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A unified framework for probabilistic component analysis
- Source :
- Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2014, 469-484, STARTPAGE=469;ENDPAGE=484;TITLE=Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2014, Machine Learning and Knowledge Discovery in Databases ISBN: 9783662448502, ECML/PKDD (2)
- Publication Year :
- 2014
- Publisher :
- Springer, 2014.
-
Abstract
- We present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood, thus providing an elegant and principled framework for creating novel component analysis models as well as constructing probabilistic equivalents of deterministic component analysis methods. Under our framework, we unify many very popular and well-studied component analysis algorithms, such as Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), Locality Preserving Projections (LPP) and Slow Feature Analysis (SFA), some of which have no probabilistic equivalents in literature thus far. We firstly define the Markov Random Fields (MRFs) which encapsulate the latent connectivity of the aforementioned component analysis techniques; subsequently, we show that the projection directions produced by all PCA, LDA, LPP and SFA are also produced by the Maximum Likelihood (ML) solution of a single joint probability density function, composed by selecting one of the defined MRF priors while utilising a simple observation model. Furthermore, we propose novel Expectation Maximization (EM) algorithms, exploiting the proposed joint PDF, while we generalize the proposed methodologies to arbitrary connectivities via parametrizable MRF products. Theoretical analysis and experiments on both simulated and real world data show the usefulness of the proposed framework, by deriving methods which well outperform state-of-the-art equivalents.
- Subjects :
- HMI-HF: Human Factors
Probabilistic Methods
Computer science
computer.software_genre
Probabilistic method
Component analysis
Prior probability
Expectation–maximization algorithm
EC Grant Agreement nr.: FP7/2007-2013
Dimensionality Reduction
EWI-25812
business.industry
Dimensionality reduction
Probabilistic logic
Unifying Framework
Pattern recognition
METIS-309931
IR-94679
Linear discriminant analysis
Random Fields
Component Analysis
Principal component analysis
EC Grant Agreement nr.: FP7/288235
Data mining
Artificial intelligence
business
computer
Subjects
Details
- ISBN :
- 978-3-662-44850-2
- ISBNs :
- 9783662448502
- Database :
- OpenAIRE
- Journal :
- Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2014, 469-484, STARTPAGE=469;ENDPAGE=484;TITLE=Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases, ECML PKDD 2014, Machine Learning and Knowledge Discovery in Databases ISBN: 9783662448502, ECML/PKDD (2)
- Accession number :
- edsair.doi.dedup.....493b39f842042df7480f7f6a3ff43857