We present an overview of eigen analysis methods and their applications to network analysis. We consider several network analysis programs/procedures (Correspondence Analysis, NEGOPY, CONCOR, CONVAR, Bonacich centrality) that are at their core eigendecomposition methods. We discuss the various matrix representations of networks used by these procedures and we give particular attention to a vari...

Eigen decomposition is a central mathematical tool in many pattern recognition and machine learning techniques. However, it becomes computationally infeasible in the presence of a large set of high-dimensional samples. Moreover, in highly dynamic domains with a continual supply of new samples, an incremental approach that keeps on updating the eigen decomposition will be more desirable than the...

The Classical Shuffle Conjecture of Haglund et al. (2005) has a symmetric function side and a combinatorial side. The combinatorial side q, t-enumerates parking functions in the n × n lattice. The symmetric function side may be simply expressed as∇en, where∇ is the Macdonald eigen-operator introduced by Bergeron and Garsia (1999) and en is the elementary symmetric function. The combinatorial si...

A random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coe<cients. Karhunen–Loeve (K–L) series expansion is based on the eigen-decomposition of the covariance function. Its applicability as a simulation tool for both stationary and non-stationary Gaussian random processes is examined numerically in this paper. The ...

In the present paper a method is proposed to investigate the free vibration of a partially liquid-filled cylindrical tank. The mechanical properties of the container are assumed to change continuously along the thickness according to volume fraction Power-law, Sigmoid or Exponential distribution. The liquid is supposed to be incompressible and in viscid and its velocity potential is formulated ...

In this paper, we propose a new optimized PID controller to stabilize the synchronous machine connected to an infinite bus. The model for the synchronous machine is 4-ordered linear Philips-Heffron synchronous machine. In this research, the parameters of the PID controller are optimally achieved by minimizing a definite fitness function to removes the unstable Eigen-value to the left side of im...

Based on the connection between a quantum spin model and an asexual biological evolution model with a single-peak fitness function in parallel mutation-selection scheme, we solve exactly both static and dynamics of the evolution model. We find that relaxation in such a parallel scheme is faster than that in a connected scheme of Eigen model. Our method can also be extended to other fitness func...

I outline a uniied approach to characterizing Fr echet, limiting Fr echet, and Clarke subgradients of an arbitrary function of the eigen-values of a real symmetric matrix. In particular, I compute various subdiierentials of the k'th largest eigenvalue. This paper summarizes the results and techniques presented in detail in 4]. 1 The author wishes to thank the University of Milan, and in particu...