CCA Module¶

src/fed_maxfuse/correlation_utils/

Canonical correlation analysis, centralized and federated. Conceptual background: Iterative Federated CCA.

Layout¶

Path	Role
`cca/centralized/`	Reference CCA (delegates to scikit-learn)
`cca/distributed/pls_w2a_node.py`	`PLSw2aNode` — federated Two-block Mode B PLS
`cca/distributed/pseudo_cca_node.py`	Pseudo-CCA variant
`cca/functions.py`	Shared CCA helpers
`pearson/correlation.py`	Pearson correlation

`PLSw2aNode`¶

Node-side implementation of Two-block Mode B PLS, decomposed so the singular-vector search can be distributed.

PLSw2aNode(n_components: int, max_iter: int = 500, target: bool = False)

Method	Corresponds to
`init_fit(data)`	Normalise the view: \(X^i_1 \leftarrow \texttt{normalize}(X^i)\)
`fit_start_iter(randomness_init_ratio)`	`NoiseInterpolation` — initialise latent scores without sharing a real data column
`fit_svpm_iter(...)`	One singular-vector power-method iteration
`sign_for_svd_flip(weights)`	Sign convention — forces the largest-magnitude element positive
`fit_finish_iter(...)`	Scores, loadings, deflation
`fit_finish()`	Assemble \(U\), \(\Gamma\)
`transform(data)`	Project: \(U\Gamma^\top X\)

Why Mode B PLS rather than classical CCA¶

Classical CCA overfits when features greatly outnumber samples, which is the single-cell regime. Two-block Mode B PLS weights indicators by predictive association and is robust when indicator quality is heterogeneous. It also decomposes: four of five per-component steps are purely local, leaving one coupled step to federate.

What crosses the wire¶

Only latent score vectors \(\xi_k, \omega_k\) (length \(N\) = samples) and a scalar convergence norm \(\delta\). Never weight vectors, which live in feature space.

`CCAType`¶

Selects the implementation:

Value	Meaning
`sklearn`	scikit-learn CCA (centralized reference)
`pseudo`	Pseudo-CCA variant
`plswtb`	Two-block Mode B PLS
`plswtb_rand_init`	Mode B PLS with noise-interpolated initialisation

Configuration¶

"cca": {
  "randomness": 0.6,
  "components": 20,
  "max_loop_iterations": 2000,
  "bad_filter_wt": 0.0
}

Key	Symbol	Notes
`components`	\(C\)	Shared components
`max_loop_iterations`	\(K\)	SVPM iteration cap; a large value is recommended
`randomness`	\(w\)	0.6 recommended; 0.0 shares a real data column
`bad_filter_wt`	—	Pairs dropped before each internal CCA fit

Cost

Message complexity is \(T \times C \times K\) round trips in the worst case, the dominant cost of the system.