IEEE Trans Neural Netw Learn Syst. 2013 Aug;24(8):1279-91. doi: 10.1109/TNNLS.2013.2254720.
Division of a time series into segments is a common technique for time-series processing, and is known as segmentation. Segmentation is traditionally done by linear interpolation in order to guarantee the continuity of the reconstructed time series. The interpolation-based segmentation methods may perform poorly for data with a level of noise because interpolation is noise sensitive. To handle the problem, this paper establishes an explicit expression for segmentation from a compact representation for piecewise linear functions using hinging hyperplanes. This expression enables the use of regression to obtain a continuous reconstructed signal and, as a consequence, application of advanced techniques in segmentation. In this paper, a least squares support vector machine with lasso using a hinging feature map is given and analyzed, based on which a segmentation algorithm and its online version are established. Numerical experiments conducted on synthetic and real-world datasets demonstrate the advantages of our methods compared to existing segmentation algorithms.
将时间序列划分为段是时间序列处理的常用技术，通常称为分段。传统上，分段是通过线性插值来保证重建时间序列的连续性。基于插值的分段方法对于具有一定噪声水平的数据可能表现不佳，因为插值对噪声敏感。为了解决这个问题，本文使用枢轴超平面从分段线性函数的紧凑表示中建立了分段的显式表达式。该表达式允许使用回归来获得连续的重建信号，从而可以应用分段的高级技术。在本文中，提出并分析了基于枢轴特征映射的带有lasso 的最小二乘支持向量机，在此基础上建立了分段算法及其在线版本。在合成和真实数据集上的数值实验表明，与现有分段算法相比，我们的方法具有优势。
