Surrogate Data Generation Algorithms

In this article, we introduce surrogate data generation algorithms that can produce artificial datasets with statistical characteristics similar to original datasets. These algorithms have broad applications in machine learning, data mining, and statistical analysis. The implementation includes: random phase method (shuffle.m shuffles time indices randomly; surrogate.m performs Fourier transform phase randomization), periodic random phase method (cycleshuffle.m maintains periodic structure while randomizing phases), and PPS algorithm (pps.m generates phase-preserving surrogates; findrho.m calculates correlation metrics for validation). The random phase method generates surrogate data by randomizing the temporal sequence of original data through index permutation in shuffle.m, while surrogate.m employs Fourier-based phase randomization in frequency domain. The periodic random phase method is an enhanced version that preserves cyclical patterns in the data by constraining phase randomization within periodic boundaries. The PPS algorithm utilizes phase plane analysis to create surrogate datasets that maintain the same autocorrelation structure as the original data through phase-space trajectory preservation techniques. These surrogate data generation algorithms serve as valuable tools for researchers conducting data analysis when limited real data is available. The MATLAB implementations provide practical functions for hypothesis testing in nonlinear dynamics, making proficiency in these algorithms significantly beneficial for research work. The code structure typically involves input validation, transformation to appropriate domain (time/frequency/phase-space), randomization operations, and inverse transformation back to time domain.