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Tensor factor analysis is the compositional consequence of several causal factors of data formation, and are well suited for multi-modal data tensor analysis. The power of the tensor framework was showcased by analyzing human motion joint angles, facial images or textures in terms of their causal factors of data formation in the following works ...
In mathematics, power iteration (also known as the power method) is an eigenvalue algorithm: given a diagonalizable matrix, the algorithm will produce a number , which is the greatest (in absolute value) eigenvalue of , and a nonzero vector , which is a corresponding eigenvector of , that is, =.
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
In ()-(), L1-norm ‖ ‖ returns the sum of the absolute entries of its argument and L2-norm ‖ ‖ returns the sum of the squared entries of its argument.If one substitutes ‖ ‖ in by the Frobenius/L2-norm ‖ ‖, then the problem becomes standard PCA and it is solved by the matrix that contains the dominant singular vectors of (i.e., the singular vectors that correspond to the highest ...
The power of the tensor framework was showcased by decomposing and representing an image in terms of its causal factors of data formation, in the context of Human Motion Signatures for gait recognition, [18] face recognition—TensorFaces [19] [20] and computer graphics—TensorTextures.
For a 3rd-order tensor , where is either or , Tucker Decomposition can be denoted as follows, = () where is the core tensor, a 3rd-order tensor that contains the 1-mode, 2-mode and 3-mode singular values of , which are defined as the Frobenius norm of the 1-mode, 2-mode and 3-mode slices of tensor respectively.
Functional principal component analysis (FPCA) is a statistical method for investigating the dominant modes of variation of functional data.Using this method, a random function is represented in the eigenbasis, which is an orthonormal basis of the Hilbert space L 2 that consists of the eigenfunctions of the autocovariance operator.
In the field of multivariate statistics, kernel principal component analysis (kernel PCA) [1] is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space .