标题： 带有领域选择的正则化线性分类器对功能片段的分类 显示英文标题

标题： Classification of functional fragments by regularized linear classifiers with domain selection

摘要： 我们研究了基于函数的一维投影的线性分类器将功能数据分为两类的问题。 我们将寻找最佳分类器的任务重新表述为一个优化问题，并通过正则化技术来解决它，即共轭梯度法（带早期停止）、主成分法和岭方法。 我们研究了具有有限训练样本的经验版本，这些样本由在域的不同子集上观察到的不完整函数组成，并表明最优的（可能为零的）错误分类概率可以在沿着可能不收敛的经验正则化路径时实现。 由于能够处理片段化的训练数据，我们提出了一种域扩展和选择程序，该程序可以在所有曲线的共同观测域之外找到最佳域。 在仿真研究中，我们比较了不同的正则化方法并调查了域选择的性能。 我们的方法在医学数据集中得到了应用，在该数据集中，我们观察到由于域扩展，分类准确性有了显著提高。 显示英文摘要

摘要： We consider the problem of classification of functional data into two groups by linear classifiers based on one-dimensional projections of functions. We reformulate the task to find the best classifier as an optimization problem and solve it by regularization techniques, namely the conjugate gradient method with early stopping, the principal component method and the ridge method. We study the empirical version with finite training samples consisting of incomplete functions observed on different subsets of the domain and show that the optimal, possibly zero, misclassification probability can be achieved in the limit along a possibly non-convergent empirical regularization path. Being able to work with fragmentary training data we propose a domain extension and selection procedure that finds the best domain beyond the common observation domain of all curves. In a simulation study we compare the different regularization methods and investigate the performance of domain selection. Our methodology is illustrated on a medical data set, where we observe a substantial improvement of classification accuracy due to domain extension.