_rng(x, Order::Largest, SmallRng::seed_from_u64(42))
.decompose(self.embedding_size)?;
// explained variance is the spectral distribution of the eigenvalues
let (_, sigma, mut v_t) = result.values_vectors();

// cut singular values to avoid numerical problems
let sigma = sigma.mapv(|x| x.max(1e-8));

// scale the embedding with the square root of the dimensionality and eigenvalue such that
// the product of the resulting matrix gives the unit covariance.
if self.apply_whitening {
let cov_scale = (dataset.nsamples() as f64 - 1.).sqrt();
for (mut v_t, sigma) in v_t.axis_iter_mut(Axis(0)).zip(sigma.iter()) {
v_t *= cov_scale / *sigma;
}
}

Ok(Pca {
embedding: v_t,
sigma,
mean,
})
}
}

/// Fitted Principal Component Analysis model
///
/// The model contains the mean and hyperplane for the projection of data.
Expand Down Expand Up @@ -150,34 +95,104 @@ pub struct Pca<F> {
mean: Array1<F>,
}

impl Pca<f64> {
macro_rules! impl_pca {
($F:ty) => {
/// Fit a PCA model given a dataset
///
/// The Principal Component Analysis takes the records of a dataset and tries to find the best
/// fit in a lower dimensional space such that the maximal variance is retained.
///
/// # Parameters
///
/// * `dataset`: A dataset with records in N dimensions
///
/// # Returns
///
/// A fitted PCA model with origin and hyperplane
impl<T, D: Data<Elem = $F>> Fit<ArrayBase<D, Ix2>, T, ReductionError> for PcaParams<$F> {
type Object = Pca<$F>;

fn fit(&self, dataset: &DatasetBase<ArrayBase<D, Ix2>, T>) -> Result<Pca<$F>> {
if dataset.nsamples() == 0 {
return Err(ReductionError::NotEnoughSamples);
} else if dataset.nfeatures() < self.embedding_size || self.embedding_size == 0 {
return Err(ReductionError::EmbeddingTooSmall(self.embedding_size));
}

let x = dataset.records();
// calculate mean of data and subtract it
// safe because of above 0 samples check
let mean = x.mean_axis(Axis(0)).unwrap();
let x = x - &mean;

// estimate Singular Value Decomposition
#[cfg(feature = "blas")]
let result =
TruncatedSvd::new(x, TruncatedOrder::Largest).decompose(self.embedding_size)?;
#[cfg(not(feature = "blas"))]
let result =
TruncatedSvd::new_with_rng(x, Order::Largest, SmallRng::seed_from_u64(42))
.decompose(self.embedding_size)?;
// explained variance is the spectral distribution of the eigenvalues
let (_, sigma, mut v_t) = result.values_vectors();

// cut singular values to avoid numerical problems
let sigma = sigma.mapv(|x| x.max(1e-8));

// scale the embedding with the square root of the dimensionality and eigenvalue such that
// the product of the resulting matrix gives the unit covariance.
if self.apply_whitening {
let cov_scale = (dataset.nsamples() as $F - 1.).sqrt();
for (mut v_t, sigma) in v_t.axis_iter_mut(Axis(0)).zip(sigma.iter()) {
v_t *= cov_scale / *sigma;
}
}

Ok(Pca {
embedding: v_t,
sigma,
mean,
})
}
}
};
}

impl_pca!(f64);
impl_pca!(f32);

impl<F: Float> Pca<F> {
/// Create default parameter set
///
/// # Parameters
///
/// * `embedding_size`: the target dimensionality
pub fn params(embedding_size: usize) -> PcaParams {
pub fn params(embedding_size: usize) -> PcaParams<F> {
PcaParams {
embedding_size,
apply_whitening: false,
_float: PhantomData,
}
}

/// Return the amount of explained variance per element
pub fn explained_variance(&self) -> Array1<f64> {
self.sigma.mapv(|x| x * x / (self.sigma.len() as f64 - 1.0))
pub fn explained_variance(&self) -> Array1<F> {
self.sigma
.mapv(|x| x * x / F::from(self.sigma.len() - 1).unwrap())
}

/// Return the normalized amount of explained variance per element
pub fn explained_variance_ratio(&self) -> Array1<f64> {
let ex_var = self.sigma.mapv(|x| x * x / (self.sigma.len() as f64 - 1.0));
pub fn explained_variance_ratio(&self) -> Array1<F> {
let ex_var = self
.sigma
.mapv(|x| x * x / F::from(self.sigma.len() - 1).unwrap());
let sum_ex_var = ex_var.sum();

ex_var / sum_ex_var
}

/// Return the singular values
pub fn singular_values(&self) -> &Array1<f64> {
pub fn singular_values(&self) -> &Array1<F> {
&self.sigma
}
}
Expand Down Expand Up @@ -234,7 +249,7 @@ mod tests {
has_autotraits::<DiffusionMapValidParams>();
has_autotraits::<DiffusionMapParams>();
has_autotraits::<ReductionError>();
has_autotraits::<PcaParams>();
has_autotraits::<PcaParams<f32>>();
has_autotraits::<Pca<f64>>();
}

Expand All @@ -248,7 +263,7 @@ mod tests {
let mut rng = SmallRng::seed_from_u64(42);

// rotate data by 45°
let tmp = Array2::random_using((300, 2), Uniform::new(-1.0f64, 1.), &mut rng);
let tmp = Array2::random_using((300, 2), Uniform::new(-1.0f32, 1.), &mut rng);
let q = array![[1., 1.], [-1., 1.]];

let dataset = Dataset::from(tmp.dot(&q));
Expand All @@ -258,7 +273,7 @@ mod tests {

// check that the covariance is unit diagonal
let cov = proj.t().dot(&proj);
assert_abs_diff_eq!(cov / (300. - 1.), Array2::eye(2), epsilon = 1e-5);
assert_abs_diff_eq!(cov / (300. - 1.), Array2::eye(2), epsilon = 1e-3);
}

/// Random number whitening test
Expand Down Expand Up @@ -296,7 +311,7 @@ mod tests {
let mut rng = SmallRng::seed_from_u64(3);

// generate normal distribution random data with N >> p
let data = Array2::random_using((1000, 500), StandardNormal, &mut rng);
let data = Array2::<f64>::random_using((1000, 500), StandardNormal, &mut rng);
let dataset = Dataset::from(data / 1000f64.sqrt());

let model = Pca::params(500).fit(&dataset).unwrap();
Expand Down Expand Up @@ -370,13 +385,13 @@ mod tests {

#[test]
fn test_explained_variance_diag() {
let dataset = Dataset::from(Array2::from_diag(&array![1., 1., 1., 1.]));
let dataset = Dataset::from(Array2::from_diag(&array![1.0f32, 1., 1., 1.]));
let model = Pca::params(3).fit(&dataset).unwrap();

assert_abs_diff_eq!(
model.explained_variance_ratio(),
array![1. / 3., 1. / 3., 1. / 3.],
epsilon = 1e-6
epsilon = 1e-3
);
}
}