{{attachment:CaGMoN_TR2.png | alt=KAG | width=250 height=90}} {{attachment:PokeGAG_TR.png | alt=KAGs | width=200 height=50}} = CAGMon - A Detchar Tool for Noise Propagation using Correlation Analysis = <> == 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 == * John J. Oh (lead, NIMS) * Young-Min Kim (UNIST) * More.... == Preliminaries == === Old Link of CAGMon Project@KGWG Wiki === * [[https://kgwg.nims.re.kr/cbcwiki/CAGMon]] === Methods === ==== Pearson's Correlation Coefficient ==== * PCC is a measure of a linear correlation between two random variables. * Pearson's r is defined as: {{{#!html \[ r=\frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^{n} (x_i-\bar{x})^2} \sqrt{\sum_{i=1}^{n} (y_i -\bar{y})^2}} \] }}} ==== Kendall's tau Coefficient ==== {{{#!html \[ \tau = \frac{2(C-D)}{n(n-1)} \] }}} 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: {{{#!html \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] {{{#!html \[ MIC(D) = \max_{xy