Orthogonal Principal Coefficients Embedding for Unsupervised Subspace Learning

As a recently proposed method for subspace learning, principal coefficients embedding (PCE) method can automatically determine the dimension of the feature space and robustly handle various corruptions in real-world applications. However, the projection matrix learned by PCE is not orthogonal, so the original data may be reconstructed improperly. To address this issue, we proposed a new method termed orthogonal PCE (OPCE). OPCE cannot only automatically determine the dimension of the feature space, but also additionally considers the orthogonal property of the projection matrix for better discriminating ability. Moreover, OPCE can be solved in closed-form, thus making it computational efficient. Extensive experimental results from multiple benchmark data sets demonstrate the effectiveness and computational efficiency of the proposed method.