Joint group and pairwise localities embedding for feature extraction

Many practical applications generate high-dimensional data, which poses challenges in terms of computational time and storage. To address this issue, feature extraction has become a popular research topic. Learning by way of graph embedding is useful for discovering potential intrinsic low-dimensional structures and has thus gained wide attention. However, traditional embedding models typically utilize only one graph or one type of multiple graphs to capture local relationships, which may be insufficient for high-dimensional data that may exhibit different kinds of local relationships. To overcome this drawback, we developed a joint embedding framework that incorporates multiple types of graphs. Under this framework, a novel joint group and pairwise locality embedding model (GPE) is proposed. The GPE model has the following distinctive merits: (1) it simultaneously incorporates simple graphs, hypergraphs, and probabilistic hypergraphs, enabling the use of not only one type of multiple graphs but also multiple types of multiple graphs; (2) it can leverage both group relationships and pairwise graphs to discover local information during feature extraction; and (3) its objective function can be solved using an alternating optimization strategy, which involves solving eigenvalue problems and quadratic programming problems, resulting in very fast convergence. Finally, we arranged classification tasks and clustering tasks on several high-dimensional real-world datasets, and the experimental results prove that the identification capability of GPE is encouraging.