The PARAFAC tensor decomposition has enjoyed an increasing success in exploratory multi-aspect data mining scenarios. A major challenge remains the estimation of the number of latent factors (i.e., the rank) of the decomposition, which yields high-quality, interpretable results. Previously, we have proposed an automated tensor mining method which leverages a well-known quality heuristic from th...

In this paper, we address the problem of multipath parameter estimation of time-varying space-time wireless channels based on PARAFAC modeling. We exploit the different varying rates in the structure of the multipath channel over multiple data-blocks to build a 3D tensor from the received signal. The proposed estimation methods make use of a training sequence that is periodically extended over ...

The objectives of this study were to evaluate the binding behavior of Cu(II) and Eu(III) with water extractable organic matter (WEOM) in soil, and assess the competitive effect of the cations. Excitation-emission matrix (EEM) fluorescence spectrometry was used in combination with parallel factor analysis (PARAFAC) to obtain four WEOM components: fulvic-like, humic-like, microbial degraded humic...

Assessing the factorial invariance of two-way rating designs such as ratings of concepts on several scales by different groups can be carried out with three-way models such as the Parafac and Tucker models. By their definitions these models are double-metric factorially invariant. The differences between these models lie in their handling of the links between the concept and scale spaces. These...

We propose two new multilinear operators for expressing the matrix compositions that are needed in the Tucker and PARAFAC (CANDECOMP) decompositions. The first operator, which we call the Tucker operator, is shorthand for performing an n-mode matrix multiplication for every mode of a given tensor and can be employed to consisely express the Tucker decomposition. The second operator, which we ca...

Several models in data analysis are estimated by minimizing the objective function defined as the residual sum of squares between the model and the data.A necessary and sufficient condition for the existence of a least squares estimator is that the objective function attains its infimum at a unique point. It is shown that the objective function for Parafac-2 need not attain its infimum, and tha...

The amounts of drug and excipient were predicted from ATR-FTIR spectra using two multi-way modelling techniques, parallel factor analysis (PARAFAC) and multi-linear partial least squares (N-PLS). Data matrices consisted of dissolved and undissolved parallel samples having different drug content and spectra, which were collected at axially cut surface of the flat-faced matrix tablets. Spectra we...

This paper studies the joint range and angle estimation of monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) radar proposes a algorithm. First, transmit direction matrix is converted into real values by unitary transformation, Vandermonde-like structure used to construct an augmented output that doubles aperture receive array. Then combined third-order tensor. Next, f...