Functional clustering is based on functional similarity measures that are adapted to functional data. However, the existing functional similarity measures account either for the position (value) or temporal deviation (bias) of extreme points of the functional curves. This may lead to erroneous conclusions on the similarities of the curves. In this case, most functional clustering measures underperform in (for example) the analysis of stock market data. To address this methodological limitation, a new similarity measure that is based on extreme point bias compensation is proposed in this paper. By penalizing the curves with the temporal deviation of extreme points and rewarding the curves that are close to each other, the new similarity measure better reflects the shape of the curve. In addition, the proposed method overcomes the difficulty of unifying the dimensions of the horizontal and vertical axes (i.e., time and function value) when calculating the distance between two adjacent extreme points. Finally, an empirical example of stock return analysis verifies the validity of this new measure.

功能聚类基于适应功能数据的功能相似性度量。但是，现有的功能相似性度量要么考虑了功能曲线的极点的位置（值），要么考虑了时间偏差（偏差）。这可能导致关于曲线相似性的错误结论。在这种情况下，大多数功能聚类度量在（例如）股票市场数据分析中表现不佳。为了解决这种方法上的局限性，本文提出了一种基于极点偏差补偿的新的相似性度量。通过用极端点的时间偏差对曲线进行惩罚并奖励彼此靠近的曲线，新的相似性度量可以更好地反映曲线的形状。此外，该方法克服了在计算两个相邻极点之间的距离时统一水平轴和垂直轴的尺寸（即时间和函数值）的困难。最后，以股票收益分析为例，验证了该新方法的有效性。