CMStatistics 2017: Start Registration
View Submission - CMStatistics
Title: Domain selection for functional data classification Authors:  Nicolas Hernandez - Universidad Carlos III de Madrid (Spain) [presenting]
Gabriel Martos - Facultad de Ciencias Exactas y Naturales - Universidad de Buenos Aires (Argentina)
Alberto Munoz - Departmento de Estadistica - Universidad Carlos III de Madrid (Spain)
Abstract: A domain selection approach is proposed for classification problems in functional data. Consider two samples of random elements $f_1,\dots,f_n$ and $g_1,\dots,g_m$ in $L^2(X)$ generated from the functional stochastic models $f_i(x) = \mu_k(x) + \varepsilon_i(x)$ for $i=1,\dots,n$ and $g_j(x) = \mu_k(x) + \varepsilon_j(x)$ for $j=1\dots,m$ respectively and defined on the same domain $X=[0,1]$. The function $\mu_k(x)$ is the mean function for $k=f,g$ and $\varepsilon(x)$ is a random and independent functional error that captures the variability within each class. In this setting, we propose to use a local--inner product parametrized by the vector $\boldsymbol \theta=(\theta_1,\theta_2)$, with $0\leqslant \theta_1 < \theta_2 \leqslant 1$, such that, $\langle f,g \rangle_{\boldsymbol \theta} = \displaystyle\int_{\theta_1}^{\theta_2} f(x)g(x)dx.$ The proposed inner--product induce a local--metric in the space of random elements $L^2(X)$. The optimization of $\boldsymbol \theta$ is presented as a domain selection technique, where the optimization goal pursue the minimization of the misclassification error rate when classifying samples of random functions.