These Python scripts are used to perform singular spectrum analysis on various signals retrieved from the internet to predict critical transitions in a time series. During a critical transition the dimensionality (v) will decrease as the system is driven towards a critical point. During the decrease in dimensionality, variance and autocorrelation will experience increases however these indicators are not known to work well for time series with a small sample size or large amounts of noise.
These scripts were created for research Takashi Nakamura was performing on SSA, and their results were shown at Montreal's High Performance Computing Symposium 2015. More research on these methods are required.
To skim down on the size of the repository, the original vibration text files and PhysioNet data (> 1 GB!) were excluded.
Here are some sample graphs produced, check data sources readme to see where the data came from.
v = dimensionality
lambda_one = largest eigenvalue
sigma^2 = variance
s = sample index
SSA on a heart EKG looking at sudden cardiac death (data from PhysioNet)
SSA on Air Temperature
SSA on Dow Jones index
Running a low-pass filter over the data before the SSA was also investigated, with the resulting graph below.
To perform the SSA analysis run one of the following: 'Climate.py', 'financial.py' ('PhysioNet.py' doesn't have required data due to size constraints)
To see the effects of adding a low-pass filter for noise, run 'CutoffGraphs.py'
'CTL.py' contains the mathematical functions used in the scripts.
'datamanager.py' contains functions to manage/parse the data in a very quick manner.
A folder named experimental contains modified scripts which add support for timestamps in the form of 'yyyy-mm-ddThh:mm:ss', and add support for Pandas dataframes. This was separated as the scripts currently run on the provided vibration examples, but haven't been converted to run on the old examples