Symplectic geometry similarity transformationFor roller bearing condition monitoring, the collected signals have complex internal structure, which can be naturally represented as matrices. Support matrix machine
In particular the similarity transformation yields a similarity transformation on a and takes c to a congruent matrix. The first step of the proof is to make a symplectic transformation so that c=0. The Frobenius decomposition of the skew matrix c says there exists U∈GL(g,Z) such that c...
After performing a similarity transforma- tion and an integration of delta functions, we can put the expression into the form of the closed string formalism and prove the relation (1.5). In both of the U(N |N + 2M ) and OSp(2N + 1|2(N + M )) theories there is a physical bound...
First, this method uses the symplectic geometry similarity transformation for the constructed trajectory matrix to obtain the characteristics and eigenvectors of useful components and noise. Linear estimation is then used to approximate the pure signal, and a Lagrange multiplier is used to enhance the ...
Symplectic geometry similarity transformationFor roller bearing condition monitoring, the collected signals have complex internal structure, which can be naturally represented as matrices. Support matrix machine (SMM), as a new classifier with matrices as inputs, makes full use of the correlation between...
We introduce a natural cell decomposition of a closed oriented surface associated with a pants decomposition, and an explicit groupoid cocycle on the cell decomposition which represents each point of the Teichm眉ller spaceTg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym...
SQSMD applies symplectic similarity transformation to the constructed quaternion Hamilton matrix by selecting embedding dimension automatically without user-defined parameter, then the transformed trajectory matrix is decomposed by quaternion singular mode decomposition to obtain quaternion eigenvectors and singular...
Symplectic geometry matrix machineSymplectic geometry similarity transformationRoller bearingFault diagnosisIn many classification problems such as roller bearing fault diagnosis, it is often met that input samples are two-dimensional matrices constructed by vibration signals, and the rows or columns in the ...
GEOMETRYMATHEMATICAL invariantsEUCLIDEAN geometryISOTROPIC propertiesA linear transformation with an invariant being a nondegenerate quadratic form is symplectic. The geometric properties of such transformations are discussed. A complete set of quadratic invariants which are pairwise in involution is explicitly ...
Therefore, a new signal decomposition algorithm, symplectic geometry mode decomposition (SGMD), is proposed in this paper to decompose a time series into a set of independent mode components. SGMD uses the symplectic geometry similarity transformation to solve the eigenvalues of the Hamiltonian matrix ...