Speaker Recognition: Gaussian probabilistic LDA (PLDA)理解

"MSR Identity Toolbox"里使用到了G-PLDA(Gaussian probabilistic LDA)。

根据文献[1]对G-PLDA的原理进行了初步的了解，记录如下。

1. 简化版的G-PLDA的模型定义如公式(3)。

这里是观察向量，m是均值，是说话人特征子空间矩阵，是说话人隐变量，是残差高斯噪声。

2. 根据文献[1]，loglikelihood ratio for this hypothesis test定义如下。分子是假定是同一说话人，分母则是假定是不同说话人。

要理解公式(4)可参考PLDA的原始论文（参考文献[2]）中的Figure 2 B. 现截图如下。

M0是说x1和xp分别来自不同人h1和h2，而M1是说x1和xp来自同一个人h1。

3. 根据另一个参考文献，公式（4）可以推导如下：

以上式子中的分母对应的是边缘分布p(w1)和p(w2)的乘积，分子则是边缘分布p(w1,w2)。

由于w1,w2都是高斯分布，因此根据参考[1]不难得出以下推导,第1项是p(w1,w2)，第2项是p(w1)和p(w2)。

参考：

[1] Analysis of I-vector Length Normalization in Speaker Recognition Systems

[2] Probabilistic Linear Discriminant Analysis for Inferences About Identity

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