Crate solow_decomposition 

solow-decomposition

Matrix-decomposition estimators complementing [solow-multivariate]’s classical PCA / factor / rotation surface.

• KernelPca — Schölkopf-Smola-Müller (1998) kernel PCA with Linear, Rbf, and Polynomial kernels; centering in feature space matches the reference KernelPCA(fit_inverse_transform=False).
• FastIca — Hyvärinen (1999) FastICA with the logcosh and exp nonlinearities and symmetric decorrelation.
• Nmf — Lee-Seung (2001) multiplicative-update non-negative matrix factorisation for the Frobenius objective.

All three consume a dense n × d matrix and produce an n × k projection (KernelPCA, FastICA) or a n × k × k × d factorisation (NMF). Deterministic under a caller-supplied seed.

Re-exports

pub use dictionary_learning::DictionaryLearning;

pub use ica::FastIca;

pub use ica::IcaFun;

pub use incremental_pca::IncrementalPCA;

pub use kernel_pca::KernelKind;

pub use kernel_pca::KernelPca;

pub use lda::LatentDirichletAllocation;

pub use minibatch_dict::MiniBatchDictionaryLearning;

pub use minibatch_nmf::MiniBatchNmf;

pub use nmf::Nmf;

pub use random_projection::johnson_lindenstrauss_min_dim;

pub use random_projection::GaussianRandomProjection;

pub use random_projection::SparseRandomProjection;

pub use sparse_pca::SparsePCA;

pub use truncated_svd::TruncatedSVD;

Modules

dictionary_learning

DictionaryLearning — sparse dictionary learning à la Mairal-Bach- Ponce-Sapiro (2009). Alternating scheme:

ica

FastICA (Hyvärinen 1999) with symmetric decorrelation.

incremental_pca

IncrementalPCA — the sequential-fit variant of PCA (Ross et al. 2008). Fits by accumulating running mean and running scatter, then decomposes at the end of the stream (or on demand).

kernel_pca

Kernel PCA (Schölkopf, Smola & Müller 1998).

lda

Latent Dirichlet Allocation (Blei-Ng-Jordan 2003) — the topic model.

minibatch_dict

MiniBatchDictionaryLearning — online update of the (D, α) pair on random mini-batches (Mairal-Bach-Ponce-Sapiro 2010).

minibatch_nmf

MiniBatchNMF — online non-negative matrix factorisation via multiplicative-update mini-batches (Févotte-Idier 2011).

nmf

Non-negative Matrix Factorisation with multiplicative updates (Lee & Seung 2001) under the Frobenius objective.

prelude

Commonly-used imports.

random_projection

GaussianRandomProjection and SparseRandomProjection — the reference Johnson-Lindenstrauss lemma-inspired dimensionality reducers.

sparse_pca

SparsePCA — L1-penalised principal-component learning (Zou-Hastie-Tibshirani 2006).

truncated_svd

Truncated singular-value decomposition (also known as LSA).