Partial Least Squares (PLS) is an efficient multivariate statistical regression technique that has proven to be particularly useful for analysis of highly collinear data. To predict response variables Y from independent variables X, PLS attempts to find a set of common orthogonal latent variables by projecting both X and Y onto a new subspace respectively. As an increasing interest in multiway ...

An accurate and generally applicable method for estimating aqueous solubilities for a diverse set of 1297 organic compounds based on multilinear regression and artificial neural network modeling was developed. Molecular connectivity, shape, and atom-type electrotopological state (E-state) indices were used as structural parameters. The data set was divided into a training set of 884 compounds a...

Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), Nonnegative Matrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (SmoCA) and Sparse Component Analysis (SCA). Moreover, tensor decompositions hav...

the acidity constants (pka) of thirty four (34) ;-substituted carboxylic acids in aqueous solution havebeen calculated using conductor-like polarizable continuum (c-pcm) solvation model. the gasphaseenergies at the density functional theory (dft-mpw1pw91) and solvation energies athartree fock (hf) are combined to estimate the pka values which are very close to the experimentalvalues where, and ...

the acidity constants (pka) of thirty four (34) ;-substituted carboxylic acids in aqueous solution havebeen calculated using conductor-like polarizable continuum (c-pcm) solvation model. the gasphaseenergies at the density functional theory (dft-mpw1pw91) and solvation energies athartree fock (hf) are combined to estimate the pka values which are very close to the experimentalvalues where, and ...

A variety of results regarding multilinear Calderón-Zygmund singular integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur’s test, and a multilinear version of the T1 Theor...

A multilinear subspace regression model based on so called latent variable decomposition is introduced. Unlike standard regression methods which typically employ matrix (2D) data representations followed by vector subspace transformations, the proposed approach uses tensor subspace transformations to model common latent variables across both the independent and dependent data. The proposed appr...

This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank constraint, a difficult non convex problem. HOLRR computes efficiently an approximate solution of this problem, with solid theoretical guarantees. A kernel extension i...

We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.