Search results for: PARAFAC

Authors: Ling Zhang, Weikai Li

Abstract:

Recently three sufficient conditions for the three-way Candecomp/Parafac (CP) model which ensure uniqueness in one of the three modes(“uni-mode uniqueness”) are given. In this paper, we generalize these uniqueness conditions to n ≤ 3 and give a sufficient conditions for the n-way Candecomp/Parafac (CP) model, which ensure uniqueness in one of the n modes.

Keywords: uni-mode uniqueness, candecomp/parafac, n-way arrays, decomposition, tensor

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Authors: Lea Lenhardt, Ivana Zeković, Tatjana Dramićanin, Miroslav D. Dramićanin

Abstract:

Fluorescence spectroscopy coupled with parallel factor analysis (PARAFAC) and artificial neural networks (ANN) were used for characterization and classification of honey. Excitation emission spectra were obtained for 95 honey samples of different botanical origin (acacia, sunflower, linden, meadow, and fake honey) by recording emission from 270 to 640 nm with excitation in the range of 240-500 nm. Fluorescence spectra were described with a six-component PARAFAC model, and PARAFAC scores were further processed with two types of ANN’s (feed-forward network and self-organizing maps) to obtain algorithms for classification of honey on the basis of their botanical origin. Both ANN’s detected fake honey samples with 100% sensitivity and specificity.

Keywords: honey, fluorescence, PARAFAC, artificial neural networks

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Authors: Lea Lenhardt, Ivana Zeković, Tatjana Dramićanin, Miroslav D. Dramićanin

Abstract:

Rapid and sensitive analytical technologies for food analysis are needed to respond to the growing public interest in food quality and safety. In this context, fluorescence spectroscopy offers several inherent advantages for the characterization of food products: high sensitivity, low price, objective, relatively fast and non-destructive. The objective of this work was to investigate the potential of fluorescence spectroscopy coupled with multi-way technique for characterization of cereal flours. Fluorescence landscape also known as excitation-emission matrix (EEM) spectroscopy utilizes multiple-color illumination, with the full fluorescence spectrum recorded for each excitation wavelength. EEM was measured on various types of cereal flours (wheat, oat, barley, rye, corn, buckwheat and rice). Obtained spectra were analyzed using PARAllel FACtor analysis (PARAFAC) in order to decompose the spectra and identify underlying fluorescent components. Results of the analysis indicated the presence of four fluorophores in cereal flours. It has been observed that relative concentration of fluorophores varies between different groups of flours. Based on these findings we can conclude that application of PARAFAC analysis on fluorescence data is a good foundation for further qualitative analysis of cereal flours.

Keywords: cereals, fluors, fluorescence, PARAFAC

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Authors: Omar Dib, Rita Yaacoub, Luc Eveleigh, Nathalie Locquet, Hussein Dib, Ali Bassal, Christophe B. Y. Cordella

Abstract:

The potential of front-face fluorescence coupled with chemometric techniques, namely parallel factor analysis (PARAFAC) and multiple linear regression (MLR) as a rapid analysis tool to characterize Lebanese virgin olive oils was investigated. Fluorescence fingerprints were acquired directly on 102 Lebanese virgin olive oil samples in the range of 280-540 nm in excitation and 280-700 nm in emission. A PARAFAC model with seven components was considered optimal with a residual of 99.64% and core consistency value of 78.65. The model revealed seven main fluorescence profiles in olive oil and was mainly associated with tocopherols, polyphenols, chlorophyllic compounds and oxidation/hydrolysis products. 23 MLR regression models based on PARAFAC scores were generated, the majority of which showed a good correlation coefficient (R > 0.7 for 12 predicted variables), thus satisfactory prediction performances. Acid values, peroxide values, and Delta K had the models with the highest predictions, with R values of 0.89, 0.84 and 0.81 respectively. Among fatty acids, linoleic and oleic acids were also highly predicted with R values of 0.8 and 0.76, respectively. Factors contributing to the model's construction were related to common fluorophores found in olive oil, mainly chlorophyll, polyphenols, and oxidation products. This study demonstrates the interest of front-face fluorescence as a promising tool for quality control of Lebanese virgin olive oils.

Keywords: front-face fluorescence, Lebanese virgin olive oils, multiple Linear regressions, PARAFAC analysis

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Authors: Jude K. Safo

Abstract:

Knowledge Graphs KG) and their relation to Graph Embeddings (GE) represent a unique data structure in the landscape of machine learning (relative to image, text and acoustic data). Unlike the latter, GEs are the only data structure sufficient for representing hierarchically dense, semantic information needed for use-cases like supply chain data and protein folding where the search space exceeds the limits traditional search methods (e.g. page-rank, Dijkstra, etc.). While GEs are effective for compressing low rank tensor data, at scale, they begin to introduce a new problem of ’data retreival’ which we observe in Large Language Models. Notable attempts by transE, TransR and other prominent industry standards have shown a peak performance just north of 57% on WN18 and FB15K benchmarks, insufficient practical industry applications. They’re also limited, in scope, to next node/link predictions. Traditional linear methods like Tucker, CP, PARAFAC and CANDECOMP quickly hit memory limits on tensors exceeding 6.4 million nodes. This paper outlines a topological framework for linear mapping between concepts in KG space and GE space that preserve cardinality. Most importantly we introduce a traceable framework for composing dense linguistic strcutures. We demonstrate performance on WN18 benchmark this model hits. This model does not rely on Large Langauge Models (LLM) though the applications are certainy relevant here as well.

Keywords: representation theory, large language models, graph embeddings, applied algebraic topology, applied knot theory, combinatorics

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