Fit a graph-Fourier discriminator on a frozen co-expression graph

Learns a single-sample circulating-miRNA discriminator by building a frozen feature-feature co-expression graph from the training set, extracting the low-frequency graph-Fourier modes of its symmetric-normalized Laplacian, and fitting a frozen linear head on per-specimen graph-spectral coordinates. Each specimen is represented by a robust centered log-ratio (rCLR) transform computed from that specimen alone: positive entries are log-transformed and centered by the mean log abundance of the specimen's own positive entries, while zeros remain neutral at 0.

Usage

fit_gsp_gft(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: cor_method, one of "spearman" or "pearson" (default "spearman"); graph_k, positive integer number of nearest neighbours retained per feature before symmetrization (default min(10L, D - 1L)); n_modes, positive integer cap on retained low-frequency graph Fourier modes (default min(10L, D)); min_features, positive integer scoring overlap floor (default 3L); and eps, positive finite numerical floor (default 1e-8).

Value

A plain list of class gsp_gft_model containing the frozen feature_universe, low-frequency basis U_low, retained eigenvalues eigvals_low, graph settings, frozen linear head, and the resolved hyperparameters.

Details

The co-expression graph is learned from training rCLR signals only. The absolute training feature-feature correlation matrix is kNN-sparsified with a deterministic feature-index tie break, symmetrized by union, and converted to the symmetric-normalized graph Laplacian $$L = I - D^{-1/2} W D^{-1/2}.$$ Its eigenvectors, ordered by increasing eigenvalue, define graph-Fourier coordinates. The retained low-frequency coordinates are standardized by frozen training means and scales and then passed to a frozen linear head. A binomial GLM is used when it is finite and converged; otherwise the fit falls back to a diagonal-LDA mean-difference head in the same standardized coordinates. Larger scores are oriented to be more case-like.

At inference, no statistic is estimated from the scoring matrix. The graph, basis, coordinate center/scale, and head coefficients are all frozen at fit time from the training data. Each row's rCLR vector uses only that row's own positive present features, with absent and zero features encoded as 0.

References

Shuman DI, Narang SK, Frossard P, Ortega A, Vandergheynst P. (2013) The emerging field of signal processing on graphs. IEEE Signal Processing Magazine 30: 83-98.

Chung FRK. (1997) Spectral Graph Theory. American Mathematical Society.

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
model <- fit_gsp_gft(X, y)
score <- score_gsp_gft(model, X)
} # }