The problem of minU,V,XLβ(U,V,X,Λj) can be solved by ADMM. Least square self-representation[2] Low-rank matrix X∈Rm×n,∃S∈Rn×n⇒X=XS , observed entries: {Mi,j,(i,j)∈Ω} minX,S‖S‖F2+λ‖X−XS‖F2s.t.diag(S)=0,Xi,j=Mi,j,(i,j)∈Ω Low-rank self...
Recently, many feature extraction methods, which are based on the matrix representation of image and matrix bidirectional projection technique, are proposed. However, these methods in solving the two projection matrices will suffer from non-optimized or non-convergent solution. To overcome this problem...
A novel penalty $\|\Phi\|_F$ is added to make the projection matrix robust when the sparse representation error (SRE) exists. Additionally, designing the projection matrix with a high dimensional dictionary improves the signal reconstruct accuracy when the compression rate is the same as in a ...
We take only the main diagonal blocks of Fnc*Rn′Fnc using Ψ2, and then converting back to representation in standard basis to get PUnc(Rn′). As the Toeplitz block matrix Rn′ is given in terms of the filter vectors, the elements of preconditioner matrix PUnc(Rn′) are also in terms...
(4.6a). If the matrix produced is T and if a h is the representation of a point (x a, y a, z a) in homogeneous coordinates, in the form of Eq. (4.6b), then a h T yields transformed homogeneous coordinates that correspond to the projection onto the two-dimensional coordinate ...
Using these matrix representations of l x,y,z and s x,y,z and the Cartesian expression for the spin-orbit operator [Eq. (11)] we can obtain an equation for the matrix of ˆ H so in the six-state Cartesian representation that is identical to Eq. (10). The advantage of using this...
In this representation, the variance estimates the spread of values along a single feature dimension, whereas covariance is a measure of shared information between features. The covariance matrix is symmetric, which means its eigenvectors form a novel orthogonal basis set that better represents the ...
linear projection-based NMF(LPBNMFfeature extractiondata representationefficiency of dimensionality reductionsparse featureoccluded face recognitionNon-negative matrix factorization(NMF) is a newly popular method for non-negative dimensionality reduction, feature extraction, data mining, etc.The mathematical model...
Our common design procedure starting point for both classical and quantum software systems is Von Neumann quantum notion of Density Operator and its Density Matrix representation. This paper formulates and demonstrates modular design in terms of projection operators obtained from a design Density Matrix ...
Mode superposition approach involves representation of the dynamic response as the --- of natural modes. 13. The coupled equations of motion [M]Q→¨+[K]Q→=P→ can be --- by assuming Q→(t)=[Q¯]η→(t) where η→(t) denotes the vector of n generalized coordinates. 14. A sy...