Multimodal Linear Discriminant Analysis via Structural Sparsity

Abstract

Linear discriminant analysis (LDA) is a widely used supervised dimensionality reduction technique. Even though the LDA method has many real-world applications, it has some limitations such as the single-modal problem that each class follows a normal distribution. To solve this problem, we propose a method called multimodal linear discriminant analysis (MLDA). By generalizing the between-class and within-class scatter matrices, the MLDA model can allow each data point to have its own class mean which is called the instance-specific class mean. Then in each class, data points which share the same or similar instance-specific class means are considered to form one cluster or modal. In order to learn the instance-specific class means, we use the ratio of the proposed generalized between-class scatter measure over the proposed generalized within-class scatter measure, which encourages the class separability, as a criterion. The observation that each class will have a limited number of clusters inspires us to use a structural sparse regularizor to control the number of unique instance-specific class means in each class. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed MLDA method.