Cross-dimensional Principal Component Analysis-A New Dimensionality Reduction Method

cross-dimensional principal component analysis (CD-PCA). It is based on the semi-tensor product of matrices theory (STP), where a new projection rule is introduced to reduce dimensionality of high-dimensional data in various linear spaces. Compared to principal component analysis (PCA) and its variants, which typically discard some principal components related to small eigenvalues for the purpose of dimensionality reduction, the methodology of CD-PCA can unite all principal components to form new components of lower dimensions. A comparitive anaylsis is conducted to characterize the potential relation of PCA and CD-PCA, which not only reveals the principle of the CD-PCA algorithms but also provides a deep insight on its properties and capabilities, ensuring its suitability for dimensionality reduction and feature extraction. Extensive experiments on classification and clustering verify the effectiveness of our approach.