Feat: implement Random Projections

[GBathie]

This PR implements random projection techniques for dimensionality reduction, as seen in the sklean.random_projection module of scikit-learn

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 8.79121% with 83 lines in your changes are missing coverage. Please review.

Project coverage is 35.87%. Comparing base (4e40ce6) to head (6b9c2a4).

Files	Patch %	Lines
...nfa-reduction/src/random_projection/hyperparams.rs	3.44%	28 Missing :warning:
...s/linfa-reduction/src/random_projection/methods.rs	0.00%	26 Missing :warning:
...infa-reduction/src/random_projection/algorithms.rs	21.87%	25 Missing :warning:
...ms/linfa-reduction/src/random_projection/common.rs	0.00%	4 Missing :warning:

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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #332      +/-   ##
==========================================
- Coverage   36.18%   35.87%   -0.32%     
==========================================
  Files          92       96       +4     
  Lines        6218     6303      +85     
==========================================
+ Hits         2250     2261      +11     
- Misses       3968     4042      +74     

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[quietlychris]

I've done a quick review; this looks good to me, but have requested @bytesnake also give it a look as he is probably more familiar with the algorithm side of things.

[bytesnake]

I've done a quick review; this looks good to me, but have requested @bytesnake also give it a look as he is probably more familiar with the algorithm side of things.

thank you for reviewing @relf @quietlychris

[GBathie]

Thank you for the reviews, and @relf for the suggestions, I have implemented them.

Changes:

• The rng field for both random projections structs is no longer optional, and defaults to Xoshiro256Plus with a fixed seed if not provided by the user.
• Renamed precision parameter to eps, as increasing this parameter results in a lower dimension embedding and often yields lower classification performance.
• Added a check that the projections reduce the dimension of the data, returning an error otherwise. Added tests for this behavior.
• Added a test for the function that computes the embedding dimension from a given epsilon, against values from scikit-learn .
• Fixed reference issue in docs and other minor issues.

[GBathie]

Thanks for your contribution and the changes. Now, gaussian and sparse random projection codes look very alike, I am wondering if you could not refactor even further by using zero-sized types and a unique RandomProjection generic type, something like:

struct Gaussian;
struct Sparse;

pub struct RandomProjectionValidParams<RandomMethod, R: Rng + Clone> {
    pub params: RandomProjectionParamsInner,
    pub rng: Option<R>,
    pub method: std::marker::PhantomData<RandomMethod>,
}

pub struct RandomProjectionParams<RandomMethod, R: Rng + Clone>(
    pub(crate) RandomProjectionValidParams<RandomMethod, R>,
);

pub struct RandomProjection<RandomMethod, F: Float> {
    projection: Array2<F>,
    method: std::marker::PhantomData<RandomMethod>,
}

pub struct GaussianRandomProjection<F: Float> = RandomProjection<Gaussian, F: Float>;
pub struct SparseRandomProjection<F: Float> = RandomProjection<Sparse, F: Float>;

impl<F, Rec, T, R> Fit<Rec, T, ReductionError> for RandomProjectionValidParams<Gausssian, R>
where
    F: Float,
    Rec: Records<Elem = F>,
    StandardNormal: Distribution<F>,
    R: Rng + Clone,
{
    type Object = RandomProjection<Gaussian, F>;

    fn fit(&self, dataset: &linfa::DatasetBase<Rec, T>) -> Result<Self::Object, ReductionError> {...}
}

impl<F, Rec, T, R> Fit<Rec, T, ReductionError> for RandomProjectionValidParams<Sparse, R>
where
    F: Float,
    Rec: Records<Elem = F>,
    StandardNormal: Distribution<F>,
    R: Rng + Clone,
{
    type Object = RandomProjection<Sparse, F>;

    fn fit(&self, dataset: &linfa::DatasetBase<Rec, T>) -> Result<Self::Object, ReductionError> {...}
}

...

What do you think?

I think that's a very good suggestion, it will be easier to maintain than the previous approach using a macro to avoid code duplication. 6b9c2a4 implements a variation of this idea: all the logic has been refactored, and behavior depending on the projection method has been encapsulated in the ProjectionMethod trait. It also makes implementing other projection methods significantly easier.