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## Unsupervised multiway data analysis: A literature survey (2008)

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Venue: | IEEE Transactions on Knowledge and Data Engineering |

Citations: | 79 - 10 self |

### Citations

1221 |
Kernel Methods for Pattern Analysis
- SHAWE-TAYLOR, CRISTIANINI
- 2004
(Show Context)
Citation Context ...these models will fail to discover nonlinear relationships between variables. Nonlinearity has been a recent topic of interest in data mining community especially since kernel methods became popular [=-=Shawe-Taylor and Cristianini 2004-=-]. Most two-way analysis techniques, e.g. PCA, Canonical Correlation Analysis (CCA), are combined with kernels in order to capture the underlying nonlinear structure among variables. Similar to a rece... |

588 |
Analysis of individual differences in multidimensional scaling via an N-way generalization of ¸SEckart-Young ˇT
- Carroll, Chang
- 1970
(Show Context)
Citation Context ...2. MULTIWAY MODELS The most well-known and commonly applied multiway models in literature are Tucker models and the PARAFAC model, which is also called CANDECOMP (Canonical Decomposition) (CANDECOMP [=-=Carroll and Chang 1970-=-] was proposed independently but considered equivalent to PARAFAC). We will briefly describe these models as well as recent models built on the principles of PARAFAC and Tucker. This survey studies mu... |

415 |
Some mathematical notes on three-mode factor analysis
- Tucker
- 1966
(Show Context)
Citation Context ...later used to interpret the underlying information content of the data. While most multiway analysis techniques preserve the multiway nature of the data, some techniques such as Tucker1 [Tucker 1964; =-=Tucker 1966-=-] are based on matricization of a multiway array, which means transforming a third or higherorder array into a two-way dataset (Figure 3). Matricization (or unfolding, flattening) has multiple definit... |

148 |
Introduction to factor analysis: What it is and how to do it
- Kim, Mueller
- 1978
(Show Context)
Citation Context ...monly followed. Once a three-way array is flattened and arranged as a two-way dataset, two-way analysis methods, e.g. Singular Value Decomposition (SVD) [Golub and Loan 1996] and other factor models [=-=Kim and Mueller 1978-=-], can be employed in understanding the structure in data. Rearranging multiway arrays as two-way datasets and analyzing them with two-way methods, though, may result in information loss and misinterp... |

121 | Orthogonal tensor decompositions - Kolda |

116 | Singular values and eigenvalues of tensors: A variational approach. in - Lim |

114 | Multi-way analysis in the food industry. Models, algorithms and applications
- Bro
- 1998
(Show Context)
Citation Context ... information loss and misinterpretation especially if the data are noisy. An intuitive example is often given on a sensory dataset, where eight judges evaluates ten breads based on eleven attributes [=-=Bro 1998-=-]. When this dataset is modeled using a PARAFAC model, the model assumes that there is a common sense of evaluation among judges and each judge pertains to this sense of evaluation at different amount... |

111 | C.: Beyond streams and graphs: dynamic tensor analysis - Sun, Tao, et al. |

95 | The N-way toolbox for MATLAB - Andersson, Bro |

91 | Sequential Karhunen-Loeve Basis Extraction and its Application to Images
- Levy, Lindenbaum
- 2000
(Show Context)
Citation Context ...2 xijk =PP p=1PQ gpqkaipbjq + eijk ̌ ̌ Tucker3 xijk =PP p=1PQ q=1PR r=1 gpqraipbjqckr + eijk ̌ ̌ S-Tucker3 xijk =PP p=1PQ q=1PR r=1 gpqra(i+sjp)pbjqckr + eijk ̌ ̌ dataset every time data are updated [=-=Levy and Lindenbaum 2002-=-]. However, the best rank-R approximation through SVD in matrices cannot be generalized to tensors [Kolda 2001; Kolda 2003]. Through a counterexample, [Kolda 2003] demonstrates that best rank-(R+1) ap... |

87 | Algorithm 862: MATLAB Tensor Classes for Fast Algorithm Prototyping - Kolda, Bader - 2006 |

84 | Towards a standardized notation and terminology in multiway analysis - Kiers - 2000 |

80 | Efficient MATLAB computations with sparse and factored tensors - Bader, Kolda - 2007 |

77 | Decomposing EEG data into space-time-frequency components using parallel factor analysis
- Miwakeichi, Martinez-Montes, et al.
(Show Context)
Citation Context ..., often frequency content of the signals, for instance signal power at p particular frequencies, also needs to be considered. In that case, EEG data can be arranged as an m × p × n three-way dataset [=-=Miwakeichi et al. 2004-=-]. Multiway analysis of a three-way EEG array then enables us to extract the signatures of brain dynamics in time, frequency and electrode domains. As opposed to two-way analysis showing brain activit... |

72 |
A comparison of algorithms for fitting the PARAFAC model
- Tomasi, Bro
- 2006
(Show Context)
Citation Context ...n algorithm satisfying the objective function based on ALS. In addition to ALS, there exist alternative algorithms for PARAFAC. These algorithms can be studied under three categories as specified in [=-=Tomasi and Bro 2006-=-]: alternating algorithms, closed form solutions and gradient-based methods. Representatives of alternating algorithms, i.e. Alternating Slice-wise Diagonalization (ASD) [Jiang et al. 2000], Self Weig... |

71 |
The multilinear engine - a table-driven, least squares program for solving multilinear problems, including the n-way parallel factor analysis model
- Paatero
- 1999
(Show Context)
Citation Context ...2.4 Alternative Models There exist several other models based on approaches other than PARAFAC and Tucker models for unsupervised multiway data analysis. We briefly introduce Multilinear Engine (ME) [=-=Paatero 1999-=-], multiway models based on STATIS [Stanimirova et al. 2004] and multiblock multiway models [Smilde et al. 2000]. ME is a program that is capable of fitting different structural models including PARAF... |

71 |
The Extension of Factor Analysis to Three-Dimensional Matrices
- Tucker
- 1964
(Show Context)
Citation Context ...ns in diverse disciplines including chemometrics, neuroscience, computer vision, and social network analysis. 1. INTRODUCTION Multiway data analysis, originating in psychometrics back in the sixties [=-=Tucker 1964-=-], is the extension of two-way data analysis to higher-order datasets. Multiway analysis is often used for extracting hidden structures and capturing underlying correlations between variables in a mul... |

70 | Multilinear image analysis for facial recognition
- Vasilescu, Terzopoulos
- 2002
(Show Context)
Citation Context ...n of the data as shown in many applications, e.g. face recognition on an image dataset, where images are affected by several factors such as viewpoints, facial expressions, lighting conditions, etc. [=-=Vasilescu and Terzopoulos 2002-=-]. Compared to SVD, which is a decomposition that represents a matrix as a sum of rank-1 matrices, HOSVD does not decompose a tensor as a sum of rank-1 tensors. In that sense, PARAFAC is considered to... |

66 | Higher-order web link analysis using multilinear algebra
- Kolda, Bader, et al.
(Show Context)
Citation Context ...es again in the context of chatroom communications. Not only chatroom but also email communications have been analyzed using multiway models [Bader et al. 2006]. In the context of web link analysis, [=-=Kolda et al. 2005-=-] and [Kolda and Bader 2006] combine hyperlink and anchor text information and rearrange web graph data as a sparse three-way tensor with modes: webpages × webpages × anchor text. Web graph is then an... |

62 | Distributed clustering using collective principal component analysis
- Kargupta, Huang, et al.
(Show Context)
Citation Context ...ilde et al. 2000]. The matrix containing summaries from different arrays can then be analyzed using bilinear factor models. This approach can be considered as a generalized version of Collective PCA [=-=Kargupta et al. 2001-=-] to higher-order datasets. 3. ALGORITHMS Algorithms for fitting multiway models are, in general, iterative algorithms and based on Alternating Least Squares (ALS). We briefly discuss the algorithms u... |

59 |
A new efficient method for determining the number of components in PARAFAC models
- Bro, Kiers
- 2003
(Show Context)
Citation Context ... There are several techniques for determining the number of factors in a PARAFAC model, i.e. residual analysis, visual appearance of loadings, number of iterations of the algorithm, core consistency [=-=Bro and Kiers 2003-=-], etc. Among these techniques, core consistency diagnostic quantifies the resemblance between a Tucker3 core and a super-diagonal PARAFAC core and suggests whether a PARAFAC model is a valid model fo... |

56 |
Parallel factor analysis as an exploratory tool for wavelet transformed event-related EEG
- Mørup, Hansen, et al.
- 2006
(Show Context)
Citation Context ...of the EEG data, respectively. PARAFAC models with nonnegativity constraints have later been used in another study on eventrelated potentials (ERP) to find the underlying structure of brain dynamics [=-=Mørup et al. 2006-=-]. These studies have also motivated the application of multiway models in understanding the structure of epileptic seizures, localizing focus origins [Acar et al. 2006] and removing artifacts using m... |

56 |
Multi-way analysis: applications in the chemical sciences
- Smilde, Bro, et al.
- 2004
(Show Context)
Citation Context ... models especially developed for supervised learning, e.g. Multilinear Partial Least Squares [Bro 1996]. We refer interested users to [Bro 1998] and to the most recent book in multiway data analysis [=-=Smilde et al. 2004-=-]. 7. DISCUSSIONS Recent studies show that multiway models have many application areas in computer science such as social network analysis, web link analysis and a variety of other problems in data mi... |

48 | On the best rank1 and rank-(r1, r2, ..., rn) approximation of higher-order tensors - Lathauwer, Moor, et al. - 2000 |

43 |
Recent developments in CANDECOMP/PARAFAC algorithms: a critical review
- Faber, Bro, et al.
(Show Context)
Citation Context ...Alternating Slice-wise Diagonalization (ASD) [Jiang et al. 2000], Self Weighted Alternating Trilinear Diagonalization (SWATLD) [Chen et al. 2000], have recently been studied and compared in depth in [=-=Faber et al. 2003-=-; Tomasi and Bro 2006]. These algorithms particularly aim to improve PARAFAC -ALS in terms of convergence rate and robustness to overfactoring, i.e. more factors than the model rank of an array are ex... |

41 |
The TOPHITS model for higher-order web link analysis, in
- Kolda, Bader
(Show Context)
Citation Context ...of chatroom communications. Not only chatroom but also email communications have been analyzed using multiway models [Bader et al. 2006]. In the context of web link analysis, [Kolda et al. 2005] and [=-=Kolda and Bader 2006-=-] combine hyperlink and anchor text information and rearrange web graph data as a sparse three-way tensor with modes: webpages × webpages × anchor text. Web graph is then analyzed using an algorithm i... |

41 |
Rank, decomposition, and uniqueness for 3-way and Nway arrays
- Kruskal
- 1989
(Show Context)
Citation Context ...r to have a compact and rather self-contained survey. There are concepts such as uniqueness properties of models and uniqueness conditions for models, e.g. well-known Kruskal’scondition for PARAFAC [=-=Kruskal 1989-=-], understanding rotations in factor models and using those rotations to simplify the interpretation of a model and handling missing data. Furthermore, most of the structural models given in Section 2... |

40 |
Multiway analysis of epilepsy tensors
- Acar, Bingol, et al.
- 2007
(Show Context)
Citation Context ...mples × emission × excitation [Andersen and Bro 2003] or wavelet-transformed multi-channel EEG arranged as a three-way array with modes: frequency × time samples × electrodes [Miwakeichi et al. 2004; =-=Acar et al. 2007-=-]. The organization of this paper is as follows: We categorize multiway models (both original models and recent derivatives of original models) and study their similarities and differences in Section ... |

37 |
Centering and scaling in component analysis
- Bro, Smilde
(Show Context)
Citation Context ...s a part of many of the algorithms, preprocessing is also a crucial step in data analysis. Similar to preprocessing in two-way data analysis, centering and scaling both generalize to multiway arrays [=-=Bro and Smilde 2003-=-]. Centering across one mode of a three-way dataset is performed by simply matricizing the data in the desired mode and applying two-way centering. Scaling, on the other hand, requires scaling each sl... |

37 |
Parallel proportional profiles and other principles for determining the choice of factors by rotation
- Cattell
- 1944
(Show Context)
Citation Context ... arrays . 2.1 PARAFAC-family 2.1.1 PARAFAC PARAFAC [Harshman 1970] is an extension of bilinear factor models to multilinear data. It is based on Cattell’s principle of Parallel Proportional Profiles [=-=Cattell 1944-=-]. The idea behind Parallel Proportional Profiles is that if the same factors are present in two samples under different conditions, then each factor in the first sample is expected to have the same p... |

36 | Tensor-CUR decompositions for tensor-based data - Mahoney, Maggioni, et al. - 2006 |

35 |
Modeling and multi-way analysis of chatroom tensors,”in ISI
- Acar, amtepe, et al.
- 2005
(Show Context)
Citation Context ...ods at certain electrodes, multiway analysis can differentiate between the brain activities with different spectral signatures. It has been shown in numerous research areas including social networks [=-=Acar et al. 2005-=-], neuroscience [Estienne et al. 2001], process analysis [Gourvnec et al. 2005] that underlying information content of the data may not be captured accurately or identified uniquely by two-way analysi... |

33 |
Selecting among three-mode principal component models of different types and complexities: A numerical convex hull based method
- Ceulemans, Kiers
- 2006
(Show Context)
Citation Context ...model fits [Kiers and Kinderen 2003]. The most recent work in finding the number of components is based on searching for the convex hull on the plot of model fit values vs. number of free parameters [=-=Ceulemans and Kiers 2006-=-]. This approach is more general than previously-proposed methods and helps in determining the model parameters in not only Tucker3 but also Tucker1, Tucker2 and PARAFAC models. Even though empirical ... |

29 |
R: Multiway Calibration Multilinear PLS
- Bro
- 1996
(Show Context)
Citation Context ...n be employed for both unsupervised and supervised learning. In addition to those, there are also multiway models especially developed for supervised learning, e.g. Multilinear Partial Least Squares [=-=Bro 1996-=-]. We refer interested users to [Bro 1998] and to the most recent book in multiway data analysis [Smilde et al. 2004]. 7. DISCUSSIONS Recent studies show that multiway models have many application are... |

29 | Robust iterative fitting of multilinear models
- Vorobyov, Rong, et al.
- 2005
(Show Context)
Citation Context ...ibuted Gaussian. However, if this assumption does not hold and measurement errors follow a Laplacian or Cauchy distribution instead, ALS does not perform as well as some recently proposed algorithms [=-=Vorobyov et al. 2005-=-], which rely on an objective function, that is least absolute error based on L1-norm rather than least squares. It has been demonstrated in the context of multiuser separation detection for a direct-... |

25 |
ERPWAVELAB a toolbox for multi-channel analysis of time-frequency transformed event related potentials
- Mørup, Hansen, et al.
- 2006
(Show Context)
Citation Context ...of the EEG data, respectively. PARAFAC models with nonnegativity constraints have later been used in another study on eventrelated potentials (ERP) to find the underlying structure of brain dynamics [=-=Mørup et al. 2006-=-]. These studies have also motivated the application of multiway models in understanding the structure of epileptic seizures, localizing focus origins [Acar et al. 2006] and removing artifacts using m... |

23 |
Practical aspects of PARAFAC modelling of fluorescence excitation-emission data
- Andersson, Bro
- 2003
(Show Context)
Citation Context ...n each mode. These models have been applied on various datasets shown to contain multilinear structure, e.g. three-way fluorescence spectroscopic datasets with modes: samples × emission × excitation [=-=Andersen and Bro 2003-=-] or wavelet-transformed multi-channel EEG arranged as a three-way array with modes: frequency × time samples × electrodes [Miwakeichi et al. 2004; Acar et al. 2007]. The organization of this paper is... |

20 | A counterexample to the possibility of an extension of the Eckart-Young low-rank approximation theorem for the orthogonal rank tensor decomposition - Kolda - 2003 |

18 | Modeling multi-way data with linearly dependent loadings
- Bro, Harshman, et al.
(Show Context)
Citation Context ...nvolutive mixtures. Convolution basically means generating a mixture by sending the sources through a filter. When convolution filter is sparse, cPARAFAC becomes equivalent to S-PARAFAC. 4. PARALIND [=-=Bro et al. 2005-=-]: A common problem that arises in real data analysis is that ranks of the component matrices may not be the same (called rank deficiency). That would require extracting different number of factors in... |

18 | Compact representation of multidimensional data using tensor rankone decomposition
- Wang, Ahuja
- 2004
(Show Context)
Citation Context ...l information. On the other hand, recently it has beenshown that when images are represented as tensors and iteratively obtained rank-one approximations of tensors are used to compress these images [=-=Wang and Ahuja 2004-=-], the error between the original and reconstructed images is less than the error obtained when PCA is used for compression. Another application of multiway models in computer vision is face recogniti... |

17 |
PARAFAC2 - Part II. Modeling chromatographic data with retention time shifts
- BRO, ANDERSSON, et al.
- 1999
(Show Context)
Citation Context ...l. This relaxation enables the use of multiway models in the cases, where a PARAFAC model cannot fully recover the underlying structure, e.g. modeling chromatographic data with retention time shifts [=-=Bro et al. 1999-=-]. Furthermore, PARAFAC2 solves the problem of modeling three-way arrays with slices of different dimensionality (dimensionality differs only in one mode). An example of such a multiway array is an en... |

16 |
PARAFAC2 - Part I. A direct fitting algorithm for the PARAFAC2
- Kiers, Berge, et al.
- 1999
(Show Context)
Citation Context ... Nevertheless, directly fitting PARAFAC2 on raw data has more advantages than indirect fitting in terms of imposing constraints, handling missing data and generalization of the model to N-way arrays [=-=Kiers et al. 1999-=-]. 2. S-PARAFAC [Harshman et al. 2003]: has been introduced in order to deal with shifting factors in sequential data such as time series or spectral data. While PARAFAC restricts the data to have the... |

16 |
Multiway multiblock component and covarission models, Journal of Chemometrics 14 (2000) 301–331. [37] Q. C tion Sys [38] T. C dec net [39] Q. tion Info [40] W. sys cat [41] S.M iga Sym [42] X. Z of l Con [43] B.V Tra [44] A. sifi [45] J.-J. con [46] V. S
- Westerhuis, Boque
(Show Context)
Citation Context ... models for unsupervised multiway data analysis. We briefly introduce Multilinear Engine (ME) [Paatero 1999], multiway models based on STATIS [Stanimirova et al. 2004] and multiblock multiway models [=-=Smilde et al. 2000-=-]. ME is a program that is capable of fitting different structural models including PARAFAC and PARAFAC2 on multiway arrays using a general-purpose optimization/curve fitting approach. Although models... |

15 |
Temporal analysis of social networks using three-way DEDICOM
- Bader, Harshman, et al.
- 2006
(Show Context)
Citation Context ...nce of collective and centralized tensor analysis approaches again in the context of chatroom communications. Not only chatroom but also email communications have been analyzed using multiway models [=-=Bader et al. 2006-=-]. In the context of web link analysis, [Kolda et al. 2005] and [Kolda and Bader 2006] combine hyperlink and anchor text information and rearrange web graph data as a sparse three-way tensor with mode... |

15 |
D.: Multi-way modelling of high-dimensionality electroencephalographic data. Chemometrics and Intelligent Laboratory Systems 58
- Estienne, Matthijs, et al.
- 2001
(Show Context)
Citation Context ...ay analysis can differentiate between the brain activities with different spectral signatures. It has been shown in numerous research areas including social networks [Acar et al. 2005], neuroscience [=-=Estienne et al. 2001-=-], process analysis [Gourvnec et al. 2005] that underlying information content of the data may not be captured accurately or identified uniquely by two-way analysis methods. Two-way analysis methods, ... |

12 | Computational analysis of epileptic focus localization
- Acar, Bingol, et al.
(Show Context)
Citation Context ...g structure of brain dynamics [Mørup et al. 2006]. These studies have also motivated the application of multiway models in understanding the structure of epileptic seizures, localizing focus origins [=-=Acar et al. 2006-=-] and removing artifacts using multilinear subspace analysis [Acar et al. 2007]. Most recently, a toolbox called ERPWAVELAB [Mørup et al. 2006] running under MATLAB [MathWorks ] has been released for ... |

12 | Collective sampling and analysis of high order tensors for chatroom communications - Acar, Çamtepe, et al. |

12 |
Parafac2: Mathematical and technical notes. UCLA working papers in phonetics 22(3044
- Harshman
- 1972
(Show Context)
Citation Context ...s with Linear Dependency (PARALIND) and Convolutive PARAFAC (cPARAFAC). We discuss these models and their similarities briefly. Their mathematical formulations are also given in Table 1. 1. PARAFAC2 [=-=Harshman 1972-=-]: is introduced as a less restrictive model than PARAFAC. For instance, indirectly fitting PARAFAC has a restriction such that PARAFAC can model data indirectly if one of the component matrices in th... |

12 | Kernel-based Multifactor Analysis for Image Synthesis and Recognition - Li, Du, et al. - 2005 |

11 |
Improving the speed of multiway algorithms part II: compression
- Bro, CA
- 1998
(Show Context)
Citation Context ...models are used instead of two-way methods. However, computational and space complexity of multiway models and algorithms have not often been discussed in literature except for few studies including [=-=Andersson and Bro 1998-=-a; Andersson and Bro 1998b], where the speed of algorithms for a Tucker3 model is compared and Tucker3 is suggested as a compression method for speeding up multiway analysis, [Zhang and Golub 2001], w... |

11 | Maximum Likelihood Fitting Using Ordinary Least Squares Algorithms
- Bro, Sidiropoulos, et al.
- 2002
(Show Context)
Citation Context ...entically distributed, a weighted least squares approach has been proposed by [Kiers 1997]. This approach has later been generalized to model data, which might have correlated measurement errors, in [=-=Bro et al. 2002-=-] by an algorithm called Maximum likelihood via Iterative Least Squares (MILES). Similarly, in another study, a generalization of maximum likelihood PCA, called maximum likelihood PARAFAC (MLPARAFAC),... |

10 | Review on multiway analysis in chemistry 2000–2005 - Bro |

9 |
A fast method for choosing the numbers of components in tucker3 analysis
- Kiers, Kinderen
- 2003
(Show Context)
Citation Context ...ber of components. However, high computational complexity of DIFFIT makes it inefficient. Therefore, it has later been improved by comparing approximate model fit values rather than exact model fits [=-=Kiers and Kinderen 2003-=-]. The most recent work in finding the number of components is based on searching for the convex hull on the plot of model fit values vs. number of free parameters [Ceulemans and Kiers 2006]. This app... |

8 |
A novel trilinear decomposition algorithm for second-order linear calibration
- Chen, Wu, et al.
- 2000
(Show Context)
Citation Context ...gradient-based methods. Representatives of alternating algorithms, i.e. Alternating Slice-wise Diagonalization (ASD) [Jiang et al. 2000], Self Weighted Alternating Trilinear Diagonalization (SWATLD) [=-=Chen et al. 2000-=-], have recently been studied and compared in depth in [Faber et al. 2003; Tomasi and Bro 2006]. These algorithms particularly aim to improve PARAFAC -ALS in terms of convergence rate and robustness t... |

8 |
Three-Way Data Resolution by Alternating Slice-Wise Diagonalization (ASD
- Jiang, Wu, et al.
(Show Context)
Citation Context ...ified in [Tomasi and Bro 2006]: alternating algorithms, closed form solutions and gradient-based methods. Representatives of alternating algorithms, i.e. Alternating Slice-wise Diagonalization (ASD) [=-=Jiang et al. 2000-=-], Self Weighted Alternating Trilinear Diagonalization (SWATLD) [Chen et al. 2000], have recently been studied and compared in depth in [Faber et al. 2003; Tomasi and Bro 2006]. These algorithms parti... |

6 | Shifted factor analysis — part I: models and properties
- Harshman, Hong, et al.
(Show Context)
Citation Context ...RAFAC2 on raw data has more advantages than indirect fitting in terms of imposing constraints, handling missing data and generalization of the model to N-way arrays [Kiers et al. 1999]. 2. S-PARAFAC [=-=Harshman et al. 2003-=-]: has been introduced in order to deal with shifting factors in sequential data such as time series or spectral data. While PARAFAC restricts the data to have the same factor in various proportions i... |

6 | Shifted factor analysis - part iii: N-way generalization and application
- Hong, Harshman
- 2003
(Show Context)
Citation Context ...econdly, PARAFAC2, similar to S-PARAFAC, can model data with shifting factors. In fact, both models have been used in the analysis of chromatographic data with retention time shifts [Bro et al. 1999; =-=Hong and Harshman 2003-=-]. However, PARAFAC2 can only capture shifts that maintain the inner product of the factors (i.e. the constraint in Equation 4) while SPARAFAC can model independent shifts at each factor. Still though... |

6 |
STATIS, a three-way method for data analysis. Application to environmental data
- Stanimirova, Walczaka, et al.
- 2004
(Show Context)
Citation Context ...iway array is an environmental dataset that contains the concentrations of some chemical compounds measured at certain time periods across several sampling sites (sampling sites × parameters × time) [=-=Stanimirova et al. 2004-=-]. It is quite common to have measurements from sampling sites for varying time periods, which would result in a three-way array with different dimensionality in one of the modes (e.g. time mode in th... |

6 | Maximum Likelihood Parallel Factor Analysis
- Vega-Montoto, Wentzell
(Show Context)
Citation Context ...lihood PCA, called maximum likelihood PARAFAC (MLPARAFAC), has been proposed in order to fit a PARAFAC model to multiway arrays containing correlated noise structure in general or in a specific mode [=-=Vega-Montoto and Wentzell 2003-=-]. While MILES has been developed as a general algorithm to fit any model with a least squares solution, MLPARAFAC has been particularly developed to fit a PARAFAC model. Even though it is often not m... |

5 |
On-line monitoring of batch processes using PARAFAC representation
- Meng, Morris, et al.
- 2003
(Show Context)
Citation Context ...analysis in general and that would require waiting till the completion of a batch. However, in-filling of missing future data and modeling using a PARAFAC model have shown to overcome this challenge [=-=Meng et al. 2003-=-] and PARAFAC has been demonstrated to be an applicable approach in controlling batch processes arranged as a three-way array with modes: batches × variables × time samples. Similarly, STATIS has been... |

4 |
Foundations of the parafac procedure:models and conditions for an 'explanatory' multi-modal factor analysis. UCLA working papers in phonetics
- Harshman
- 1970
(Show Context)
Citation Context ...tually explain noise rather than a certain structure. Thus, multiway models are more advantageous in terms of interpretation and accuracy compared to two-way models. Multilinear models (i.e. PARAFAC [=-=Harshman 1970-=-], Tucker [Tucker 1964; Tucker 1966] and their derivatives) capture the multilinear structure in data. Multilinearity of the model denotes that the model is linear in each mode and factors extracted f... |

4 |
The act (statis method
- Lavit, Escoufier, et al.
- 1994
(Show Context)
Citation Context ... wider range of structures in data compared to PARAFAC, Tucker3, etc. Another model focusing on three-way data analysis is STATIS [Stanimirova et al. 2004] originally studied in [Carlier et al. 1989; =-=Lavit et al. 1994-=-]. When compared to N-way analysis methods, which explore each mode simultaneously, this STATIS-based model explores each mode separately. It considers each observation/sample as a slice of a three-wa... |

3 | Sparse nonnegative tensor 2d deconvolution (sntf2d) for multichannel time-frequency analysis. DTU Informatics and Mathematical Modeling Technical Report - Mørup, Schmidt - 2006 |

3 |
A robust version of the tucker3 model
- Pravdova, Estienne, et al.
(Show Context)
Citation Context ...so algorithms that particularly focus on robustness to outliers and different types of noise/measurement errors. In the area of outlier detection, robust algorithms for both Tucker3 (Robust Tucker3) [=-=Pravdova et al. 2001-=-] and PARAFAC (Robust PARAFAC) [Engelen and Hubert 2005] have been developed. The motivation in these robust algorithms is to improve ALS method, which can dramatically suffer from outliers. In these ... |

2 |
A comparative review of methods which handle a set of indexed data
- Lavit, Pernin, et al.
- 1989
(Show Context)
Citation Context ... engine can explore a wider range of structures in data compared to PARAFAC, Tucker3, etc. Another model focusing on three-way data analysis is STATIS [Stanimirova et al. 2004] originally studied in [=-=Carlier et al. 1989-=-; Lavit et al. 1994]. When compared to N-way analysis methods, which explore each mode simultaneously, this STATIS-based model explores each mode separately. It considers each observation/sample as a ... |

2 | M.: A robust PARAFAC method
- Engelen, Hubert
- 2005
(Show Context)
Citation Context ...to outliers and different types of noise/measurement errors. In the area of outlier detection, robust algorithms for both Tucker3 (Robust Tucker3) [Pravdova et al. 2001] and PARAFAC (Robust PARAFAC) [=-=Engelen and Hubert 2005-=-] have been developed. The motivation in these robust algorithms is to improve ALS method, which can dramatically suffer from outliers. In these algorithms, PARAFAC and Tucker3 are combined with metho... |

2 |
D.: Monitoring batch processes with the statis approach
- Gourvénec, Stanimirova, et al.
- 2005
(Show Context)
Citation Context ... brain activities with different spectral signatures. It has been shown in numerous research areas including social networks [Acar et al. 2005], neuroscience [Estienne et al. 2001], process analysis [=-=Gourvnec et al. 2005-=-] that underlying information content of the data may not be captured accurately or identified uniquely by two-way analysis methods. Two-way analysis methods, e.g. factor models, suffer from rotationa... |

2 |
CuBatch, a MATLAB interface for n-mode data analysis
- Gourvénec, Tomasi, et al.
(Show Context)
Citation Context ... brain activities with different spectral signatures. It has been shown in numerous research areas including social networks [Acar et al. 2005], neuroscience [Estienne et al. 2001], process analysis [=-=Gourvnec et al. 2005-=-] that underlying information content of the data may not be captured accurately or identified uniquely by two-way analysis methods. Two-way analysis methods, e.g. factor models, suffer from rotationa... |

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Block-parafac decompositions and applications in wireless communications
- Almeida, Favier, et al.
- 2006
(Show Context)
Citation Context ...about the data and constraints can be incorporated into the model. In addition to the extensions of PARAFAC model discussed so far, there is also another recent model called Constrainedblock PARAFAC [=-=Almeida et al. 2006-=-]. Constrained-block PARAFAC proposes to model a multiway array as a sum of PARAFAC blocks. Each block is modeled using a PARAFAC model but has certain constraints enforced by the constraint matrices ... |

1 | A novel approach to personalized web search - Cubesvd - 2000 |