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Register a new userClassification of Functional Data with k-Nearest-Neighbor Ensembles by Fitting Constrained Multinomial Logit Models
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Karen Fuchs
Publication date
2016
fields
Mathematical Statistics
and research's language is
English
Authors
Karen Fuchs
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During the last decades, many methods for the analysis of functional data including classification methods have been developed. Nonetheless, there are issues that have not been adressed satisfactorily by currently available methods, as, for example, feature selection combined with variable selection when using multiple functional covariates. In this paper, a functional ensemble is combined with a penalized and constrained multinomial logit model. It is shown that this synthesis yields a powerful classification tool for functional data (possibly mixed with non-functional predictors), which also provides automatic variable selection. The choice of an appropriate, sparsity-inducing penalty allows to estimate most model coefficients to exactly zero, and permits class-specific coefficients in multiclass problems, such that feature selection is obtained. An additional constraint within the multinomial logit model ensures that the model coefficients can be considered as weights. Thus, the estimation results become interpretable with respect to the discriminative importance of the selected features, which is rated by a feature importance measure. In two application examples, data of a cell chip used for water quality monitoring experiments and phoneme data used for speech recognition, the interpretability as well as the selection results are examined. The classification performance is compared to various other classification approaches which are in common use.
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This article is concerned with the fitting of multinomial regression models using the so-called Poisson Trick. The work is motivated by Chen & Kuo (2001) and Malchow-M{o}ller & Svarer (2003) which have been criticized for being computationally inefficient and sometimes producing nonsense results. We first discuss the case of independent data and offer a parsimonious fitting strategy when all covariates are categorical. We then propose a new approach for modelling correlated responses based on an extension of the Gamma-Poisson model, where the likelihood can be expressed in closed-form. The parameters are estimated via an Expectation/Conditional Maximization (ECM) algorithm, which can be implemented using functions for fitting generalized linear models readily available in standard statistical software packages. Compared to existing methods, our approach avoids the need to approximate the intractable integrals and thus the inference is exact with respect to the approximating Gamma-Poisson model. The proposed method is illustrated via a reanalysis of the yogurt data discussed by Chen & Kuo (2001).
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