Abstract-- Online sensing plays an important role in advancing modern manufacturing. The real-time sensor signals, which can be stored as high-resolution time series data, contain rich information about the operation status. One of its popular usages is online process monitoring, which can be achieved by effective anomaly detection from the sensor signals. However, most existing approaches either heavily rely on labeled data for training supervised models, or are designed to detect only extreme outliers, thus are ineffective at identifying subtle semantic off-track anomalies to capture where new regimes or unexpected routines start. T o address this challenge, we propose an matrix profile-based unsupervised anomaly detection algorithm that captures fabrication cycle similarity and performs semantic segmentation to precisely identify the onset of defect anomalies in additive manufacturing. The effectiveness of the proposed method is demonstrated by the experiments on real-world sensor data.

The Matrix Profile (MP), a versatile tool for time series data mining, has been shown effective in time series anomaly detection (TSAD). This paper delves into the problem of anomaly detection in multidimensional time series, a common occurrence in real-world applications. For instance, in a manufacturing factory, multiple sensors installed across the site collect time-varying data for analysis. The Matrix Profile, named for its role in profiling the matrix storing pairwise distance between subsequences of univariate time series, becomes complex in multidimensional scenarios. If the input univariate time series has n subsequences, the pairwise distance matrix is a n x n matrix. In a multidimensional time series with d dimensions, the pairwise distance information must be stored in a n x n x d tensor. In this paper, we first analyze different strategies for condensing this tensor into a profile vector. We then investigate the potential of extending the MP to efficiently find k-nearest neighbors for anomaly detection. Finally, we benchmark the multidimensional MP against 19 baseline methods on 119 multidimensional TSAD datasets. The experiments covers three learning setups: unsupervised, supervised, and semi-supervised. MP is the only method that consistently delivers high performance across all setups.

Data-driven methods have gained extensive attention in estimating the state of health (SOH) of lithium-ion batteries. Accurate SOH estimation requires degradation-relevant features and alignment of statistical distributions between training and testing datasets. However, current research often overlooks these needs and relies on arbitrary voltage segment selection. To address these challenges, this paper introduces an innovative approach leveraging spatio-temporal degradation dynamics via graph convolutional networks (GCNs). Our method systematically selects discharge voltage segments using the Matrix Profile anomaly detection algorithm, eliminating the need for manual selection and preventing information loss. These selected segments form a fundamental structure integrated into the GCN-based SOH estimation model, capturing inter-cycle dynamics and mitigating statistical distribution incongruities between offline training and online testing data. Validation with a widely accepted open-source dataset demonstrates that our method achieves precise SOH estimation, with a root mean squared error of less than 1%.

Knowing who follows whom and what patterns they are following are crucial steps to understand collective behaviors (e.g. a group of human, a school of fish, or a stock market). Time series is one of resources that can be used to get insight regarding following relations. However, the concept of following patterns or motifs and the solution to find them in time series are not obvious. In this work, we formalize a concept of following motifs between two time series and present a framework to infer following patterns between two time series. The framework utilizes one of efficient and scalable methods to retrieve motifs from time series called the Matrix Profile Method. We compare our proposed framework with several baselines. The framework performs better than baselines in the simulation datasets. In the dataset of sound recording, the framework is able to retrieve the following motifs within a pair of time series that two singers sing following each other. In the cryptocurrency dataset, the framework is capable of capturing the following motifs within a pair of time series from two digital currencies, which implies that the values of one currency follow the values of another currency patterns. Our framework can be utilized in any field of time series to get insight regarding following patterns between time series.

The matrix profile is an effective data mining tool that provides similarity join functionality for time series data. Users of the matrix profile can either join a time series with itself using intra-similarity join (i.e., self-join) or join a time series with another time series using inter-similarity join. By invoking either or both types of joins, the matrix profile can help users discover both conserved and anomalous structures in the data. Since the introduction of the matrix profile five years ago, multiple efforts have been made to speed up the computation with approximate joins; however, the majority of these efforts only focus on self-joins. In this work, we show that it is possible to efficiently perform approximate inter-time series similarity joins with error bounded guarantees by creating a compact "dictionary" representation of time series. Using the dictionary representation instead of the original time series, we are able to improve the throughput of an anomaly mining system by at least 20X, with essentially no decrease in accuracy. As a side effect, the dictionaries also summarize the time series in a semantically meaningful way and can provide intuitive and actionable insights. We demonstrate the utility of our dictionary-based inter-time series similarity joins on domains as diverse as medicine and transportation.

Publishing and sharing data is crucial for the data mining community, allowing collaboration and driving open innovation. However, many researchers cannot release their data due to privacy regulations or fear of leaking confidential business information. To alleviate such issues, we propose the Time Series Synthesis Using the Matrix Profile (TSSUMP) method, where synthesized time series can be released in lieu of the original data. The TSSUMP method synthesizes time series by preserving similarity join information (i.e., Matrix Profile) while reducing the correlation between the synthesized and the original time series. As a result, neither the values for the individual time steps nor the local patterns (or shapes) from the original data can be recovered, yet the resulting data can be used for downstream tasks that data analysts are interested in. We concentrate on similarity joins because they are one of the most widely applied time series data mining routines across different data mining tasks. We test our method on a case study of ECG and gender masking prediction. In this case study, the gender information is not only removed from the synthesized time series, but the synthesized time series also preserves enough information from the original time series. As a result, unmodified data mining tools can obtain near-identical performance on the synthesized time series as on the original time series.

The matrix profile (MP) is a data structure computed from a time series which encodes the data required to locate motifs and discords, corresponding to recurring patterns and outliers respectively. When the time series contains noisy data then the conventional approach is to pre-filter it in order to remove noise but this cannot apply in unsupervised settings where patterns and outliers are not annotated. The resilience of the algorithm used to generate the MP when faced with noisy data remains unknown. We measure the similarities between the MP from original time series data with MPs generated from the same data with noisy data added under a range of parameter settings including adding duplicates and adding irrelevant data. We use three real world data sets drawn from diverse domains for these experiments Based on dissimilarities between the MPs, our results suggest that MP generation is resilient to a small amount of noise being introduced into the data but as the amount of noise increases this resilience disappears.

Gas is the transaction-fee metering system of the Ethereum network. Users of the network are required to select a gas price for submission with their transaction, creating a risk of overpaying or delayed/unprocessed transactions in this selection. In this work, we investigate data in the aftermath of the London Hard Fork and shed insight into the transaction dynamics of the net-work after this major fork. As such, this paper provides an update on work previous to 2019 on the link between EthUSD BitUSD and gas price. For forecasting, we compare a novel combination of machine learning methods such as Direct Recursive Hybrid LSTM, CNNLSTM, and Attention LSTM. These are combined with wavelet threshold denoising and matrix profile data processing toward the forecasting of block minimum gas price, on a 5-min timescale, over multiple lookaheads. As the first application of the matrix profile being applied to gas price data and forecasting we are aware of, this study demonstrates that matrix profile data can enhance attention-based models however, given the hardware constraints, hybrid models outperformed attention and CNNLSTM models. The wavelet coherence of inputs demonstrates correlation in multiple variables on a 1 day timescale, which is a deviation of base free from gas price. A Direct-Recursive Hybrid LSTM strategy outperforms other models. Hybrid models have favourable performance up to a 20 min lookahead with performance being comparable to attention models when forecasting 25/50-min ahead. Forecasts over a range of lookaheads allow users to make an informed decision on gas price selection and the optimal window to submit their transaction in without fear of their transaction being rejected. This, in turn, gives more detailed insight into gas price dynamics than existing recommenders, oracles and forecasting approaches, which provide simple heuristics or limited lookahead horizons.

Lithium-ion batteries (LiBs) degrade slightly until the knee onset, after which the deterioration accelerates to end of life (EOL). The knee onset, which marks the initiation of the accelerated degradation rate, is crucial in providing an early warning of the battery's performance changes. However, there is only limited literature on online knee onset identification. Furthermore, it is good to perform such identification using easily collected measurements. To solve these challenges, an online knee onset identification method is developed by exploiting the temporal information within the discharge data. First, the temporal dynamics embedded in the discharge voltage cycles from the slight degradation stage are extracted by the dynamic time warping. Second, the anomaly is exposed by Matrix Profile during subsequence similarity search. The knee onset is detected when the temporal dynamics of the new cycle exceed the control limit and the profile index indicates a change in regime. Finally, the identified knee onset is utilized to categorize the battery into long-range or short-range categories by its strong correlation with the battery's EOL cycles. With the support of the battery categorization and the training data acquired under the same statistic distribution, the proposed SOH estimation model achieves enhanced estimation results with a root mean squared error as low as 0.22%.

The development of compact and energy-efficient wearable sensors has led to an increase in the availability of biosignals. To analyze these continuously recorded, and often multidimensional, time series at scale, being able to conduct meaningful unsupervised data segmentation is an auspicious target. A common way to achieve this is to identify change-points within the time series as the segmentation basis. However, traditional change-point detection algorithms often come with drawbacks, limiting their real-world applicability. Notably, they generally rely on the complete time series to be available and thus cannot be used for real-time applications. Another common limitation is that they poorly (or cannot) handle the segmentation of multidimensional time series. Consequently, the main contribution of this work is to propose a novel unsupervised segmentation algorithm for multidimensional time series named Latent Space Unsupervised Semantic Segmentation (LS-USS), which was designed to work easily with both online and batch data. When comparing LS-USS against other state-of-the-art change-point detection algorithms on a variety of real-world datasets, in both the offline and real-time setting, LS-USS systematically achieves on par or better performances.