| Notations | Definitions | | | | | ---------------------------- | -------------------------------------------------------- | --- | --- | ------------------------------------------------------------ | | $n$, $N$ | Number of monitoring metrics, Number of components | | | | | $w$ | Observation lookback window size | | | | | $C = \{c_{j} | j = 1,2,...,| N|\}$ | Components set, each component | | $M = \{m_i|i=1,2,...,n\}$, $M = \{\bm{m}_{c_{j}} | j = 1,2,..., | N | \}$ | Metrics set, linked to each component | | $M = \{M^{A}, M^{B},M^{C}\}$ | Metrics set of its types A, B, C | | | | | $\bm{x}_{t}^{i} = [x_{t-w+1}^{i},x_{t-w+2}^{i},...,x_{t}^i]$ | Univariate time series of the i-th monitoring metrics | | $\bm{X}_{t}=[\bm{x}_t^1,\bm{x}_t^2,...,\bm{x}_t^n]$, $\bm{X}_{t} = \{X_{c_j}|j=1,2,...,|N|\}$ | Multivariate time series, monitored from component $c_j$ | | | | | $\bm{p} = \{\bm{p}_{c_{j}} | j = 1,2,..., | N | \}$ | Change points indices in monitored metrics in j-th component | | $\bm{S} = \{\bm{s}_{c_{j}} | j = 1,2,...,|N|\}$ | Segments set consits of segments | $\newcommand{\bm}[1]{\boldsymbol{#1}}$ $ \bm{X}_t = [\bm{x}_t^1,\bm{x}_t^2,...,\bm{x}_t^n] $ $ \bm{x}_{t}^{i} = [x_{t-w+1}^{i},x_{t-w+2}^{i},...,x_{t}^i] $ metric -> monitoring metric > We denote a multivariate time series at time t as Xt = [xt1,xt2..., xtn]T, where xti = [xti−w+1,xti−w+2,...,xti] is the univariate time series of the ith monitoring metric, n is the number of metrics, and w is the observation window size. from [[2021__ATC__Jump-Starting Multivariate Time Series Anomaly Detection for Online Service Systems|JumpStarter]] ## Problem Definition $M$, $w$, $\bm{X}_t$ が与えられたときに、$M$から$M^{A} \cup M^B$を抽出することである。 metricとunivariate time series