IEEE Trans Pattern Anal Mach Intell. 2018 Jan;40(1):77-91. doi: 10.1109/TPAMI.2017.2665545. Epub 2017 Feb 7.
Since the observables at particular time instants in a temporal sequence exhibit dependencies, they are not independent samples. Thus, it is not plausible to apply i.i.d. assumption-based dimensionality reduction methods to sequence data. This paper presents a novel supervised dimensionality reduction approach for sequence data, called Linear Sequence Discriminant Analysis (LSDA). It learns a linear discriminative projection of the feature vectors in sequences to a lower-dimensional subspace by maximizing the separability of the sequence classes such that the entire sequences are holistically discriminated. The sequence class separability is constructed based on the sequence statistics, and the use of different statistics produces different LSDA methods. This paper presents and compares two novel LSDA methods, namely M-LSDA and D-LSDA. M-LSDA extracts model-based statistics by exploiting the dynamical structure of the sequence classes, and D-LSDA extracts the distance-based statistics by computing the pairwise similarity of samples from the same sequence class. Extensive experiments on several different tasks have demonstrated the effectiveness and the general applicability of the proposed methods.
由于时间序列中特定时间点的观测值存在依赖性，因此它们不是独立的样本。因此，应用基于独立同分布假设的降维方法对序列数据是不合理的。本文提出了一种新的序列数据监督降维方法，称为线性序列判别分析（Linear Sequence Discriminant Analysis，LSDA）。它通过最大化序列类别的可分离性来学习序列特征向量在低维子空间中的线性判别投影，从而整体上对序列进行判别。序列类别可分离性是基于序列统计量构建的，使用不同的统计量会产生不同的 LSDA 方法。本文提出并比较了两种新的 LSDA 方法，即 M-LSDA 和 D-LSDA。M-LSDA 通过利用序列类别的动态结构提取基于模型的统计量，而 D-LSDA 通过计算来自同一序列类的样本之间的成对相似度来提取基于距离的统计量。在几个不同任务上的大量实验表明了所提出方法的有效性和普遍适用性。
