Sparse Fisher's linear discriminant analysis for partially labeled data

Classification is an important tool with many useful applications. Fisher's linear discriminant analysis (LDA) is a traditional model‐based classification method which makes use of the Gaussian distributional information. However, in the high‐dimensional, low‐sample‐size setting,LDAcannot be directly deployed because the sample covariance is not invertible. While there are modern methods for high‐dimensional data, they may not fully use the information asLDAdoes. Hence in some situations, it is still desirable to use a model‐based method for classification. This paper exploits the potential ofLDAin a more complicated data setting. In many real applications, it is costly to manually place labels on observations; consequently, often only a small portion of labeled data is available while a large number of observations are left without labels. It is a great challenge to obtain good classification performance through the labeled data alone, especially in the high‐dimensional setting. In order to overcome this issue, we propose a semisupervised sparseLDAclassifier to take advantage of the seemingly useless unlabeled data, which helps to boost the classification performance in some situa