ON THE RANDOMNESS OF EIGENVECTORS GENERATED FROM NETWORKS WITH RANDOM TOPOLOGIES

@article{Silverstein1979ONTR,
  title={ON THE RANDOMNESS OF EIGENVECTORS GENERATED FROM NETWORKS WITH RANDOM TOPOLOGIES},
  author={Jack W. Silverstein},
  journal={Siam Journal on Applied Mathematics},
  year={1979},
  volume={37},
  pages={235-245}
}
  • J. W. Silverstein
  • Published 1 October 1979
  • Mathematics
  • Siam Journal on Applied Mathematics
A model for the generation of neural connections at birth led to the study of W, a random, symmetric, nonnegative definite linear operator defined on a finite, but very large, dimensional Euclidean space [1]. A limit law, as the dimension increases, on the eigenvalue spectrum of W was proven, implying that realizations of W (being identified with organisms in a species) appear totally different on the microscopic level and yet have almost identical spectral densities.The present paper considers… 

Figures from this paper

DESCRIBING THE BEHAVIOR OF EIGENVECTORS OF RANDOM MATRICES USING SEQUENCES OF MEASURES ON ORTHOGONAL GROUPS

A conjecture has previously been made on the chaotic behavior of the eigenvectors of a class of n-dimensional random matrices, where n is very large [J. Silverstein, SIAM J. Appl. Math., 37 (1979),

Statistical decomposition of chaotic attractors by the eigenvectors of Oseledec matrix-active and passive information dynamics

SummaryCorrelated sets of physical variables or coordinates of the equations of motion are extracted from the distribution of eigenvectors of theOseledec matrix. These coordinates characterize the

Weak Convergence of random functions defined by the eigenvectors of sample covariance matrices

Let {v ij }, i, j = 1, 2,..., be i.i.d. symmetric random variables with E(v 4 11 ) 0 as n → ∞. Denote by O n Λ n O T n the spectral decomposition of M n . Define X ∈ D[0,1] by X n (t) = √n/2Σ [nt]

METHODOLOGIES IN SPECTRAL ANALYSIS OF LARGE DIMENSIONAL RANDOM MATRICES , A REVIEW

In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but the

Random Matrix Methods for Wireless Communications

This book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks.

A tribute to P.R. Krishnaiah

Cross -validation for unsupervised learning

This thesis discusses some extensions of cross-validation to unsupervised learning, specifically focusing on the problem of choosing how many principal components to keep, and introduces the latent factor model, an objective criterion, and shows how CV can be used to estimate the intrinsic dimensionality of a data set.

Weak Convergence of a Collection of Random Functions Defined by the Eigenvectors of Large Dimensional Random Matrices

For each n, let Un be Haar distributed on the group of n × n unitary matrices. Let xn,1, . . . ,xn,m denote orthogonal nonrandom unit vectors in C n and let un,k = (uk, . . . , u n k) ∗ = U∗ nxn,k, k

References

SHOWING 1-4 OF 4 REFERENCES

Spectral Analysis of Networks with Random Topologies

A class of neural models is introduced in which the topology of the neural network has been generated by a controlled probability model. It is shown that the resulting linear operator has a spectral

Asymptotics applied to a neural network

A mathematical model of neural processing is proposed which incorporates a theory for the storage of information that lends support to a distributive theory of memory using synaptic modification.

Lectures in pattern theory