Idiap Research Institute and Ecole Polytechnique Fédérale de Lausanne, Martigny 1920, Switzerland.
IEEE Trans Pattern Anal Mach Intell. 2013 Jul;35(7):1788-94. doi: 10.1109/TPAMI.2013.38.
In this paper, we present a scalable and exact solution for probabilistic linear discriminant analysis (PLDA). PLDA is a probabilistic model that has been shown to provide state-of-the-art performance for both face and speaker recognition. However, it has one major drawback: At training time estimating the latent variables requires the inversion and storage of a matrix whose size grows quadratically with the number of samples for the identity (class). To date, two approaches have been taken to deal with this problem, to 1) use an exact solution that calculates this large matrix and is obviously not scalable with the number of samples or 2) derive a variational approximation to the problem. We present a scalable derivation which is theoretically equivalent to the previous nonscalable solution and thus obviates the need for a variational approximation. Experimentally, we demonstrate the efficacy of our approach in two ways. First, on labeled faces in the wild, we illustrate the equivalence of our scalable implementation with previously published work. Second, on the large Multi-PIE database, we illustrate the gain in performance when using more training samples per identity (class), which is made possible by the proposed scalable formulation of PLDA.
在本文中，我们提出了一种可扩展且精确的概率线性判别分析（PLDA）解决方案。PLDA 是一种概率模型，已被证明在人脸识别和说话人识别方面都具有最先进的性能。然而，它有一个主要的缺点：在训练时，估计潜在变量需要对矩阵进行逆运算和存储，而该矩阵的大小随身份（类）的样本数量呈二次增长。迄今为止，已经有两种方法来解决这个问题，一种是使用精确的解决方案，该解决方案计算这个大型矩阵，显然不能随样本数量扩展，另一种是对问题进行变分近似。我们提出了一种可扩展的推导方法，该方法在理论上与以前的不可扩展解决方案等效，因此不需要变分近似。在实验中，我们通过两种方式证明了我们的方法的有效性。首先，在野外标记的面部图像上，我们说明了我们的可扩展实现与以前发表的工作的等效性。其次，在大型 Multi-PIE 数据库上，我们说明了在每个身份（类）使用更多训练样本时性能的提高，这是通过提出的 PLDA 的可扩展公式实现的。
