Kernel Alignment Inspired Linear Discriminant Analysis
This is an incremental improvement for classification tasks, particularly in handling multi-label data.
The authors tackled the problem of improving Linear Discriminant Analysis (LDA) by proposing kernel alignment LDA (kaLDA), which maximizes alignment between subspace-transformed data and class indicator kernels, and showed it performs well on 8 single-label and 6 multi-label datasets.
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two kernels, data kernel and class indicator kernel. The problem is to find a subspace to maximize the alignment between subspace-transformed data kernel and class indicator kernel. Surprisingly, the kernel alignment induced kaLDA objective function is very similar to classical LDA and can be expressed using between-class and total scatter matrices. This can be extended to multi-label data. We use a Stiefel-manifold gradient descent algorithm to solve this problem. We perform experiments on 8 single-label and 6 multi-label data sets. Results show that kaLDA has very good performance on many single-label and multi-label problems.