# On the generalized low rank approximation of the correlation matrices arising in the asset portfolio

## TL;DR

This paper introduces a new method for approximating correlation matrices in asset portfolios using a Gramian-based transformation and conjugate gradient optimization, demonstrating effectiveness through numerical examples.

## Contribution

It characterizes the feasible set via Gramian and trigonometric transforms and converts the problem into an unconstrained optimization, solved efficiently with conjugate gradient methods.

## Key findings

- Method is feasible and effective for correlation matrix approximation.
- Transforms the problem into an unconstrained optimization for easier solving.
- Numerical examples validate the approach's practicality.

## Abstract

In this paper, we consider the generalized low rank approximation of the correlation matrices problem which arises in the asset portfolio. We first characterize the feasible set by using the Gramian representation together with a special trigonometric function transform, and then transform the generalized low rank approximation of the correlation matrices problem into an unconstrained optimization problem. Finally, we use the conjugate gradient algorithm with the strong Wolfe line search to solve the unconstrained optimization problem. Numerical examples show that our new method is feasible and effective.