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Near-Convex Archetypal Analysis [article]

Pierre De Handschutter, Nicolas Gillis, Arnaud Vandaele, Xavier Siebert
2019 arXiv   pre-print
In this letter, we introduce near-convex archetypal analysis (NCAA) which combines the advantages of both AA and NMF.  ...  Archetypal analysis (AA), also referred to as convex NMF, is a well-known NMF variant imposing that the basis elements are themselves convex combinations of the data points.  ...  In this work, we propose a new model, dubbed near-convex archetypal analysis (NCAA), which benefits from the advantages of both NMF via low reconstruction error and AA via interpretability.  ... 
arXiv:1910.00821v1 fatcat:ou44mgf4qvabplwkcteuwpfvxq

Theories of Optimization, Form and Function in Branching Architecture in Plants

K. D. Farnsworth, K. J. Niklas
1995 Functional Ecology  
Note that the projection of a convex hull is also a convex hull. Thus we are still left with significant informationthe values of the measured traits are still convex combinations of the archetypes.  ...  The species near vertices -large ground finch, small ground finch and cactus finch -suggest the nature of the three archetypes, as detailed below. ( Figure S6B ).  ... 
doi:10.2307/2389997 fatcat:ftrazo76srdv3nc5ghxyrw53be

Convex representations using deep archetypal analysis for predicting glaucoma

Anshul Thakur, Michael Goldbaum, Siamak Yousefi
2020 IEEE Journal of Translational Engineering in Health and Medicine  
Deep archetypal analysis models may impact clinical practice in effectively identifying at-risk glaucoma patients well prior to disease development.  ...  Methods: We developed a deep archetypal analysis to identify patterns of glaucomatous vision loss, and then projected visual fields over the identified patterns.  ...  The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.  ... 
doi:10.1109/jtehm.2020.2982150 pmid:32596065 pmcid:PMC7316201 fatcat:4qsp3z7e2jhshptydraptz3zni

Archetypal analysis of galaxy spectra

B. H. P. Chan, D. A. Mitchell, L. E. Cram
2003 Monthly notices of the Royal Astronomical Society  
We show that archetypal analysis is robust in the presence of various types of noise.  ...  Archetypal analysis represents each individual member of a set of data vectors as a mixture (a constrained linear combination) of the pure types or archetypes of the data set.  ...  Archetypal analysis is a representation using basis vectors lying on the data convex hull.  ... 
doi:10.1046/j.1365-8711.2003.06099.x fatcat:f4r3g6iqejb2jbyz74m4cpkz7y

Unsupervised Learning of Artistic Styles with Archetypal Style Analysis [article]

Daan Wynen, Cordelia Schmid, Julien Mairal
2018 arXiv   pre-print
Our method is based on archetypal analysis, which is an unsupervised learning technique akin to sparse coding with a geometric interpretation.  ...  After training the model, the style of a new image, which is characterized by local statistics of deep visual features, is approximated by a sparse convex combination of archetypes.  ...  Figure 1 : 1 Using deep archetypal style analysis, we can represent an artistic image (a) as a convex combination of archetypes.  ... 
arXiv:1805.11155v2 fatcat:e4cv3kcak5grfb6zkhd32vencm

Probabilistic Archetypal Analysis [article]

Sohan Seth, Manuel J. A. Eugster
2014 arXiv   pre-print
Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes.  ...  We also present an appropriate visualization tool to summarize archetypal analysis solution better.  ...  Introduction Archetypal analysis (AA) represents observations as composition of pure patterns, i.e., archetypes, or equivalently convex combinations of extreme values (Cutler and Breiman, 1994) .  ... 
arXiv:1312.7604v2 fatcat:mpvvr5txpfa7plugctmoewq55a

Probabilistic archetypal analysis

Sohan Seth, Manuel J. A. Eugster
2015 Machine Learning  
Archetypal analysis represents a set of observations as convex combinations of pure patterns, or archetypes.  ...  We also present an appropriate visualization tool to summarize archetypal analysis solution better.  ...  They assumed the archetypes to be convex combinations of observations, and the observations to be convex combinations of the archetypes.  ... 
doi:10.1007/s10994-015-5498-8 fatcat:p4vqog6p3rapfdxq6vhpqmjxze

Archetypal personalities of software engineers and their work preferences: a new perspective for empirical studies

Makrina Viola Kosti, Robert Feldt, Lefteris Angelis
2015 Empirical Software Engineering  
We also discuss how Archetypal Analysis, the heart of the proposed methodology, combined with multi-correspondence analysis might be of general use in empirical SE.  ...  Then, the method examines the placement of all individuals in the dataset in relation to the archetypes.  ...  For our dataset, we observe two formations with individuals centered near Archetypes 3 and 1.  ... 
doi:10.1007/s10664-015-9395-3 fatcat:4oxeuqcm5rdg3dnrkl2w352e5q

A Geometric Approach to Archetypal Analysis via Sparse Projections

Vinayak Abrol, Pulkit Sharma
2020 International Conference on Machine Learning  
Archetypal analysis (AA) aims to extract patterns using self-expressive decomposition of data as convex combinations of extremal points (on the convex hull) of the data.  ...  In the transformed space, GAA employs an iterative subset selection approach to identify archetypes based on the sparsity of convex representations.  ...  Here, GAA seems to be favouring the points near the top-right edge.  ... 
dblp:conf/icml/AbrolS20 fatcat:w24qvvtb7fahlmvig5nsxt76f4

Archetypal Analysis: Mining Weather and Climate Extremes

A. Hannachi, N. Trendafilov
2017 Journal of Climate  
This paper explores a different method, the archetypal analysis (AA), which focuses precisely on the extremes.  ...  AA seeks to approximate the convex hull of the data in state space by finding "corners" that represent "pure" types or archetypes through computing mixture weight matrices.  ...  This paper explores a different analysis tool, the archetypal analysis (AA), to identify ''pure'' types or archetypes of the data where these archetypes are expressed as a mixture (or convex combination  ... 
doi:10.1175/jcli-d-16-0798.1 fatcat:ucfp5f4c3ne6rba6zncbj55mne

Archetypal analysis for machine learning

Morten Morup, Lars Kai Hansen
2010 2010 IEEE International Workshop on Machine Learning for Signal Processing  
Archetypal analysis (AA) proposed by Cutler and Breiman in [1] estimates the principal convex hull of a data set.  ...  As such AA favors features that constitute representative 'corners' of the data, i.e. distinct aspects or archetypes.  ...  ARCHETYPAL ANALYSIS AND THE PRINCIPAL CONVEX HULL The convex hull also denoted the convex envelope of a data matrix X is the minimal convex set containing X.  ... 
doi:10.1109/mlsp.2010.5589222 fatcat:d7un7jsmprayfgbbjkckzed66q

Prototypal Analysis and Prototypal Regression [article]

Chenyue Wu, Esteban G. Tabak
2017 arXiv   pre-print
Same as archetypal analysis, prototypal analysis finds prototypes through convex combination of the data points and approximates the data through convex combination of the archetypes, but it adds a penalty  ...  Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool.  ...  Archetypal Analysis Archetypal analysis approximates data points by convex combination of "archetypes", which are themselves convex combinations of the data points (see Cutler and Breiman, 1994) .  ... 
arXiv:1701.08916v2 fatcat:uqanze2pyba3pijd33rwcp47yi

Combining electro- and magnetoencephalography data using directional archetypal analysis

Anders S. Olsen, Rasmus M. T. Høegh, Jesper L. Hinrich, Kristoffer H. Madsen, Morten Mørup
2022 Frontiers in Neuroscience  
We present multimodal, multisubject directional archetypal analysis as a scale and polarity invariant extension to archetypal analysis using a loss function based on the Watson distribution.  ...  The input data is reconstructed as convex combinations of archetypes using a subject- and modality-specific continuous archetypal mixing matrix.  ...  The solutions obtained using conventional Euclidean archetypal analysis and directional archetypal analysis with K = 3 components and the convex hull spanned by the archetypes, as well as centroids determined  ... 
doi:10.3389/fnins.2022.911034 pmid:35968377 pmcid:PMC9374169 fatcat:zj5rcs5vqzcr5kr2ah3y6ozpea

Probabilistic methods for approximate archetypal analysis [article]

Ruijian Han, Braxton Osting, Dong Wang, Yiming Xu
2021 arXiv   pre-print
Archetypal analysis is an unsupervised learning method for exploratory data analysis.  ...  , our method can effectively reduce the scaling of archetypal analysis.  ...  In particular, we show that the reduced archetypal analysis gives a near-optimal solution but has significantly reduced complexity provided that the data is low-dimensional and approximately described  ... 
arXiv:2108.05767v2 fatcat:ozuyigxcqzhsvjxt6kpk5isv5u

Learning Extremal Representations with Deep Archetypal Analysis

Sebastian Mathias Keller, Maxim Samarin, Fabricio Arend Torres, Mario Wieser, Volker Roth
2020 International Journal of Computer Vision  
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.  ...  Deep Archetypal Analysis Deep Archetypal Analysis can then be formulated in the following way.  ... 
doi:10.1007/s11263-020-01390-3 pmid:34720403 pmcid:PMC8550171 fatcat:x5bnaoyflzg2zpyqnzdkbxpbhm
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