Joint Diagonalization Based on Fourth-Order Cumulants

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Resource Overview

Implementation of joint diagonalization using fourth-order cumulants, featuring two distinct computation methods with code-level explanations for better understanding. This advanced algorithm (similar to JADE in Independent Component Analysis) demonstrates practical approaches for cumulant matrix construction and orthogonal transformation techniques.

Detailed Documentation

This document presents a joint diagonalization algorithm based on fourth-order cumulants. The implementation incorporates two different computational methods for fourth-order cumulant calculation, providing alternative approaches for algorithm comprehension. While this algorithm presents considerable complexity, it holds significant importance for researchers delving into Independent Component Analysis (ICA). The implementation typically involves constructing cumulant matrices through tensor operations or moment-based approximations, followed by Jacobi-like rotation techniques for joint diagonalization. For those interested in this methodology, we recommend studying the JADE (Joint Approximate Diagonalization of Eigenmatrices) algorithm as a reference, which utilizes similar fourth-order statistics and orthogonal transformation principles for blind source separation applications.

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