Signal and Noise in Correlation Matrix

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance (correlation) matrix. Results can be applied in various problems where one experimentally estimates correlations in a system with many degrees of freedom, like in statistical physics, lattice measurements of field theory, genetics, quantitative finance and other applications of multivariate statistics.Comment: 17 pages, 3 figures, corrected typos, revtex style changed to elsar

Correlation, hierarchies, and networks in financial markets

We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Specifically, we discuss how to define and obtain hierarchical trees, correlation based trees and networks from a correlation matrix. The hierarchical clustering and other procedures performed on the correlation matrix to detect statistically reliable aspects of the correlation matrix are seen as filtering procedures of the correlation matrix. We also discuss a method to associate a hierarchically nested factor model to a hierarchical tree obtained from a correlation matrix. The information retained in filtering procedures and its stability with respect to statistical fluctuations is quantified by using the Kullback-Leibler distance.Comment: 37 pages, 9 figures, 3 table

Chemical structure matching using correlation matrix memories

This paper describes the application of the Relaxation By Elimination (RBE) method to matching the 3D structure of molecules in chemical databases within the frame work of binary correlation matrix memories. The paper illustrates that, when combined with distributed representations, the method maps well onto these networks, allowing high performance implementation in parallel systems. It outlines the motivation, the neural architecture, the RBE method and presents some results of matching small molecules against a database of 100,000 models

Random Correlation Matrix and De-Noising

In Finance, the modeling of a correlation matrix is one of the important problems. In particular, the correlation matrix obtained from market data has the noise. Here we apply the de-noising processing based on the wavelet analysis to the noisy correlation matrix, which is generated by a parametric function with random parameters. First of all, we show that two properties, i.e. symmetry and ones of all diagonal elements, of the correlation matrix preserve via the de-noising processing and the efficiency of the de-nosing processing by numerical experiments. We propose that the de-noising processing is one of the effective methods in order to reduce the noise in the noisy correlation matrix.correlation matrix, calibration, rank reduction, de-noising, wavelet analysis