# CAGMon - A Detchar Tool for Noise Propagation using Correlation Analysis

Contents

## 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 and Virgo 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 possibility to apply three different correlation methods - maximal information coefficient, Pearson's correlation coefficient, and Kendall's tau coefficient - in the gravitational wave data from LIGO detector.

## Participants

- 오정근 (lead)
- Young-Min Kim (UNIST)

## Preliminaries

### Methods

#### Pearson's Correlation Coefficient

- PCC is a measure of a linear correlation between two random variables.
- Pearson's r is defined as:

- \[ r=\frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i-\bar{x})^2} \sqrt{\sum_{i=1}^{n} (y_i -\bar{y})^2}} \]

#### Kendall's tau Coefficient

- \[ \tau = \frac{2(C-D)}{n(n-1)} \]

where C and D are number of concordant and disconcordant pairs, respectively.

#### Maximal Information Coefficient

Basically, maximal information coefficient is defined using the mutual information score following the Ref. [1]. Formally, the mutual information of two discrete random variables X and Y can be defined as: \begin{align} I(X;Y) = \sum_{y\in Y} \sum_{x\in X} p(x, y) \log \left(\frac{p(x, y)}{p(x)p(y)}\right) \end{align}

where p(x,y) is the joint probability distribution function of X and Y, and p(x) and p(y) are the marginal probability distribution functions of X and Y respectively. Intuitively, mutual information measures the information that X and Y share: it measures how much knowing one of these variables reduces uncertainty about the other. For example, if X and Y are independent, then knowing X does not give any information about Y and vice versa, so their mutual information is zero [Wikipedia].

It measures non-linear correlation between two data samples while the PCC (Pearson correlation coefficient) and the Spearman coefficient are only for the linear relationship.

With this definition of mutual information, MIC is defined by [2] \[ MIC(D) = \max_{xy

### Preliminary Knowledges

#### Previous Study Results

#### References

CAGMonLKR3 Guide : to be updated

GitLab: to be pushed

D. N. Reshef, Y. A. Reshef, H. K. Finucane, S. R. Grossman, G. McVean, P. J. Turnbaugh, E. S. Lander, M. Mitzenmacher, P. C. Sabeti,

**Science**,**334**, 1518 (2011).

#### System Requirements for KAGMon

- python 3
- numpy
- scipy
- matplotlib
- minepy
- gwpy

## Data & Code Preparation

### KAGRA ER2 Data

- location: ldg-ui @ sdfarm -- /data/kagra/archive/data/full/
1247024298 / 5 hours (2019. Jul. 13 12:38:00- 17:57:50) http://gwwiki.icrr.u-tokyo.ac.jp/JGWwiki/KAGRA/Subgroups/DET/RUN/ER190713

Summary page: Run Status -- https://www.icrr.u-tokyo.ac.jp/~yuzu/bKAGRA_summary/html/20190713_GlitchPlot.html

- TStride = 30, FStride = 8 / dur = 240 / 80 Jobs
- Main Channel: K1:CAL-CS_PROC_MICH_DISPLACEMENT_DQ
- Aux Channels: 464 DQ Channels (+ unsafe)

### LIGO Data

O3 glitches and their witness channels : https://wiki.ligo.org/DetChar/GlitchesandWitnesses

- list of glitches
- Magnetometer set
- gpstimes: /home/cavaglia/karoo_omicron_O2endxmag/data/gpstimes_endxmag_triggers_sorted_analyzed_ready_1-2049.txt @LLO (ldas-pcdev1.ligo-la.caltech.edu)

- Air Compressor set
- gpstimes: /home/cavaglia/karoo_omicron_O1aircompressor/data/gpstimes_O1aircompressor_sorted.txt @ LHO(ldas-pcdev1.ligo-wa.caltech.edu)

- Magnetometer set

### Scheme & Goal

## Preliminary Run Tests:

Summary of 19200s Run: KAGRA-CAGMonTest.key

## Observing Run Test of KAGRA O1

### Trigger-based Analysis

- Data: April 19 2020
- Observing Information:

- Loudest events by SNR:
- 10 loudest K1:CAL-CS_PROC_C00_STRAIN_DBL_DQ (Omicron) events by SNR with minimum 8s separation. Launch omega scans

GPS time |
UTC time |
Duration |
Peak frequency |
Central freq. |
Bandwidth |
SNR |

1271311593.609 |
April 19 2020 06:06:15.609 |
0.031 |
121.192 |
121.195 |
1.723 |
288.743 |

1271302217.998 |
April 19 2020 03:29:59.998 |
0.004 |
111.850 |
112.298 |
20.032 |
221.521 |

1271356741.438 |
April 19 2020 18:38:43.437 |
0.125 |
41.141 |
41.142 |
0.585 |
202.916 |

1271337318.002 |
April 19 2020 13:15:00.0 |
0.00|4 |
111.850 |
112.298 |
20.032 |
170.477 |

1271340918.001 |
April 19 2020 14:15:00.000 |
0.002 |
133.756 |
134.291 |
23.955 |
166.644 |

1271325225.998 |
April 19 2020 09:53:27.998 |
0.004 |
111.850 |
112.298 |
20.032 |
164.685 |

1271313018.002 |
April 19 2020 06:30:00.001 |
0.004 |
111.850 |
112.298 |
20.032 |
162.386 |

1271303583.984 |
April 19 2020 03:52:45.984 |
0.031 |
121.192 |
121.195 |
1.723 |
161.520 |

1271296947.422 |
April 19 2020 02:02:09.421 |
0.031 |
121.192 |
121.195 |
1.723 |
161.284 |

1271336417.998 |
April 19 2020 12:59:59.998 |
0.004 |
111.850 |
112.298 |
20.032 |
160.725 |

## Working Paper

- JKPS Special Issue: