Predicting Concentration Profiles from Fixed Spectra#

After fitting an MCR-NMF model using MinVol, FroALS, or FroFPGM, you may want to reuse the estimated \(W\) matrix (pure component spectra) to estimate \(H\) (concentration profiles) for new measurements \(X\).

The FPGM class provides a fast projected gradient method to solve the following problem:

\[\min_{H \geq 0} \; \|X - WH\|_F^2\]

It supports the same chemical constraints on \(H\) used in the main models: closure, normalization, unimodality, and fixed known values.

This makes it ideal for downstream applications like:

  • Reaction monitoring where new data arrives over time

  • High-throughput screening where spectra from new mixtures are analyzed

  • Scenarios where pure components are fixed and known from prior runs

Basic Usage Example#

Here’s how to reuse a previously estimated \(W\) to estimate \(H\) for new data.

from mcrnmf.datasets import load_rxn_spectra
from mcrnmf import SNPA, MinVol, FPGM

# Load the reference dataset
X, wv, time = load_rxn_spectra()
# splitting the X into two subsets for illustration
X_train, X_new = X[:, :-5], X[:, -5:]

num_components = 4
# Use SNPA to generate initial estimate for W and H from X_train
snpa = SNPA(rank=num_components)
snpa.fit(X_train)
Wi, Hi = snpa.W, snpa.H

# estimate W from X_train using MinVol
mvol = MinVol(
    rank=num_components,
    constraint_kind=1,
    unimodal={"H": True},
    lambdaa=1e-4,
    iter_max=2000
)
mvol.fit(X=X_train, Wi=Wi, Hi=Hi)
# the value of W we will use for predicting H for X_new
W = mvol.W

# Create FPGM solver with same constraints on H as specified for MinVol
fpgm = FPGM(constraint_kind=1, tol=1e-4, iter_max=500)

# Solve for H on new data with unimodality
H_new, converged = fpgm.solve(X=X_new, W=W, unimodal_H=True)

print(f"Converged: {converged}")
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