Inferring multilinear dependences within multi-way data can be performed by tensor decompositions. Because of the presence of noise or modeling errors, the problem actually requires an approximation of lower rank. We concentrate on the case of real 3-way data arrays with nonnegative values, and propose an unconstrained algorithm resorting to an hyperspherical parameterization implemented in a novel way, and to a global line search. To illustrate the contribution, we report computer experiments allowing to detect and identify toxic molecules in a solvent with the help of fluorescent spectroscopy measurements.