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首页> 外文会议>Asilomar Conference on Signals, Systems and Computers >Nonstationary linear discriminant analysis
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Nonstationary linear discriminant analysis

机译：非平稳线性判别分析

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摘要

Changes in population distributions over time are common in many applications. However, the vast majority of statistical learning theory takes place under the assumption that all points in the training data are identically distributed (and independent), that is, non-stationarity of the data is disregarded. In this paper, a version of the classic Linear Discriminant Analysis (LDA) classification rule is proposed for nonstationary data, using a linear-Gaussian state space model. This Nonstationary LDA (NSLDA) classification rule is based on the Kalman Smoother algorithm to estimate the evolving population parameters. In case the dynamics of the system are not fully known, a combination of the Expectation-Maximization (EM) algorithm and the Kalman Smoother is employed to simultaneously estimate population and statespace equation parameters. Performance is assessed in a set of numerical experiments using simulated data, where the average error rates obtained by NSLDA are compared to the error produced by a naive application of LDA to the pooled nonstationary data. Results demonstrate the promise of the proposed NSLDA classification rule.
机译：人口分布随时间的变化在许多应用中很常见。但是，绝大多数统计学习理论都是在训练数据中的所有点都相同分布（且独立）的前提下发生的，也就是说，数据的非平稳性被忽略了。在本文中，使用线性高斯状态空间模型，针对非平稳数据，提出了经典线性判别分析（LDA）分类规则的一种版本。此非平稳LDA（NSLDA）分类规则基于Kalman平滑器算法来估计演化的种群参数。如果无法完全了解系统的动力学特性，则采用最大期望（EM）算法和卡尔曼平滑器的组合来同时估计总体和状态空间方程参数。在一组使用模拟数据的数值实验中评估了性能，将通过NSLDA获得的平均错误率与通过将LDA天真的应用到合并的非平稳数据所产生的错误进行比较。结果证明了提出的NSLDA分类规则的希望。

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