Pdf of the presentation - Universitat de València

22 Pages·2013·4.05 MB·English

Archetypes and Archetypoids: Contributions for
estimating boundary cases in Anthropometry
and Ergonomics
Guillermo Vinu´e Visu´s
PhD student
Faculty of Mathematics
University of Valencia, Spain
Jointly with Irene Epifanio Lo´pez (University Jaume I of Castello´n) and
Sandra Alemany Mut (Biomechanics Institute of Valencia)
XIV Conferencia Espan˜ola de Biometr´ıa, 22-24 May 2013, Ciudad Real,
Spain
AccommodationprobleminAnthropometryandErgonomics
Usualapproaches
Archetypalanalysis
Ourcontributions
Conclusions
Basicreferences
Outline
1 Accommodation problem in Anthropometry and Ergonomics
2 Usual approaches
3 Archetypal analysis
What’s an archetype?
Statistical definition of archetype
4 Our contributions
Archetypal analysis vs PCA
Archetypoid analysis
5 Conclusions
6 Basic references
GuillermoVinu´eVisu´s ArchetypesandArchetypoids 2/20
AccommodationprobleminAnthropometryandErgonomics
Usualapproaches
Archetypalanalysis
Ourcontributions
Conclusions
Basicreferences
Accommodation problem in Anthropometry and
Ergonomics
Theaccommodationistheprocessofmutualadaptationbetweenpersons.
Products intended to fit the users must be designed considering their size
and shape → Generation of several representative human models.
The human models represents the anthropometric variability of the target
population.
The appropriate selection of this small group is critical.
If the hard to fit extreme individuals are previously identified, the time
and cost of the design process is reduced.
GuillermoVinu´eVisu´s ArchetypesandArchetypoids 3/20
AccommodationprobleminAnthropometryandErgonomics
Usualapproaches
Archetypalanalysis
Ourcontributions
Conclusions
Basicreferences
Usual approaches
Percentile analysis: Traditional method used.
Drawbacks: Univariate approach. They are not additive.
(Image taken of Robinette et al. (1981))
GuillermoVinu´eVisu´s ArchetypesandArchetypoids 4/20
AccommodationprobleminAnthropometryandErgonomics
Usualapproaches
Archetypalanalysis
Ourcontributions
Conclusions
Basicreferences
Regression: An alternative to approximate a percentile person.
The predicted numbers are additive.
Drawback: It only provides average values for the predicted
measurements.
Principal component analysis (PCA):
ItconsidersthefirstPC
andselectsseveralextremepoints
inanellipse(orcircle)whichcovers
acertainpercentageofthedata.
Drawbacks: Partofthedatavariation
isremoved. Thenumberofcaseswould
increaseifwewantedtoconsidermore
variation.
Our proposal: ARCHETYPAL ANALYSIS (AA) (Cutler et al. (1994)).
GuillermoVinu´eVisu´s ArchetypesandArchetypoids 5/20
AccommodationprobleminAnthropometryandErgonomics
Usualapproaches
Archetypalanalysis What’sanarchetype?
Ourcontributions Statisticaldefinitionofarchetype
Conclusions
Basicreferences
In our everyday language...
GuillermoVinu´eVisu´s ArchetypesandArchetypoids 6/20
AccommodationprobleminAnthropometryandErgonomics
Usualapproaches
Archetypalanalysis What’sanarchetype?
Ourcontributions Statisticaldefinitionofarchetype
Conclusions
Basicreferences
But in Statistics???
AND:
Source: Paquet,E.ExploringAnthropometricDataThroughClusterAnalysis.
PublishedinDigitalHumanModelingforDesignandEngineering(DHM).June15-17,
2004. OaklandUniversity,Rochester,Michigan,USA.NRC46564.
An archetype is not a prototype!!!
GuillermoVinu´eVisu´s ArchetypesandArchetypoids 7/20
AccommodationprobleminAnthropometryandErgonomics
Usualapproaches
Archetypalanalysis What’sanarchetype?
Ourcontributions Statisticaldefinitionofarchetype
Conclusions
Basicreferences
Statistical definition of archetype
Let be an n×m matrix X, multivariate database.
The AA aims at obtaining the n×k matrices α and β which minimize:
n k n k n
RSS =(cid:88)(cid:107)x −(cid:88)α z(cid:107)2 =(cid:88)(cid:107)x −(cid:88)α (cid:88)β x(cid:107)2
i ij j i ij jl l
i=1 j=1 i=1 j=1 l=1
under the constraints
k k
(cid:88) (cid:88)
1) α =1 with α ≥0 and i =1,...,n =⇒ ˆx = α z
ij ij i ij j
j=1 j=1
n
(cid:88)
2) β =1 with β ≥0 and j =1,...,k
jl jl
l=1
ARCHETYPE: extreme member of the data set that is a mixture of the
n
(cid:88)
actual data points: z = β x
j jl l
l=1
Archetypes can be computed with the R package archetypes.
GuillermoVinu´eVisu´s ArchetypesandArchetypoids 8/20
AccommodationprobleminAnthropometryandErgonomics
Usualapproaches
Archetypalanalysis ArchetypalanalysisvsPCA
Ourcontributions Archetypoidanalysis
Conclusions
Basicreferences
Archetypal analysis vs PCA
The goal of AA is to obtain extreme individuals.
The level of accommodation is reached with AA.
Archetypes cannot be obtained with PCA.
The number of archetypes can be decided by the user or by a criterion.
GuillermoVinu´eVisu´s ArchetypesandArchetypoids 9/20
AccommodationprobleminAnthropometryandErgonomics
Usualapproaches
Archetypalanalysis ArchetypalanalysisvsPCA
Ourcontributions Archetypoidanalysis
Conclusions
Basicreferences
Archetypoid analysis
The archetypes do not correspond to observed individuals:
n n
(cid:88) (cid:88)
zj = βjlxl with βjl =1 and βjl ≥0
l=1 l=1
In some cases it is critical that the archetypes are real subjects.
So far the nearest individuals to archetypes are computed in two ways:
1 nearest: Subjects who have the closest dE to archetypes.
2 which: Subjects with the greatest α for each archetype.
The identified archetypes can be artificial: “no economist in our sample
fits this archetype to 100%” (Seiler et al. (2013)).
A new archetypal concept is proposed: the ARCHETYPOID:
n n
(cid:88) (cid:88)
zj = βjlxl with βjl =1 and βjl ∈{0,1}
l=1 l=1
An archetypoid is a real observed individual.
The archetypoids might not be the same as the nearest/which.
The archetypoids always exist even when the features are unavailable.
GuillermoVinu´eVisu´s ArchetypesandArchetypoids 10/20