Geodesic Based Semi-supervised Multi-manifold Feature Extraction

Manifold learning is an important feature extraction approach in data mining. This paper presents a new semi-supervised manifold learning algorithm, called Multi-Manifold Discriminative Analysis (Multi-MDA). The proposed method is designed to explore the discriminative information hidden in geodesic distances. The main contributions of the proposed method are: 1) we propose a semi-supervised graph construction method which can effectively capture the multiple manifolds structure of the data, 2) each data point is replaced with an associated feature vector whose elements are the graph distances from it to the other data points. Information of the nonlinear structure is contained in the feature vectors which are helpful for classification, 3) we propose a new semi-supervised linear dimension reduction method for feature vectors which introduces the class information into the manifold learning process and establishes an explicit dimension reduction mapping. Experiments on benchmark data sets are conducted to show the effectiveness of the proposed method.