Fit a Nystrom diffusion-map discriminator on frozen landmarks

Learns a single-sample circulating-miRNA discriminator by selecting frozen training landmarks, building a diffusion-map geometry on their per-sample rCLR coordinates, embedding every training specimen by the Nystrom out-of-sample formula, and fitting a frozen linear head. The rCLR transform is computed independently for each specimen: positive entries are log transformed and centered by that specimen's own mean log-positive abundance, while zero entries remain at 0.

Usage

fit_man_nystrom(X_train, y_train, meta_train = NULL, hp = list())

Arguments

X_train: Numeric matrix (samples $\times$ features) of non-negative abundance values. Columns must be uniquely named feature ids.
y_train: Integer/numeric 0/1 labels aligned to X_train; 1 is case/disease and 0 is control.
meta_train: Optional per-sample metadata. Accepted for interface uniformity and ignored by this method.
hp: List of frozen hyperparameters: n_landmarks positive integer landmark cap (default min(200L, nrow(X_train))); n_components positive integer diffusion-coordinate cap (default 10L); t positive integer diffusion time (default 1L); gamma positive RBF bandwidth, or NULL for the landmark median heuristic (default NULL); eig_floor non-negative eigenvalue floor for retained non-trivial modes (default 1e-6); min_features positive integer scoring overlap floor (default 3L); eps positive numerical floor (default 1e-8); and seed non-negative integer used only for deterministic landmark subsampling while restoring the global RNG state (default 1L).

Value

A plain list of class man_nystrom_model containing the frozen training feature_universe, rCLR landmarks, landmark_idx, frozen gamma, diffusion settings, cached full-universe geometry, frozen linear head, and resolved hp.

Details

The landmark graph is learned once from training data. For landmarks $L_j$, the RBF kernel $W_{ij}=\exp(-\gamma\|L_i-L_j\|^2)$ is symmetrically degree-normalized and eigendecomposed. The trivial top diffusion pair is dropped; retained right eigenvectors of the row-stochastic transition matrix define the diffusion coordinates. A new specimen $z$ is embedded from only its own affinities to the frozen landmarks: $$\Psi_k(z)=\lambda_k^{t-1}\sum_j p_j(z)\psi_{jk},$$ where $p_j(z)$ is the row-normalized RBF affinity of $z$ to landmark $j$. These coordinates are standardized by frozen training means/scales and passed to a frozen binomial-GLM head, with a diagonal-LDA mean-difference fallback if the GLM fit is numerically unsafe. Larger scores are oriented to be more case-like.

No scored-batch statistic is used. At scoring, the present feature set is intersect(model$feature_universe, colnames(X)); the landmark geometry is re-derived from frozen landmark coordinates restricted to those features, and each scored row contributes only its own per-sample rCLR vector and its own affinity row to the frozen landmarks. If fewer than hp$min_features model features are present, the documented neutral score 0 is returned for every row.

References

Coifman RR, Lafon S. (2006) Diffusion maps. Applied and Computational Harmonic Analysis 21: 5-30.

Bengio Y, Paiement JF, Vincent P, Delalleau O, Le Roux N, Ouimet M. (2004) Out-of-sample extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering. Advances in Neural Information Processing Systems 16.

Examples

if (FALSE) { # \dontrun{
set.seed(1)
X <- matrix(stats::rgamma(60 * 30, shape = 3), nrow = 60,
            dimnames = list(NULL, paste0("miR-", seq_len(30))))
y <- rep(c(0, 1), each = 30)
X[y == 1, 1:6] <- X[y == 1, 1:6] + 20
X[y == 0, 7:12] <- X[y == 0, 7:12] + 20
model <- fit_man_nystrom(X, y)
score <- score_man_nystrom(model, X)
} # }