Copula Archetypal Analysis

Kaufmann, Dinu; Keller, Sebastian Mathias; Röth, Volker

doi:10.1007/978-3-319-24947-6_10

Cited by 3 publications

(3 citation statements)

References 17 publications

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“…An extension of the original Archetypal Analysis model to non-linear kernel Archetypal Analysis is proposed by Bauckhage and Manshaei (2014); Mørup and Hansen (2012). In Kaufmann et al (2015), the authors use a copula based approach to make AA independent of strictly monotone transformations of the input data. The reasoning is that such transformations should in general not influence which points are identified as archetypes.…”

Section: Related Workmentioning

confidence: 99%

Learning Extremal Representations with Deep Archetypal Analysis

et al. 2020

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Archetypes represent extreme manifestations of a population with respect to specific characteristic traits or features. In linear feature space, archetypes approximate the data convex hull allowing all data points to be expressed as convex mixtures of archetypes. As mixing of archetypes is performed directly on the input data, linear Archetypal Analysis requires additivity of the input, which is a strong assumption unlikely to hold e.g. in case of image data. To address this problem, we propose learning an appropriate latent feature space while simultaneously identifying suitable archetypes. We thus introduce a generative formulation of the linear archetype model, parameterized by neural networks. By introducing the distance-dependent archetype loss, the linear archetype model can be integrated into the latent space of a deep variational information bottleneck and an optimal representation, together with the archetypes, can be learned end-to-end. Moreover, the information bottleneck framework allows for a natural incorporation of arbitrarily complex side information during training. As a consequence, learned archetypes become easily interpretable as they derive their meaning directly from the included side information. Applicability of the proposed method is demonstrated by exploring archetypes of female facial expressions while using multi-rater based emotion scores of these expressions as side information. A second application illustrates the exploration of the chemical space of small organic molecules. By using different kinds of side information we demonstrate how identified archetypes, along with their interpretation, largely depend on the side information provided.

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Section: Related Workmentioning

confidence: 99%

Learning Extremal Representations with Deep Archetypal Analysis

et al. 2020

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“…An extension of the original archetypal analysis model to non-linear kernel archetypal analysis is proposed by Bauckhage and Manshaei (2014); Mørup and Hansen (2012). In Kaufmann et al (2015), the authors use a copula based approach to make AA independent of strictly monotone transformations of the input data. The reasoning is that such transformations should in general not influence which points are identified as archetypes.…”

Section: Related Workmentioning

confidence: 99%

Learning Extremal Representations with Deep Archetypal Analysis

Keller¹,

Samarin²,

Torres³

et al. 2020

Preprint

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Archetypes are typical population representatives in an extremal sense, where typicality is understood as the most extreme manifestation of a trait or feature. In linear feature space, archetypes approximate the data convex hull allowing all data points to be expressed as convex mixtures of archetypes. However, it might not always be possible to identify meaningful archetypes in a given feature space. As features are selected a priori, the resulting representation of the data might only be poorly approximated as a convex mixture. Learning an appropriate feature space and identifying suitable archetypes simultaneously addresses this problem. This paper introduces a generative formulation of the linear archetype model, parameterized by neural networks. By introducing the distance-dependent archetype loss, the linear archetype model can be integrated into the latent space of a variational autoencoder, and an optimal representation with respect to the unknown archetypes can be learned end-to-end. The reformulation of linear Archetypal Analysis as a variational autoencoder naturally leads to an extension of the model to a deep variational information bottleneck, allowing the incorporation of arbitrarily complex side information during training. As a consequence, the answer to the question "What is typical in a given data set?" can be guided by this additional information. Furthermore, an alternative prior, based on a modified Dirichlet distribution, is proposed. On a theoretical level, this makes the relation to the original archetypal analysis model more explicit, where observations are mod-

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“…An extension to Kernel AA is proposed by (Bauckhage & Manshaei, 2014), algorithmic improvements by adapting a Frank-Wolfe type algorithm to calculate the archetypes are made by (Bauckhage et al, 2015) and the extension by (Seth & Eugster, 2016) introduces a probabilistic version of AA. In (Prabhakaran et al, 2012) the authors are concerned with model selection by asking for the optimal number of archetypes for a given dataset while (Kaufmann et al, 2015) addresses in part the shortcoming of AA we describe in the introduction under (ii). Although AA did not prevail as a commodity tool for pattern analysis it has for example been used by (Bauckhage & Thurau, 2009) to find archetypal images in large image collections or by (Canhasi & Kononenko, 2015) to perform the analogous task for large document collections.…”

Section: Introductionmentioning

confidence: 99%

Deep Archetypal Analysis

Keller

Samarin

Wieser

et al. 2019

Lecture Notes in Computer Science

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Deep Archetypal Analysis" generates latent representations of high-dimensional datasets in terms of fractions of intuitively understandable basic entities called archetypes. The proposed method is an extension of linear "Archetypal Analysis" (AA), an unsupervised method to represent multivariate data points as sparse convex combinations of extremal elements of the dataset. Unlike the original formulation of AA, "Deep AA" can also handle side information and provides the ability for data-driven representation learning which reduces the dependence on expert knowledge. Our method is motivated by studies of evolutionary trade-offs in biology where archetypes are species highly adapted to a single task. Along these lines, we demonstrate that "Deep AA" also lends itself to the supervised exploration of chemical space, marking a distinct starting point for de novo molecular design. In the unsupervised setting we show how "Deep AA" is used on CelebA to identify archetypal faces. These can then be superimposed in order to generate new faces which inherit dominant traits of the archetypes they are based on.

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Copula Archetypal Analysis

Cited by 3 publications

References 17 publications

Learning Extremal Representations with Deep Archetypal Analysis

Learning Extremal Representations with Deep Archetypal Analysis

Learning Extremal Representations with Deep Archetypal Analysis

Deep Archetypal Analysis

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