predict.nmfkc.signed: Predict method for nmfkc.signed

In nmfkc: Non-Negative Matrix Factorization with Kernel Covariates

Predict method for nmfkc.signed

Description

Computes \widehat Y = X \, C \, A_{\mathrm{new}} (= X (C_{+} - C_{-})(A_{+}^{\mathrm{new}} - A_{-}^{\mathrm{new}})). For type = "response" the raw prediction is returned (possibly signed).

With signed covariates the scores \bm b_n = C\bm a_n can be negative, so the NMF-LAB recipe of normalizing \bm b_n to a membership vector does not apply. Since X is column-stochastic, \widehat{\bm y}_n = X\bm b_n still sums to \sum_q b_{qn} (close to one for one-hot targets) and is the least-squares estimate of the class indicator; for type = "prob" it is mapped to the probability simplex by the Euclidean projection

\widehat{\bm p}_n = \mathop{\mathrm{arg\,min}}_{\bm p \ge 0,\ \bm 1^\top \bm p = 1} \lVert \bm p - \widehat{\bm y}_n \rVert^2 = \max(\widehat{\bm y}_n - \tau_n \bm 1, 0),

the closest probability vector in the same Frobenius geometry the fit minimizes (Duchi et al. 2008; Wang & Carreira-Perpinan 2013; O(P \log P) per column by sorting). The former rule – clip negatives to zero and renormalize – is kept as prob.method = "clip". type = "class" is \arg\max_p \widehat y_{pn}, which both rules preserve.

Usage

## S3 method for class 'nmfkc.signed'
predict(object, newA = NULL, type = c("response", "prob", "class"), ...)

Arguments

object	A fitted "nmfkc.signed" object.
newA	Real-valued D \times N_{\mathrm{new}} covariate matrix.
type	Output: "response" (raw signed), "prob", or "class".
...	Hidden option prob.method: how type = "prob" maps \widehat{\bm y}_n to the simplex, "simplex" (default; Euclidean projection) or "clip" (clip negatives, renormalize).

Value

A numeric matrix ("response" or "prob") or a character vector ("class").

Lifecycle

This function is experimental. The interface may change in future versions.

References

Ding, C. H. Q., Li, T., & Jordan, M. I. (2010). Convex and semi-nonnegative matrix factorizations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(1), 45–55.

Duchi, J., Shalev-Shwartz, S., Singer, Y., & Chandra, T. (2008). Efficient projections onto the l1-ball for learning in high dimensions. Proceedings of the 25th International Conference on Machine Learning (ICML), 272–279.

Wang, W., & Carreira-Perpinan, M. A. (2013). Projection onto the probability simplex: an efficient algorithm with a simple proof, and an application. arXiv:1309.1541.

See Also

nmfkc.signed, nmfkc, nmfkc.signed.cv

nmfkc documentation built on Oct. 30, 2026, 9:06 a.m.