## Solving Particularization with Supervised Clustering Competition Scheme

### BibTeX

@MISC{Pujol_solvingparticularization,

author = {Oriol Pujol and Petia Radeva},

title = {Solving Particularization with Supervised Clustering Competition Scheme},

year = {}

}

### OpenURL

### Abstract

Abstract. The process of mixing labelled and unlabelled data is being recently studied in semi-supervision techniques. However, this is not the only scenario in which mixture of labelled and unlabelled data can be done. In this paper we propose a new problem we have called particularization and a way to solve it. We also propose a new technique for mixing labelled and unlabelled data. This technique relies in the combination of supervised and unsupervised processes competing for the classification of each data point. Encouraging results on improving the classification outcome are obtained on MNIST database. 1

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(Show Context)
Citation Context ...β ) where β is a normalization term. Let the monotone increasing function f(·) be, f(·) =(·) γ , γ > 0 Therefore, the complete similarity measure Js(x) is, Js(x) = c∑ n∑ i=1 j=1 ( − e ‖zj −xi‖2 ) γ β =-=(3)-=- The parameter β is superfluous in this scheme and can be defined as the sample variance, ∑n j=1 ‖zj − ¯z‖ 2 β = where ¯z = ∑ n j=1 zj n n The parameter γ gains a considerable importance in this schem... |

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Citation Context ...centers by the unlabelled data points z 0 = x 0 , UF(x) =Js(x) = Getting its gradient, we obtain, ∇UF(x) =−2 γ n∑ β j=1 n∑ j=1 ( − e ‖zj −xk‖2 ) γ, β k =1...n ( − e ‖zj −xk‖2 ) γ(zj β − xk), k =1...n =-=(4)-=- 2.2 Supervised Classifier Functional The definition of the supervised classifier functional should be made so that both processes can interact with each other. Therefore, we must reformulate the supe... |

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(Show Context)
Citation Context ... scheme is, xt+1 = xt −△t ·∇F (x)Solving Particularization with Supervised Clustering Competition Scheme 13 where ∇F (x) ={∂F(x)/∂xi}. Therefore, ∂x ∂t ∇SF(x) ∇UF(x) = −α − (1 − α) ‖∇SF(x)‖ ‖∇UF(x)‖ =-=(2)-=- The next step is to define the minimization process that represent the supervised classification and the clustering process. Similarity Clustering. When considering the unsupervised functional, we ar... |

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Citation Context ...m, since we want the minimums to represent each of the classes. It can be easily seen that the following family of functions satisfies the requirement, SF = −(f(x|c = A) − f(x|c = B)) 2N , ∀N ∈{1..∞} =-=(5)-=- In order to obtain a feasible closed form of the functional we can restrict the density estimation process to a Gaussian mixture model, Mk ∑ SF(x) =fK(x) = πigi(x,θi) where Mk is the model order and ... |

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Citation Context ...daptation. J.S. Marques et al. (Eds.): IbPRIA 2005, LNCS 3523, pp. 11–18, 2005. c○ Springer-Verlag Berlin Heidelberg 200512 Oriol Pujol and Petia Radeva On the image domain, the work of Kumar et al. =-=[10]-=- use an EM based refinement of a generative model to infer the particularities of the new data, in what they call specification. Here, the particularization problem refers to all those problems in whi... |

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Citation Context ...data set is a particular subset of the general training data set. On the other hand, this problem is widely recognized in other domains, such as human learning theory [8]ornatural language processing =-=[9]-=-. In those domains, research is done in the line of finding the context of the application given a wide training set. In particular, a general language training corpus has to be changed for domain-spe... |

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1 |
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Citation Context ...wledge of the fact that our test data set is a particular subset of the general training data set. On the other hand, this problem is widely recognized in other domains, such as human learning theory =-=[8]-=-ornatural language processing [9]. In those domains, research is done in the line of finding the context of the application given a wide training set. In particular, a general language training corpus... |