Time Series Discord Research Articles

Discord-based counterfactual explanations for time series classification

The opacity inherent in machine learning models presents a significant hindrance to their widespread incorporation into decision-making processes. To address this challenge and foster trust among stakeholders while ensuring decision fairness, the data mining community has been actively advancing the explainable artificial intelligence paradigm. This paper contributes to the evolving field by focusing on counterfactual generation for time series classification models, a domain where research is relatively scarce. We develop, a post-hoc, model agnostic counterfactual explanation algorithm that leverages the Matrix Profile to map time series discords to their nearest neighbors in a target sequence and use this mapping to generate new counterfactual instances. To our knowledge, this is the first effort towards the use of time series discords for counterfactual explanations. We evaluate our algorithm on the University of California Riverside and University of East Anglia archives and compare it to three state-of-the-art univariate and multivariate methods.

The Swiss army knife of time series data mining: ten useful things you can do with the matrix profile and ten lines of code

The recently introduced data structure, the Matrix Profile, annotates a time series by recording the location of and distance to the nearest neighbor of every subsequence. This information trivially provides answers to queries for both time series motifs and time series discords, perhaps two of the most frequently used primitives in time series data mining. One attractive feature of the Matrix Profile is that it completely divorces the high-level details of the analytics performed, from the computational “heavy lifting.” The Matrix Profile can be computed using the appropriate computational paradigm for the task at hand: CPU, GPU, FPGA, distributed computing, anytime computation, incremental computation, and so forth. However, all the details of such computation can be hidden from the analyst who only needs to think about her analytical need. In this work, we expand on this philosophy and ask the following question: If we assume that we get the Matrix Profile for free, what interesting analytics can we do, writing at most ten lines of code? As we will show, the answer is surprisingly large and diverse. Our aim here is not to establish or compete with state-of-the-art results, but merely to show that we can both reproduce the results of many existing algorithms and find novel regularities in time series data collections with very little effort.

Time series joins, motifs, discords and shapelets: a unifying view that exploits the matrix profile

The last decade has seen a flurry of research on all-pairs-similarity-search (or similarity joins) for text, DNA and a handful of other datatypes, and these systems have been applied to many diverse data mining problems. However, there has been surprisingly little progress made on similarity joins for time series subsequences. The lack of progress probably stems from the daunting nature of the problem. For even modest sized datasets the obvious nested-loop algorithm can take months, and the typical speed-up techniques in this domain (i.e., indexing, lower-bounding, triangular-inequality pruning and early abandoning) at best produce only one or two orders of magnitude speedup. In this work we introduce a novel scalable algorithm for time series subsequence all-pairs-similarity-search. For exceptionally large datasets, the algorithm can be trivially cast as an anytime algorithm and produce high-quality approximate solutions in reasonable time and/or be accelerated by a trivial porting to a GPU framework. The exact similarity join algorithm computes the answer to the time series motif and time series discord problem as a side-effect, and our algorithm incidentally provides the fastest known algorithm for both these extensively-studied problems. We demonstrate the utility of our ideas for many time series data mining problems, including motif discovery, novelty discovery, shapelet discovery, semantic segmentation, density estimation, and contrast set mining. Moreover, we demonstrate the utility of our ideas on domains as diverse as seismology, music processing, bioinformatics, human activity monitoring, electrical power-demand monitoring and medicine.

Finding time series discord based on bit representation clustering

The problem of finding time series discord has attracted much attention recently due to its numerous applications and several algorithms have been suggested. However, most of them suffer from high computation cost and cannot satisfy the requirement of real applications. In this paper, we propose a novel discord discovery algorithm BitClusterDiscord which is based on bit representation clustering. Firstly, we use PAA (Piecewise Aggregate Approximation) bit serialization to segment time series, so as to capture the main variation characteristic of time series and avoid the influence of noise. Secondly, we present an improved K-Medoids clustering algorithm to merge several patterns with similar variation behaviors into a common cluster. Finally, based on bit representation clustering, we design two pruning strategies and propose an effective algorithm for time series discord discovery. Extensive experiments have demonstrated that the proposed approach can not only effectively find discord of time series, but also greatly improve the computational efficiency.

Weighted spherical 1-mean with phase shift and its application in electrocardiogram discord detection

Detecting discords in time series is a special novelty detection task that has found many interesting applications. Unlike the traditional novelty detection methods which can make use of a separate set of normal samples to build up the model, discord detection is often provided with mixed data containing both normal and abnormal data. The objective of this work is to present an effective method to detect discords in unsynchronized periodic time series data. The task of discord detection is considered as a problem of unsupervised learning with noise data. A new clustering algorithm named weighted spherical 1-mean with phase shift (PS-WS1M) is proposed in this work. It introduces a phase adjustment procedure into the iterative clustering process and produces a set of anomaly scores based upon which an unsupervised approach is employed to locate the discords automatically. A theoretical analysis on the robustness and convergence of PS-WS1M is also given. The proposed algorithm is evaluated via real-world electrocardiograms datasets extracted from the MIT-BIH database. The experimental results show that the proposed algorithm is effective and competitive for the problem of discord detection in periodic time series. Meanwhile, the robustness of PS-WS1M is also experimentally verified. As compared to some of the other discord detection methods, the proposed algorithm can always achieve ideal FScore values with most of which exceeding 0.98. The proposed PS-WS1M algorithm allows the integration of a phase adjustment procedure into the iterative clustering process and it can be successfully applied to detect discords in time series.

A novel discords detector for periodic time series based on weighted spherical single means with phase shift

The traditional one-class classifiers are not suitable for detecting discords in periodic time series. A novel one-class classifier PS-WS1M-OCC is proposed in this paper. In our method, the phase problem in time series is solved by introducing phase shift into the clustering procedure. Meanwhile, a novel criterion for adaptively choosing threshold is proposed. In this way, the proposed classifier is insensitive to noise in the training set. Experimental results show that our PS-WSKM-OCC is more robust than the existing one-class classifiers when it is applied to the problem of discord detection in the periodic time series.

Disk aware discord discovery: finding unusual time series in terabyte sized datasets

The problem of finding unusual time series has recently attracted much attention, and several promising methods are now in the literature. However, virtually all proposed methods assume that the data reside in main memory. For many real-world problems this is not be the case. For example, in astronomy, multi-terabyte time series datasets are the norm. Most current algorithms faced with data which cannot fit in main memory resort to multiple scans of the disk /tape and are thus intractable. In this work we show how one particular definition of unusual time series, the time series discord, can be discovered with a disk aware algorithm. The proposed algorithm is exact and requires only two linear scans of the disk with a tiny buffer of main memory. Furthermore, it is very simple to implement. We use the algorithm to provide further evidence of the effectiveness of the discord definition in areas as diverse as astronomy, web query mining, video surveillance, etc., and show the efficiency of our method on datasets which are many orders of magnitude larger than anything else attempted in the literature.

Finding the most unusual time series subsequence: algorithms and applications

In this work we introduce the new problem of finding time seriesdiscords. Time series discords are subsequences of longer time series that are maximally different to all the rest of the time series subsequences. They thus capture the sense of the most unusual subsequence within a time series. While discords have many uses for data mining, they are particularly attractive as anomaly detectors because they only require one intuitive parameter (the length of the subsequence) unlike most anomaly detection algorithms that typically require many parameters. While the brute force algorithm to discover time series discords is quadratic in the length of the time series, we show a simple algorithm that is three to four orders of magnitude faster than brute force, while guaranteed to produce identical results. We evaluate our work with a comprehensive set of experiments on diverse data sources including electrocardiograms, space telemetry, respiration physiology, anthropological and video datasets.

Finding Unusual Medical Time-Series Subsequences: Algorithms and Applications

In this work, we introduce the new problem of finding time series discords. Time series discords are subsequences of longer time series that are maximally different to all the rest of the time series subsequences. They thus capture the sense of the most unusual subsequence within a time series. While discords have many uses for data mining, they are particularly attractive as anomaly detectors because they only require one intuitive parameter (the length of the subsequence), unlike most anomaly detection algorithms that typically require many parameters. While the brute force algorithm to discover time series discords is quadratic in the length of the time series, we show a simple algorithm that is three to four orders of magnitude faster than brute force, while guaranteed to produce identical results. We evaluate our work with a comprehensive set of experiments on electrocardiograms and other medical datasets.