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| == Descripstion == | == Description == |
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| the Maximal Information coefficient(MIC) of a set D of two-variable data with sample size n and grid less than B(n) is given by | |
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| r=\frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i-\bar{x})^2} \sqrt{\sum_{i=1}^{n} (y_i -\bar{y})^2}} \] |
MIC(D)=\underset{xy<B(n)}{\max}{\left\{ \frac{I^{*}(D,x,y)}{\log \min \left\{x,y \right\}} \right \}} \], where \[\omega(1)<B(n)\le O(n^{1-\epsilon}) \] for some \[ 0<\epsilon<1 \] ==== Pearson's Correlation Coefficient (PCC) ==== Pearson Correlation Coefficient(PCC) is a statistic that explains the amount of variance accounted for in the relationship between two (or more) variables by \[ R={{\sum_{i=1}^{n} (X_i - \overline{X})(Y_i - \overline{Y})} \over {\sqrt{\sum_{i=1}^{n} (X_i - \overline{X}) \sum_{i=1}^{n} (Y_i - \overline{Y})}}} \], where \[ \overline{X} \] and \[ \overline{Y} \] are the mean of X and Y, respectively |
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| ==== Pearson's Correlation Coefficient (PCC) ==== | ==== Kendall's tau Coefficient ==== |
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| ==== Kendall's tau Coefficient ==== | Kendall’s tau with a random samples n of observations from two variables measures the strength of the relationship between two ordinal level variables by \[ \tau =\frac{c-d}{{n \choose 2}} \], where c is the number of concordant pairs, and d is the number of discordant pairs ==== Flow chart ==== |
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| * the script gathered functions medel required | * the script gathered functions the medel required |
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| 1. Earthquake effects during O3GK * Datetime: 19 April 2020 20:39 UTC * Purpose * Test to run CAGMon algorithm with a remarkable event * To figure out the cause of lock-loss in KAGRA * Results * [[https://ldas-jobs.ligo.caltech.edu/~pil-jong.jung/CAGMon/2020-04-19_K1:CAL-CS_PROC_C00_STRAIN_DBL_DQ_1271363358-1271364078(5)/ | Summary page with stride 5 seconds]] * [[https://ldas-jobs.ligo.caltech.edu/~pil-jong.jung/CAGMon/2020-04-19_K1:CAL-CS_PROC_C00_STRAIN_DBL_DQ_1271363358-1271364078/ | Summary page with stride 20 seconds]] * [[https://ldas-jobs.ligo.caltech.edu/~pil-jong.jung/CAGMon/2020-04-19_K1:CAL-CS_PROC_C00_STRAIN_DBL_DQ_1271363358-1271364078(30)/ | Summary page with stride 30 seconds]] |
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| [[https://gwdoc.icrr.u-tokyo.ac.jp/cgi-bin/private/DocDB/ShowDocument?docid=12481|JGW-G2112481-v1]] |
CAGMon etude
Description
The CAGMon etude is a study version of CAGMon that evaluates the dependence between the primary and auxiliary channels.
Project goal
The goal of this project is to find a systematic way of identifying the abnormal glitches in the gravitational-wave data using various methods of correlation analysis. Usually, the community such as LIGO, Virgo, and KAGRA uses a conventional way of finding glitches in auxiliary channels of the detector - Klein-Welle, Omicron, Ordered Veto Lists, etc. However, some different ways can be possible to find and monitor them in a (quasi-) realtime. Also, the method can point out which channel is responsible for the found glitch. In this project, we study its possible to apply three different correlation methods - maximal information coefficient, Pearson's correlation coefficient, and Kendall's tau coefficient - in the gravitational wave data from the KAGRA detector.
Participants
- John.J Oh (NIMS)
- Young-Min Kim (UNIST)
- Pil-Jong Jung (NIMS)
Methods and Frameworks
Maximal Information Coefficient (MIC)
the Maximal Information coefficient(MIC) of a set D of two-variable data with sample size n and grid less than B(n) is given by
\[ MIC(D)=\underset{xy<B(n)}{\max}{\left\{ \frac{I^{*}(D,x,y)}{\log \min \left\{x,y \right\}} \right \}} \],
where \[\omega(1)<B(n)\le O(n^{1-\epsilon}) \] for some \[ 0<\epsilon<1 \]
Pearson's Correlation Coefficient (PCC)
Pearson Correlation Coefficient(PCC) is a statistic that explains the amount of variance accounted for in the relationship between two (or more) variables by \[ R=} \],
where \[ \overline{X} \] and \[ \overline{Y} \] are the mean of X and Y, respectively
Kendall's tau Coefficient
Kendall’s tau with a random samples n of observations from two variables measures the strength of the relationship between two ordinal level variables by
\[ \tau =\frac{c-d} \],
where c is the number of concordant pairs, and d is the number of discordant pairs
Flow chart
Code development
GitHub
TBA
Code version
- CAGMon Etude Alpha
- for the basic test and evaluation of the LASSO regression method developed by LIGO
- reproduced original CAGMon methods and idea
- CAGMon Etude Beta
- added coefficient trend plots with LASSO beta, coherence, MIC, PCC, and Kendall's tau
- CAGMon Etude Delta
- fixed a critical problem that sucked enormous memory when it used the matplotlib module
- CAGMon Etude Eta
- fixed memory issues
- fixed minor bugs
- added the range limitation of stride
- CAGMon Etude Flat (latest version)
- fixed minor issues and optimized scripts
- added the script of HTML summary page
- added coefficient distribution plots
Structure of scripts
- Agrement.py
- the script gathered functions the medel required
- Melody.py
- the script to calcutate each coefficient and to save trend data as csv
- Conchord.py
- the script to make plots, such as coefficient trend, coefficient distribution trend, time-series, and scatter plots
- Echo.py
- the script to save the result as HTML web page
- CAGMonEtudeFlat.py
- the script to run each script
Exemplary results
1. Earthquake effects during O3GK
- Datetime: 19 April 2020 20:39 UTC
- Purpose
- Test to run CAGMon algorithm with a remarkable event
- To figure out the cause of lock-loss in KAGRA
- Results
Beyond
References
Presentation materials