Curve Classification Based on Mean-Variance Feature Weighting and Its Application

The classification of functional data has drawn much attention in recent years. The main challenge is representing infinite-dimensional functional data by finite-dimensional features while utilizing those features to achieve better classification accuracy. In this paper, we propose a mean-variance-based (MV) feature weighting method for classifying functional data or functional curves. In the feature extraction stage, each sample curve is approximated by B-splines to transfer features to the coefficients of the spline basis. After that, a feature weighting approach based on statistical principles is introduced by comprehensively considering the between-class differences and within-class variations of the coefficients. We also introduce a scaling parameter to adjust the gap between the weights of features. The new feature weighting approach can adaptively enhance noteworthy local features while mitigating the impact of confusing features. The algorithms for feature weighted K-nearest neighbor and support vector machine classifiers are both provided. Moreover, the new approach can be well integrated into existing functional data classifiers, such as the generalized functional linear model and functional linear discriminant analysis, resulting in a more accurate classification. The performance of the mean-variance-based classifiers is evaluated by simulation studies and real data. The results show that the new feature weighting approach significantly improves the classification accuracy for complex functional data.