A comparison of algorithms for fitting the PARAFAC model

Tomasi, Giorgio; Bro, Rasmus

doi:10.1016/j.csda.2004.11.013

Cited by 352 publications

(363 citation statements)

References 32 publications

Supporting

Mentioning

351

Contrasting

Unclassified

Order By: Relevance

“…To improve efficiency, various numerical techniques have been tested, such as ridge regression (Rayens & Mitchell, 1997), line search (Bro, 1998;Tomasi, 2006;Rajih et al, 2008), and gradient-based methods (Franc, 1992;Paatero, 1999;Tomasi, 2006). Although performance of an algorithm depends on the data and the fit model, the ALS algorithm in Appendix A seems to provide the most accurate Parafac solution at the cost of slow convergence (see Faber et al, 2003;Tomasi & Bro, 2006). Andersson and Bro (2000) provide an excellent open-source MATLAB toolbox with techniques for fitting various multimode component models, including the ALS algorithm for fitting the Parafac model.…”

Section: Fitting the Pca And Parafac Modelsmentioning

confidence: 99%

Parallel Factor Analysis of gait waveform data: A multimode extension of Principal Component Analysis

Helwig

Hong

Polk

2012

Human Movement Science

View full text Add to dashboard Cite

Gait data are typically collected in multivariate form, so some multivariate analysis is often used to understand interrelationships between observed data. Principal Component Analysis (PCA), a data reduction technique for correlated multivariate data, has been widely applied by gait analysts to investigate patterns of association in gait waveform data (e.g., interrelationships between joint angle waveforms from different subjects and/or joints). Despite its widespread use in gait analysis, PCA is for two-mode data, whereas gait data are often collected in higher-mode form. In this paper, we present the benefits of analyzing gait data via Parallel Factor Analysis (Parafac), which is a component analysis model designed for three-or higher-mode data. Using three-mode joint angle waveform data (subjects × time × joints), we demonstrate Parafac's ability to (a) determine interpretable components revealing the primary interrelationships between lowerlimb joints in healthy gait and (b) identify interpretable components revealing the fundamental differences between normal and perturbed subjects' gait patterns across multiple joints. Our results offer evidence of the complex interconnections that exist between lower-limb joints and limb segments in both normal and abnormal gaits, confirming the need for the simultaneous analysis of multi-joint gait waveform data (especially when studying perturbed gait patterns).ii To my loving and supportive family.iii

show abstract

Section: Fitting the Pca And Parafac Modelsmentioning

confidence: 99%

Parallel Factor Analysis of gait waveform data: A multimode extension of Principal Component Analysis

Helwig

Hong

Polk

2012

Human Movement Science

View full text Add to dashboard Cite

show abstract

“…Further, noise E is added to X pure , in the same way as is suggested in Tomasi and Bro [29] to obtain the data cube X ¼ X pure þ E E IÂJK ¼ Noise% 100 À Noise% X IÂJK pure FẼ IÂJK (8Þ Here,Ẽ IÂJK is generated from a normal distribution bNð0; SẼÞ and normalized to the Frobenius norm of 1. We have putẼ equal to 10 * I, with I the identity matrix.…”

Section: Appendixmentioning

confidence: 99%

A fully robust PARAFAC method for analyzing fluorescence data

Engelen

Frosch

Jørgensen

2009

Journal of Chemometrics

View full text Add to dashboard Cite

Parallel factor analysis (PARAFAC) is a widespread method for modeling fluorescence data by means of an alternating least squares procedure. Consequently, the PARAFAC estimates are highly influenced by outlying excitation-emission landscapes (EEM) and element-wise outliers, like for example Raman and Rayleigh scatter. Recently, a robust PARAFAC method that circumvents the harmful effects of outlying samples has been developed. For removing the scatter effects on the final PARAFAC model, different techniques exist. Newly, an automated scatter identification tool has been constructed. However, there still exists no robust method for handling fluorescence data encountering both outlying EEM landscapes and scatter. In this paper, we present an iterative algorithm where the robust PARAFAC method and the scatter identification tool are alternately performed. A fully automated robust PARAFAC method is obtained in that way. The method is assessed by means of simulations and a laboratory-made data set.

show abstract

“…It was introduced in [3,4]. The CPD and related decompositions have numerous applications [5,6,7,8,9,10,11,12], and various iterative CPD algorithms are available [13]. Unfortunately, for R ≥ 2 the problem may not have an optimal solution because the set S R (I, J, K) is not closed [14].…”

Section: Introductionmentioning

confidence: 99%

On best rank-2 and rank-(2,2,2) approximations of order-3 tensors

Stegeman

Friedland

2016

Linear and Multilinear Algebra

View full text Add to dashboard Cite

It is well known that a best rank-R approximation of order-3 tensors may not exist for R ≥ 2. A best rank-(R, R, R) approximation always exists, however, and is also a best rank-R approximation when it has rank (at most) R. For R = 2 and real order-3 tensors it is shown that a best rank-2 approximation is also a local minimum of the best rank-(2,2,2) approximation problem. This implies that if all rank-(2,2,2) minima have rank larger than 2, then a best rank-2 approximation does not exist. This provides an easy-to-check criterion for existence of a best rank-2 approximation. The result is illustrated by means of simulations.

show abstract

A comparison of algorithms for fitting the PARAFAC model

Cited by 352 publications

References 32 publications

Parallel Factor Analysis of gait waveform data: A multimode extension of Principal Component Analysis

Parallel Factor Analysis of gait waveform data: A multimode extension of Principal Component Analysis

A fully robust PARAFAC method for analyzing fluorescence data

On best rank-2 and rank-(2,2,2) approximations of order-3 tensors

Contact Info

Product

Resources

About