| 1. |
- Gyllenberg, Mats, et al.
(författare)
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Non-uniqueness of numerical taxonomic structures
- 1993
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Ingår i: Binary Computing in Microbiology. - 0266-304X. ; 5:4, s. 138-144
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Tidskriftsartikel (refereegranskat)abstract
- The most important methods of numerical taxonomy in microbiology are based on so called reference matrices giving the frequencies of positive binary features of the different taxa. Microbiologists seem to have been tacitly assuming that every well-defined classification method, that is, every algorithm for constructing a reference matrix from data, leads to a unique classification (reference matrix). We use a mathematical result-that a finite mixture of multivariate Bernoulli distributions is always unidentifiable-to disprove this assumption. We show that the same classification method applied to the same data can always lead to different classifications. This result is of importance for the foundations of computational microbial taxonomy. It is illustrated by simple examples from the two main methods of classification and identification: the one where classification is performed first and then followed by identification, and cumulative classification where classification and identification are carried out simultaneously. The consequences of the non-uniqueness result for microbiological practice are discussed
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| 2. |
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| 3. |
- Austin, Brian, et al.
(författare)
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Sliding window discretization : A new method for multiple band matching of bacterial genotyping fingerprints
- 2004
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Ingår i: Bulletin of Mathematical Biology. - : Springer Science and Business Media LLC. - 0092-8240 .- 1522-9602. ; 66:6, s. 1575-1596
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Tidskriftsartikel (refereegranskat)abstract
- Microbiologists have traditionally applied hierarchical clustering algorithms as their mathematical tool of choice to unravel the taxonomic relationships between micro-organisms. However, the interpretation of such hierarchical classifications suffers from being subjective, in that a variety of ad hoc choices must be made during their construction. On the other hand, the application of more profound and objective mathematical methods - such as the minimization of stochastic complexity - for the classification of bacterial genotyping fingerprints data is hampered by the prerequisite that such methods only act upon vectorized data. In this paper we introduce a new method, coined sliding window discretization, for the transformation of genotypic fingerprint patterns into binary vector format. In the context of an extensive amplified fragment length polymorphism (AFLP) data set of 507 strains from the Vibrionaceae family that has previously been analysed, we demonstrate by comparison with a number of other discretization methods that this new discretization method results in minimal loss of the original information content captured in the banding patterns. Finally, we investigate the implications of the different discretization methods on the classification of bacterial genotyping fingerprints by minimization of stochastic complexity, as it is implemented in the BinClass software package for probabilistic clustering of binary vectors. The new taxonomic insights learned from the resulting classification of the AFLP patterns will prove the value of combining sliding window discretization with minimization of stochastic complexity, as an alternative classification algorithm for bacterial genotyping fingerprints.
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| 4. |
- Corander, Jukka, et al.
(författare)
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Bayesian model learning based on a parallel MCMC strategy
- 2006
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Ingår i: Statistics and computing. - : Springer Science and Business Media LLC. - 0960-3174 .- 1573-1375. ; 16:4, s. 355-362
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a novel Markov chain Monte Carlo algorithm for estimation of posterior probabilities over discrete model spaces. Our learning approach is applicable to families of models for which the marginal likelihood can be analytically calculated, either exactly or approximately, given any fixed structure. It is argued that for certain model neighborhood structures, the ordinary reversible Metropolis-Hastings algorithm does not yield an appropriate solution to the estimation problem. Therefore, we develop an alternative, non-reversible algorithm which can avoid the scaling effect of the neighborhood. To efficiently explore a model space, a finite number of interacting parallel stochastic processes is utilized. Our interaction scheme enables exploration of several local neighborhoods of a model space simultaneously, while it prevents the absorption of any particular process to a relatively inferior state. We illustrate the advantages of our method by an application to a classification model. In particular, we use an extensive bacterial database and compare our results with results obtained by different methods for the same data.
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| 5. |
- Corander, Jukka, et al.
(författare)
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Bayesian unsupervised classification framework based on stochastic partitions of data and a parallel search strategy
- 2009
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Ingår i: Advances in Data Analysis and Classification. - : Springer Berlin/Heidelberg. - 1862-5347 .- 1862-5355. ; 3:1, s. 3-24
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Tidskriftsartikel (refereegranskat)abstract
- Advantages of statistical model-based unsupervised classification over heuristic alternatives have been widely demonstrated in the scientific literature. However, the existing model-based approaches are often both conceptually and numerically instable for large and complex data sets. Here we consider a Bayesian model-based method for unsupervised classification of discrete valued vectors, that has certain advantages over standard solutions based on latent class models. Our theoretical formulation defines a posterior probability measure on the space of classification solutions corresponding to stochastic partitions of observed data. To efficiently explore the classification space we use a parallel search strategy based on non-reversible stochastic processes. A decision-theoretic approach is utilized to formalize the inferential process in the context of unsupervised classification. Both real and simulated data sets are used for the illustration of the discussed methods.
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| 6. |
- Corander, Jukka, et al.
(författare)
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Learning Genetic Population Structures Using Minimization of Stochastic Complexity
- 2010
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Ingår i: Entropy. - : MDPI AG. - 1099-4300. ; 12:5, s. 1102-1124
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Tidskriftsartikel (refereegranskat)abstract
- Considerable research efforts have been devoted to probabilistic modeling of genetic population structures within the past decade. In particular, a wide spectrum of Bayesian models have been proposed for unlinked molecular marker data from diploid organisms. Here we derive a theoretical framework for learning genetic population structure of a haploid organism from bi-allelic markers for which potential patterns of dependence are a priori unknown and to be explicitly incorporated in the model. Our framework is based on the principle of minimizing stochastic complexity of an unsupervised classification under tree augmented factorization of the predictive data distribution. We discuss a fast implementation of the learning framework using deterministic algorithms.
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| 7. |
- Corander, Jukka, et al.
(författare)
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Random partition models and exchangeability for Bayesian identification of population structure
- 2007
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Ingår i: Bulletin of Mathematical Biology. - : Springer Science and Business Media LLC. - 0092-8240 .- 1522-9602. ; 69:3, s. 797-815
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a Bayesian theoretical formulation of the statistical learning problem concerning the genetic structure of populations. The two key concepts in our derivation are exchangeability in its various forms and random allocation models. Implications of our results to empirical investigation of the population structure are discussed.
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| 8. |
- Dawyndt, Peter, et al.
(författare)
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A complementary approach to systematics
- 2005
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Ingår i: Microbiology Today. - 1464-0570. ; :February, s. 38-38
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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