PARAFAC and missing values

Tomasi, Giorgio; Bro, Rasmus

doi:10.1016/j.chemolab.2004.07.003

Cited by 235 publications

(151 citation statements)

References 22 publications

Supporting

Mentioning

151

Contrasting

Order By: Relevance

“…This interpolation step is necessary because the robust PARAFAC method cannot cope with missing values yet. From the results of Tomasi and Bro [23], we expect that it will be possible to analyze data with missing values in a robust way. Nevertheless, this demands an elaborate study on this matter and work is still in progress.…”

Section: The Combined Robust Algorithmmentioning

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

Section: The Combined Robust Algorithmmentioning

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

show abstract

“…When alternatingly solving for loadings of each mode this method can be speed up by saving the active set from previous iterations of the alternating least squares procedure [24]. Missing values are handled by only considering a row of R at a time and including only columns j of X and H in which the elements R ij = 1 in the subproblem (3) [9].…”

Section: Active Setmentioning

confidence: 99%

“…2) Marginalization or weighted regression, in which the missing values are ignored during the optimization of the cost function. The latter approach has been shown to handle more data being missing including systematic patterns of missing data [9]. For the case of unconstrained tensor factorization marginalization has been shown to scale well to larger datasets where recovery of the underlying components of synthetic data was possible when up to 99% of the data is missing [11].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Non-negative Tensor Factorization with missing data for the modeling of gene expressions in the Human Brain

Nielsen

Mørup

2014

2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP)

View full text Add to dashboard Cite

Non-negative Tensor Factorization (NTF) has become a prominent tool for analyzing high dimensional multi-way structured data. In this paper we set out to analyze gene expression across brain regions in multiple subjects based on data from the Allen Human Brain Atlas [1] with more than 40 % data missing in our problem. Our analysis is based on the non-negativity constrained Canonical Polyadic (CP) decomposition where we handle the missing data using marginalization considering three prominent alternating least squares procedures; multiplicative updates, column-wise, and row-wise updating of the component matrices. We examine three gene expression prediction scenarios based on data missing at random, whole genes missing and whole areas missing within a subject. We find that the column-wise updating approach also known as HALS performs the most efficient when fitting the model. We further observe that the non-negativity constrained CP model is able to predict gene expressions better than predicting by the subject average when data is missing at random. When whole genes and whole areas are missing it is in general better to predict by subject averages. However, we find that when whole genes are missing from all subjects the model based predictions are useful. When analyzing the structure of the components derived for one of the best predicting model orders the components identified in general constitute localized regions of the brain. Non-negative tensor factorization based on marginalization thus forms a promising framework for imputing missing values and characterizing gene expression in the human brain. However, care also has to be taken in particular when predicting the genetic expression levels at a whole region of the brain missing as our analysis indicates that this requires a substantial amount of subjects with data for this region in order for the model predictions to be reliable.

show abstract

“…As in the two-dimensional case, these types of data may be affected by the presence of missing values. For multiway data, different behaviors for missing data can be observed [3,4]. The simplest case is when missing values are random without any pattern, denoted as RMV in [3].…”

Section: Introductionmentioning

confidence: 99%

Missing Values in Dissimilarity-Based Classification of Multi-way Data

Porro-Muñoz

Duin

Talavera

2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract.Missing values can occur frequently in many real world situations. Such is the case of multi-way data applications, where objects are usually represented by arrays of 2 or more dimensions e.g. biomedical signals that can be represented as time-frequency matrices. This lack of attributes tends to influence the analysis of the data. In classification tasks for example, the performance of classifiers is usually deteriorated. Therefore, it is necessary to address this problem before classifiers are built. Although the absence of values is common in these types of data sets, there are just a few studies to tackle this problem for classification purposes. In this paper, we study two approaches to overcome the missing values problem in dissimilarity-based classification of multi-way data. Namely, imputation by factorization, and a modification of the previously proposed Continuous Multi-way Shape measure for comparing multi-way objects.

show abstract

PARAFAC and missing values

Cited by 235 publications

References 22 publications

A fully robust PARAFAC method for analyzing fluorescence data

A fully robust PARAFAC method for analyzing fluorescence data

Non-negative Tensor Factorization with missing data for the modeling of gene expressions in the Human Brain

Missing Values in Dissimilarity-Based Classification of Multi-way Data

Contact Info

Product

Resources

About