Coresets for Data Discretization and Sine Wave Fitting

• URL: http://arxiv.org/abs/2203.03009v1
• Date: Sun, 6 Mar 2022 17:07:56 GMT
• Title: Coresets for Data Discretization and Sine Wave Fitting
• Authors: Alaa Maalouf and Murad Tukan and Eric Price and Daniel Kane and Dan Feldman
• Abstract summary: A stream of integers in $[N]:=1,cdots,N$ is received from a sensor. The goal is to approximate the $n$ points received so far in $P$ by a single frequency. We prove that emphevery set $P$ of $n$ has a weighted subset $Ssubseteq P$.
• Score: 39.18104905459739
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the \emph{monitoring} problem, the input is an unbounded stream $P={p_1,p_2\cdots}$ of integers in $[N]:=\{1,\cdots,N\}$, that are obtained from a sensor (such as GPS or heart beats of a human). The goal (e.g., for anomaly detection) is to approximate the $n$ points received so far in $P$ by a single frequency $\sin$, e.g. $\min_{c\in C}cost(P,c)+\lambda(c)$, where $cost(P,c)=\sum_{i=1}^n \sin^2(\frac{2\pi}{N} p_ic)$, $C\subseteq [N]$ is a feasible set of solutions, and $\lambda$ is a given regularization function. For any approximation error $\varepsilon>0$, we prove that \emph{every} set $P$ of $n$ integers has a weighted subset $S\subseteq P$ (sometimes called core-set) of cardinality $|S|\in O(\log(N)^{O(1)})$ that approximates $cost(P,c)$ (for every $c\in [N]$) up to a multiplicative factor of $1\pm\varepsilon$. Using known coreset techniques, this implies streaming algorithms using only $O((\log(N)\log(n))^{O(1)})$ memory. Our results hold for a large family of functions. Experimental results and open source code are provided.

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