An Optimization Framework for Regularized Linearly Coupled Matrix-Tensor Factorization

Schenker, Carla; Cohen, Jérémy E.; Acar, Evrim

doi:10.23919/eusipco47968.2020.9287459

Cited by 9 publications

(8 citation statements)

References 18 publications

(33 reference statements)

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“…We can solve Eq. 28 by computing the gradient and then using a first-order optimization method [Schenker et al 2021]. Afterwards, we have…”

Section: Pvisrecmentioning

confidence: 99%

“…34. However, we can also leverage a variety of different optimization schemes including cyclic/block coordinate descent [Kim et al 2014;Rossi and Zhou 2016], stochastic gradient descent [Oh et al 2015;Yun et al 2014], among others [Balasubramaniam et al 2020;Bouchard et al 2013;Choi et al 2019;Schenker et al 2021;Singh and Gordon 2008].…”

Section: Pvisrec (Acm Only)mentioning

confidence: 99%

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Personalized Visualization Recommendation

Qian¹,

Rossi²,

Du³

et al. 2021

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Visualization recommendation work has focused solely on scoring visualizations based on the underlying dataset, and not the actual user and their past visualization feedback. These systems recommend the same visualizations for every user, despite that the underlying user interests, intent, and visualization preferences are likely to be fundamentally different, yet vitally important. In this work, we formally introduce the problem of personalized visualization recommendation and present a generic learning framework for solving it. In particular, we focus on recommending visualizations personalized for each individual user based on their past visualization interactions (e.g., viewed, clicked, manually created) along with the data from those visualizations. More importantly, the framework can learn from visualizations relevant to other users, even if the visualizations are generated from completely different datasets. Experiments demonstrate the effectiveness of the approach as it leads to higher quality visualization recommendations tailored to the specific user intent and preferences. To support research on this new problem, we release our user-centric visualization corpus consisting of 17.4k users exploring 94k datasets with 2.3 million attributes and 32k user-generated visualizations.

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“…We can solve Eq. 28 by computing the gradient and then using a first-order optimization method [Schenker et al 2021]. Afterwards, we have…”

Section: Pvisrecmentioning

confidence: 99%

Section: Pvisrec (Acm Only)mentioning

confidence: 99%

Personalized Visualization Recommendation

Qian¹,

Rossi²,

Du³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In our preliminary results, we have previously demonstrated the promise of AO-ADMM approach for Frobenius norm loss and exact linear couplings [35]. Here, we provide a more detailed derivation and discussion of the algorithm, and the extension to other loss functions.…”

Section: Introductionmentioning

confidence: 96%

A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings

Schenker,

Cohen,

Acar

2020

Preprint

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Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges in data fusion and require to employ various regularizations, constraints, loss functions and different types of coupling structures between datasets. In this paper, we propose a flexible algorithmic framework for coupled matrix and tensor factorizations which utilizes Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The framework facilitates the use of a variety of constraints, loss functions and couplings with linear transformations in a seamless way. Numerical experiments on simulated and real datasets demonstrate that the proposed approach is accurate, and computationally efficient with comparable or better performance than available CMTF methods for Frobenius norm loss, while being more flexible. Using Kullback-Leibler divergence on count data, we demonstrate that the algorithm yields accurate results also for other loss functions.

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“…In this paper, we propose fitting PARAFAC2 using an alternating optimization (AO) scheme with the alternating direction method of multipliers (ADMM). Recently, Huang et al introduced the AO-ADMM scheme for constrained CP models [29], and Schenker et al extended this framework to regularized linearly coupled matrixtensor decompositions [42,43]. AO-ADMM has also been successfully used to impose proximal constraints on the non-evolving factor matrices of the PARAFAC2 model [3].…”

Section: Introductionmentioning

confidence: 99%

An AO-ADMM approach to constraining PARAFAC2 on all modes

Roald,

Schenker,

Calhoun

et al. 2021

Preprint

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Analyzing multi-way measurements with variations across one mode of the dataset is a challenge in various fields including data mining, neuroscience and chemometrics. For example, measurements may evolve over time or have unaligned time profiles. The PARAFAC2 model has been successfully used to analyze such data by allowing the underlying factor matrices in one mode (i.e., the evolving mode) to change across slices. The traditional approach to fit a PARAFAC2 model is to use an alternating least squares-based algorithm, which handles the constant cross-product constraint of the PARAFAC2 model by implicitly estimating the evolving factor matrices. This approach makes imposing regularization on these factor matrices challenging. There is currently no algorithm to flexibly impose such regularization with general penalty functions and hard constraints. In order to address this challenge and to avoid the implicit estimation, in this paper, we propose an algorithm for fitting PARAFAC2 based on alternating optimization with the alternating direction method of multipliers (AO-ADMM). With numerical experiments on simulated data, we show that the proposed PARAFAC2 AO-ADMM approach allows for flexible constraints, recovers the underlying patterns accurately, and is computationally efficient compared to the state-of-the-art. We also apply our model to a realworld chromatography dataset, and show that constraining the evolving mode improves the interpretability of the extracted patterns.

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An Optimization Framework for Regularized Linearly Coupled Matrix-Tensor Factorization

Cited by 9 publications

References 18 publications

Personalized Visualization Recommendation

Personalized Visualization Recommendation

A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings

An AO-ADMM approach to constraining PARAFAC2 on all modes

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