Deep Linear Discriminant Analysis
This addresses the challenge of improving classification performance by enhancing feature separability in deep learning, though it is incremental as it builds on classic LDA.
The paper tackles the problem of learning linearly separable latent representations by introducing Deep Linear Discriminant Analysis (DeepLDA), a non-linear extension of classic LDA that trains a deep neural network to produce features with low intra-class variance and high inter-class variance. It achieves competitive results on MNIST and CIFAR-10 and outperforms a cross-entropy baseline on STL-10.
We introduce Deep Linear Discriminant Analysis (DeepLDA) which learns linearly separable latent representations in an end-to-end fashion. Classic LDA extracts features which preserve class separability and is used for dimensionality reduction for many classification problems. The central idea of this paper is to put LDA on top of a deep neural network. This can be seen as a non-linear extension of classic LDA. Instead of maximizing the likelihood of target labels for individual samples, we propose an objective function that pushes the network to produce feature distributions which: (a) have low variance within the same class and (b) high variance between different classes. Our objective is derived from the general LDA eigenvalue problem and still allows to train with stochastic gradient descent and back-propagation. For evaluation we test our approach on three different benchmark datasets (MNIST, CIFAR-10 and STL-10). DeepLDA produces competitive results on MNIST and CIFAR-10 and outperforms a network trained with categorical cross entropy (same architecture) on a supervised setting of STL-10.