SAX Navigator: Time Series Exploration through Hierarchical Clustering

Abstract

Figure 1: SAX Navigator shows the hierarchical clustering result for 2,000 astronomical observations (i.e., time series). Tree diagram (a) showing the global patterns derived from the hierarchical clustering of all time series. Tree branches are highlighted based on the user-specified pattern expressed in the visual query interface (b). Each tree node features a cluster heat map (c) representing the general shape of all time series in the cluster. A details-on-demand display (d) shows local observations of a single cluster. ABSTRACTComparing many long time series is challenging to do by hand. Clustering time series enables data analysts to discover relevance between and anomalies among multiple time series. However, even after reasonable clustering, analysts have to scrutinize correlations between clusters or similarities within a cluster. We developed SAX Navigator, an interactive visualization tool, that allows users to hierarchically explore global patterns as well as individual observations across large collections of time series data. Our visualization provides a unique way to navigate time series that involves a "vocabulary of patterns" developed by using a dimensionality reduction technique, Symbolic Aggregate approXimation (SAX). With SAX, the time series data clusters efficiently and is quicker to query at scale. We demonstrate the ability of SAX Navigator to analyze patterns in large time series data based on three case studies for an astronomy data set. We verify the usability of our system through a think-aloud study with an astronomy domain scientist.

Hexadecimal Aggregate Approximation Representation and Classification of Time Series Data

“…Auto-regressive (AR) model 1971 T4 [36,37] Discrete Fourier Transform(DFT) 1993 T1 O(n(log(n))) [13,38] Discrete Wavelet Transform (DWT) 1999 T1 O(n) [12,39] Singular Value Decomposition (SVD) 1997 T2 [40] Discrete Cosine Transformation (DCT) 1997 T1 - [40] Piecewise Linear Approximation (PLA) 1998 T2 O(n(log(n))) [17] Hidden Markov models (HMMs) 1998 T4 - [41] Piecewise Aggregate Approximation (PAA) or Segmented Means 2000 T1 O(n) [42] Piecewise Constant Approximation (PCA) 2000 T2 - [43] Adaptive Piecewise Constant Approximation (APCA) 2002 T2 O(n) [16] Perceptually important point (PIP) 2001 T1 - [44] Chebyshev Polynomials (CHEB) 2004 T1 - [45] Symbolic Aggregate Approximation (SAX) 2003 T2 O(n) [19,22] HOT SAX 2005 T2 [46] Clipped Data 2005 T3 - [47] Group SAX 2006 T2 [48] Extended SAX 2006 T2 [49] Combining SAX and Piecewise Linear Approximation 2007 T2 [50] Indexable Piecewise Linear Approximation (IPLA) 2007 T1 - [51] 1d-SAX 2013 T2 [52] Move-Split-Merge (MSM) 2013 [53] SAX-VSM 2013 T2 [54] SAX-EFG 2014 T2 [55] Tree-based Representations 2015 [56] SC-DTW 2015 T1 [57] Representation based on Local Autopatterns 2016 [58] Grid Representation 2019 [59] SAX Navigator 2019 T2 [60] SAX-ARM 2020 T2 [61] SAX-BD 2020 T2 [62] Data-driven Kernel-based Probabilistic SAX 2021 T2 [63] The most commonly used approximation representations are the PAA [42] and SAX [19,…”

PSEUDo: Interactive Pattern Search in Multivariate Time Series with Locality-Sensitive Hashing and Relevance Feedback

“…Examples range from QuerySketch [58] over Query-Lines [51] to Zenvisage++ [35]. It gives users more freedom, especially when the initial example is hard to find [46]. It is an active research area as capturing the unbiased concept from the user's drawing is challenging [35].…”

PRAGMA: Interactively Constructing Functional Brain Parcellations

“…Hierarchical Clustering Explorer [30] is a pioneering bio-informatics system for the interactive discovery of patterns. Since then, many approaches have been proposed for augmenting interactive clustering, by the means of finding the right clustering algorithm and parameters, and supporting exploratory clustering with visual and statistical analysis [3,19,21,24].…”