基于Karhunen-Loève展开的函数主成分分析的线性相位型概率建模及其在阻变存储器中的应用
Linear-Phase-Type probability modelling of functional PCA with applications to resistive memories
AI总结：
本研究引入线性相位型分布对函数主成分分析中的主成分得分进行建模，并通过Karhunen-Loève展开证明过程的一维分布属于该类，应用于阻变存储器重置过程建模。
摘要：
基于Karhunen-Loève展开的函数主成分分析能够描述与多个系统和设备相关的主要特征的随机演化。识别主成分得分的概率分布对于表征整个过程至关重要。本工作的目标是考虑一族能够精确拟合先前变换的统计分布。为此，引入了一类新的分布——线性相位型分布，用于对主成分进行建模。对该类分布进行了详细研究，以通过KL展开证明过程在每个时间点的某些线性变换服从相位型分布。这样，过程的一维分布属于同一线性相位型类。最后，开发并解释了应用于阻变存储器重置过程建模的实例。
英文摘要：
Functional principal component analysis based on Karhunen Loeve expansion allows to describe the stochastic evolution of the main characteristics associated to multiple systems and devices. Identifying the probability distribution of the principal component scores is fundamental to characterize the whole process. The aim of this work is to consider a family of statistical distributions that could be accurately adjusted to a previous transformation. Then, a new class of distributions, the linear-phase-type, is introduced to model the principal components. This class is studied in detail in order to prove, through the KL expansion, that certain linear transformations of the process at each time point are phase-type distributed. This way, the one-dimensional distributions of the process are in the same linear-phase-type class. Finally, an application to model the reset process associated with resistive memories is developed and explained.
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