Dimensionality reduction using graph-embedded probability-based semi-supervised discriminant analysis

Probabilistic semi-supervised discriminant analysis (PSDA) is a recently proposed semi-supervised dimensionality reduction approach. It quantifies class membership probability to each unlabeled sample by using a well-designed soft assignment technique. Then discriminant analysis is performed over both labeled and unlabeled data which bears an analogy to the Fisher criterion. However, PSDA mainly focuses on discriminative information hidden in unlabeled data and ignores the local geometric information which is critical to reveal the intrinsic distribution of data points, especially for face image data. In this paper, we develop a graph-based semi-supervised learning method based on PSDA, termed as graph-embedded probability-based semi-supervised discriminant analysis (GPSDA) for dimensionality reduction. By introducing a similarity measurement of fuzzy sets to investigate the inexact class information of unlabeled data, an adjacency graph is modeled based on both neighborhood structure and category information, which is more relevant to classification compared with the unsupervised graph constructed in traditional graph-based semi-supervised dimensionality reduction technique. Since more information is learnt from unlabeled data, GPSDA is expected to enhance performance in classification task. We present experimental evidence on face and facial expression recognition suggesting that our algorithm is able to use unlabeled data effectively.