Symbolic Aggregate Approximation Research Articles

Reservoir fluid identification based on multi-head attention with UMAP

Gas logging curves obtained during drilling, along with conventional well logs, typically serve as foundational data for identifying reservoir fluids. Traditional methods for identifying layers containing oil or gas often suffer from limitations such as inadequate feature extraction, underutilization of differences in data points, and limited applicability. These limitations lead to reduced accuracy in predicting reservoir fluid segmentation. To address the challenge of spatiotemporal feature extraction in logging curves, this paper presents a fluid identification method based on deep learning networks and multivariate sequence classification. The method takes into account both the sequential variations in geological strata and the relationships among different curves for fluid prediction. Our proposed method utilizes a Transformer multi-head attention mechanism and follows a series of steps. First, an improved Symbolic Aggregate approXimation (SAX) is employed to assess the response characteristics of the logging curves to the target fluid and identify sensitive curves based on information similarity. Subsequently, the semi-supervised learning method UMAP is applied to identify layers with high interpretability. Hierarchical training is then employed to mitigate the impact of noise and high-dimensional nonlinearity on identification results. Finally, the processed vector curves are input into the attention module layer, where features of each layer are extracted in an encoding-decoding manner. This method has been tested and validated using gas logging data from 12 wells in a gas field offshore China. The overall prediction accuracy can exceed 94%, and the prediction accuracy for a single gas layer is over 88%. When compared to other machine learning approaches, such as K-means, decision tree, and XGBoost, this method exhibits superior identification accuracy and generalization ability, especially for unbalanced samples.

Symbolic Aggregate Approximation-Based Clustering of Monthly Natural Gas Consumption

Natural gas is an indispensable non-renewable energy source for many countries. It is used in many different areas such as heating and kitchen appliances in homes, and heat treatment and electricity generation in industry. Natural gas is an essential component of the transportation sector, providing a cleaner alternative to traditional fuels in vehicles and fleets. Moreover, natural gas plays a vital role in boosting energy efficiency through the development of combined heat and power systems. These systems produce electricity and useful heat concurrently. As nations move towards more sustainable energy solutions, natural gas has gained prominence as a transitional fuel. This is due to its lower carbon emissions when compared to coal and oil, thus making it an essential component of the global energy framework. In this study, monthly natural gas consumption data of 28 different European countries between 2014 and 2022 are used. Symbolic Aggregate Approximation method is used to analyse the data. Analyses are made with different numbers of segments and numbers of alphabet sizes, and alphabet vectors of each country are created. These letter vectors are used in hierarchical clustering and dendrogram graphs are created. Furthermore, the elbow method is used to determine the appropriate number of clusters. Clusters of countries are created according to the determined number of clusters. In addition, it is interpreted according to the consumption trends of the countries in the determined clusters.

Fast and accurate ECG signal peaks detection using symbolic aggregate approximation

Fast and accurate ECG signal peaks detection using symbolic aggregate approximation

A machine learning-based Anomaly Detection Framework for building electricity consumption data

A suboptimal management or system malfunction can often lead to abnormal energy consumptions in buildings, which result in a significant waste of energy. For this reason, the adoption of advanced monitoring systems, based on Machine Learning (ML) and visualization techniques, is crucial to avoid possible deviations from the baseline energy consumption. However, the historical data on which analyses are based generally do not report the occurrence of anomalies. Therefore, the application of supervised ML techniques is limited and unsupervised approaches are favored. Moreover, domain experts find most Machine Learning (ML) techniques hard to interpret, and thus find it difficult to contextualize anomalies. To overcome these issues, this work proposes a machine learning-based Anomaly Detection Framework (ADF) that involves the use of two complementary semi-supervised ML applications to obtain a highly interpretable and accurate detection of anomalies. Both techniques use Symbolic Aggregate approXimation (SAX) encoding to extract the most relevant information from load profiles. The aim of the first approach is to maximize the interpretability of the definition and distinction between anomalous and normal behavior. This is achieved using a Classification And Regression Tree (CART), albeit at the expense of a coarser output granularity. The second approach exploits an Multi-Layer Perceptron (MLP) algorithm to obtain a higher and more accurate output resolution, although it leads to a less interpretable definition of any anomalous behavior. The ADF has been applied to a real case study using electricity consumption data provided by a large telecommunications service provider. The results show that combining both ML models enhances the accuracy and interpretability of the detected anomalies.

Distributional Representation of Cyclic Alternating Patterns for A-Phase Classification in Sleep EEG

This article describes a detailed methodology for the A-phase classification of the cyclic alternating patterns (CAPs) present in sleep electroencephalography (EEG). CAPs are a valuable EEG marker of sleep instability and represent an important pattern with which to analyze additional characteristics of sleep processes, and A-phase manifestations have been linked to some specific conditions. CAP phase detection and classification are not commonly carried out routinely due to the time and attention this problem requires (and if present, CAP labels are user-dependent, visually evaluated, and hand-made); thus, an automatic tool to solve the CAP classification problem is presented. The classification experiments were carried out using a distributional representation of the EEG data obtained from the CAP Sleep Database. For this purpose, data symbolization was performed using the one-dimensional symbolic aggregate approximation (1d-SAX), followed by the vectorization of symbolic data with a trained Doc2Vec model and a final classification with ten classic machine learning models for two separate validation strategies. The best results were obtained using a support vector classifier with a radial basis kernel. For hold-out validation, the best F1 Score was 0.7651; for stratified 10-fold cross-validation, the best F1 Score was 0.7611 ± 0.0133. This illustrates that the proposed methodology is suitable for CAP classification.

Ensemble Learning for Alcoholism Classification Using EEG Signals

Excessive drinking is a major risk factor that leads to many health complications. The diagnosis of alcoholism is challenging, especially when the standard diagnostic tests rely on blood tests and questionnaires that are subjective to the patient and the examiner. The study’s major goal is to find new EEG classification methods to improve past findings and construct a robust EEG classification algorithm to generate accurate predictions with explainable results. The EEG records were examined from two different perspectives and combined with an ensemble of classification models. The first approach was temporal data, and the second was images derived from the original signals. Using fast Fourier transform (FFT) and independent component analysis (ICA), we convert 64-channel temporal data into images along with applying the Symbolic Aggregate approXimation (SAX) technique. Our model combines input data in tabular, temporal, and image formats with an ensemble of linear neural networks, long short-term memory (LSTM), and efficient-net classification models. We have evaluated our method using a publicly available dataset for EEG classification of alcoholic and non-alcoholic subjects. Overall, our algorithm’s highest cross-validation classification accuracy is 85.52% compared to the state-of-the-art EEG-NET’s accuracy of 81.19%.

Similarity Measurement and Classification of Temporal Data Based on Double Mean Representation

Time series data typically exhibit high dimensionality and complexity, necessitating the use of specific approximation methods to perform computations on the data. The currently employed compression methods suffer from varying degrees of feature loss, leading to potential distortions in similarity measurement results. Considering the aforementioned challenges and concerns, this paper proposes a double mean representation method, SAX-DM (Symbolic Aggregate Approximation Based on Double Mean Representation), for time series data, along with a similarity measurement approach based on SAX-DM. Addressing the trade-off between compression ratio and accuracy in the improved SAX representation, SAX-DM utilizes the segment mean and the segment trend distance to represent corresponding segments of time series data. This method reduces the dimensionality of the original sequences while preserving the original features and trend information of the time series data, resulting in a unified representation of time series segments. Experimental results demonstrate that, under the same compression ratio, SAX-DM combined with its similarity measurement method achieves higher expression accuracy, balanced compression rate, and accuracy, compared to SAX-TD and SAX-BD, in over 80% of the UCR Time Series dataset. This approach improves the efficiency and precision of similarity calculation.

Knowledge Discovery and Diagnosis Using Temporal-Association-Rule-Mining-Based Approach for Threshing Cylinder Blockage

Accurately diagnosing blockages in a threshing cylinder is crucial for ensuring efficiency and quality in combine harvester operations. However, in terms of blockage diagnostic methods, the current state of affairs is characterized by model-based approaches that can be highly time-consuming and difficult to implement, while data-driven approaches lack interpretability. To address this situation, we propose a temporal association rule mining (TARM)-based fault diagnosis method for identifying threshing cylinder blockages and discovering knowledge. This study performs field trials by varying the actual feed rate and obtains datasets for three blockage classes (slight, moderate, and severe). Firstly, a symbolic aggregate approximation (SAX) method is employed to reduce the data dimensionality and to construct the transaction set with a sliding window. Next, a cSpade method is used to mine and extract strong association rules by applying improved support, confidence, and lift indicators. With the established strong association rules, this study can comprehensively elucidate the variation pattern of each characteristic under several blockage failure conditions and can effectively identify blockage faults. The results demonstrate that the proposed method effectively distinguishes between three levels of blockage faults, achieving an overall diagnostic accuracy of 0.94. And the method yields precisions of 0.90, 0.92, and 0.99 and corresponding recalls of 0.90, 0.93, and 0.98 for slight, medium, and severe levels of blockage faults, respectively. Specifically, the knowledge acquired from the extracted strong association rules can effectively explain the operational characteristics of a combine harvester when its threshing cylinders are blocked. Furthermore, the proposed approach in this study can provide a reasonable and reliable reference for future research on threshing cylinder blockages.

Sum of Gaussian Feature-Based Symbolic Representations of Eddy Current Defect Signatures

ABSTRACT This study investigates a novel symbolic representation method based on Symbolic Aggregate Approximation (SAX) of time series that focuses on differential coil (D-coil) eddy current (EC) defect responses. The method uses the Sum of Gaussian (SoG) approximation of the defect response, Fuzzy C-means (FCM) clustering, and the extrema values in the approximation to provide a reduced representation that can effectively analyze possible fault conditions in the defect response. Comparisons to existing SAX methods are performed with the new method indicating significant classification accuracy improvement.

Urban Mobility and Knowledge Extraction from Chaotic Time Series Data: A Comparative Analysis for Uncovering COVID-19 Effects

The COVID-19 pandemic exerted devastating effects on the global economy, public health, and urban life. The geographical consequences lie in spatial time series dimensions, but the chaotic characteristics hinder intuitive understanding. Aiming to discover the variance of urban mobility in the pandemic context, this article presents a hybrid clustering technique called whole time sequence mixture (WTSM). The combination of whole time and subsequence techniques ensures robustness to data volume, dimensionality, sampling, distortion tasks, and a prior constraint. For yellow taxi trips in New York City, the case study spanned the pre-, mid-, and postpandemic periods and compared the performance of the established methods (symbolic aggregate approximation and dynamic time warping) and WTSM techniques. Findings revealed COVID-19 trends and social restriction-induced mobility variations and determined that vaccine supply did not lead to immediate mobility restoration. Meanwhile, concepts of validation indexes and computational complexity corroborate the superiority of WTSM. The transient cluster arising from temporal dissimilarity is a unique finding of WTSM, which led to high cluster cohesion and separation. WTSM can obtain new knowledge and rationale for urgent government intervention and epidemic management, not sacrificing computational efficiency and clustering quality. With the improved storage capability and desire for multidimensional pattern extraction, the increased accessibility to the chaotic time series data sets could promote further studies and help administrative schemes.

SLAFusion: Attention fusion based on SAX and LSTM for dangerous driving behavior detection

Dangerous driving behaviors are the main cause of most traffic accidents, and the detection of these behaviors is one of the extremely important researches in Intelligent Transportation System (ITS). Although some recent approaches consider dangerous driving behavior as a process containing multiple instantaneous points, which is ignored by traditional methods, they fail to take into account the loss of temporal information due to the reasonable division of instantaneous points. Therefore, this paper proposes a Symbolic Aggregate approXimation (SAX) and Long Short-Term Memory (LSTM)-based Attention Fusion method (SLAFusion) to detect dangerous driving behavior more accurately. This method evaluates various granularity of driving processes and explores the association between adjacent processes. First, a D-value Piecewise Aggregate Approximation (DPAA) is designed to model the change of vehicle state in mining driving processes with diverse granularity. Then, the features of multiple driving processes are fused to enhance each other to solve the problem of information loss due to segmentation of driving processes. Further, the auxiliary information is fused to incorporate the environmental features of the vehicle during driving. Finally, the experimental results on real datasets indicate that the proposed SLAFusion method improves the recall and F-score by 3.2% and 2.6% respectively in comparison with the existing benchmark methods.

Anomaly Detection in Automatic Meter Intelligence System Using Positive Unlabeled Learning and Multiple Symbolic Aggregate Approximation.

With the development of automatic electrical devices in smart grids, the data generated by time and transmitted are vast and thus impossible to control consumption by humans. The problem of abnormal detection in power consumption is crucial in monitoring and controlling smart grids. This article proposes the detection of electrical meter anomalies by detecting abnormal patterns and learning unlabeled data. Furthermore, a framework for big data and machine learning-based anomaly detection framework are introduced. The experimental results show that the time series anomaly detection for electric meters has better results in accuracy and time than the expert alternatives.

Parallel symbolic aggregate approximation and its application in intelligent fault diagnosis

Fault diagnosis is of great significance for industrial equipment maintenance, and feature extraction is a key step of the entire diagnosis scheme. The symbolic aggregate approximation (SAX) is a popular feature extraction approach with great potential recently. In spite of the achievements the SAX has made, the adverse information aliasing still exists in its calculation procedure, and it may make the SAX fail to guarantee the information correctness. This work focuses on analyzing the information aliasing phenomenon of the SAX, followed by developing a novel alternative method, i.e. parallel symbolic aggregate approximation (PSAX). In the proposed PSAX, the information aliasing is suppressed by designing anti-aliasing procedure, and the average of the symbolic results of several intermediate sequence is adopted to replace the final symbolic result. The Case Western Reserve University (CWRU) rolling bearing data together with the gas valve data of an actual reciprocating compressor assist in verifying the superiority exhibited by the suggested method. The experimental results show that, compared with other methods, the accuracy advantage of the PSAX on the 2 datasets can reach 1% –5%, indicating it is capable of providing high-quality feature vector for intelligent fault diagnosis.

Palmprint authentication using symbolic aggregate approximation features with improved enhancement techniques

The palmprint enhancement is a pre-processing stage of palmprint authentication. The accuracy of the recognition rate can be improved by incorporating effective palmprint enhancement methods. So far, only a little work has been done in palmprint enhancement. Little attention is given to incorporate the enhancement techniques in palmprint authentication system to achieve performance improvement. This work presents robust enhancement methods which provide better performance and accuracy. Palmprint enhancement using curvelet and Recursive Histogram Equalization (RHE) overcomes the drawbacks of the existing systems and makes palmprint recognition simpler and more accurate with enhanced palm image as input. Palmprint recognition system uses the Symbolic Aggregate Approximation (SAX) features from the enhanced palmprint image. The recognition rate is optimum when both curvelet and RHE methods are used for enhancement of palmprint. Here we compared different types of enhancement methods and we have obtained maximum recognition rate with a combination of recursive histogram equalization and curvelet transform. The performance of the palmprint authentication is measured by False Acceptance Rate (FAR), False Rejection Rate (FRR) and Total Success Rate (TSR). The comparison of recognition rate with enhancement is done using minimum distance classifier, Support Vector Machine, Random Forest and Bayesian. Random Forest classifier provides better results.

Energy signature-based clustering using open data for urban building energy analysis toward carbon neutrality: A case study on electricity change under COVID-19

Under the necessity for urban energy savings and the importance of energy demand changes, this paper proposes energy analytics of urban buildings using a novel clustering method with open data. In the proposed method, the concept of energy signatures is introduced, and the signatures are defined as the representative symbols in the symbolic hierarchical clustering. This method can advance the existing clustering method or symbolic aggregate approximation (SAX) with limited energy usage patterns by introducing energy signatures with various pieces of energy information into the symbolic transformation. The proposed method can scientifically support tracking building energy usage and patterns, evaluating the existing concepts (such as green retrofitting and zero energy buildings) and advanced technologies, and the decision-making process for new policies under the global carbon neutrality scenarios. In a case study applied to a city using open energy data (in South Korea), the proposed method determined five representative clusters/areas, revealing the open data quality problems (anomaly and missing data), energy usage changes (e.g., energy usage polarization) caused by COVID-19, and the necessity of classifying building types in terms of energy usage patterns. Specifically, the cluster for decreasing energy patterns accounted for approximately 37%, and the increasing patterns accounted for 25%. Educational buildings accounted for 70% of the decreasing patterns, and technical and medical research facilities accounted for 76% of the increasing patterns under the COVID-19. Approximately 93% of missing data was found in the residential buildings. Anomaly data accounted for 10.9% in the total data.

An ensemble learning algorithm based on discretized Time Series: application on smartphone-inertial measurement

This paper presents a novel learning algorithm formulated as a classification problem with smartphone-inertial measurement as predictor. For this reason, we will focus on the Symbolic Aggregate approXimation (SAX) as a low-cost classification algorithm resulting from its ability of the data dimensionality reduction through symbolic discretization. Since the first publication of the SAX, a lot of extension with novel SAX-distance measure are published. Each of them attempts to integrate additional statistical features in order to improve original SAX average-based feature. However, none of them can fit the overall shape-characteristics of the data and give the superiority to an individual SAX-based classifier. In order to combine the prediction of each single SAX-based classifier, we propose a collection of several SAX-feature to compose a multi-SAX feature ensemble classification. The proposed algorithm is validated on experimental data addressing (i) the character recognition when using a smartphone as a pen and (ii) the road profile estimation using a smartphone mounted in the interior of a vehicle while driving.

Association Rules Discovery of Deviant Events in Multivariate Time Series: An Analysis and Implementation of the SAX-ARM Algorithm

In this work, we propose an open-source Python implementation of the SAX-ARM algorithm introduced by Park and Jung (2019). This algorithm mines association rules efficiently among the deviant events of multivariate time series. To do so, the algorithm combines two existing methods, namely the Symbolic Aggregate approXimation (SAX) from Lin et al. (2003) - a symbolic representation of time series - and the Apriori algorithm from Agrawal et al. (1996) - a data mining method which outputs all frequent itemsets and association rules from a transactional dataset. A detailed description of the underlying principles is given along with their numerical implementation. The choice of relevant parameters is thoroughly discussed and evaluated using a public dataset on the topic of temperature and energy consumption.

Operational signature-based symbolic hierarchical clustering for building energy, operation, and efficiency towards carbon neutrality

Buildings are considered the enormous source of untapped energy efficiency potential in the global carbon neutrality. It is necessary to ensure that buildings are energy-efficient using operational pattern analytics and diagnostics. Therefore, this study proposes a novel symbolic hierarchical clustering method (named HOS-SAX) to evaluate the building system operation, efficiency, and energy usage patterns. The proposed HOS-SAX method is intended to enhance the existing methods that focus only on the energy usage characteristics and thus offer limited insights on the building system and operational efficiency. The proposed method consists of: (1) Holistic Operational Signature (HOS) and (2) HOS-based symbolic aggregate approximation (SAX) analyses. A HOS analysis is conducted to derive the representative operational signatures for building operation and efficiency using system-, building-, and weather-level data. Then, SAX is performed with the operational signatures derived from the HOS to cluster the building operation patterns. In a case study for a district heating substation serving residential buildings, the HOS-SAX cluster analysis showed 15 sections in the cluster map that visualize the: (1) energy usage, (2) design efficiency, and (3) control efficiency. The cluster map revealed that the sections that operated inefficiently account for approximately 71% of the entire operation period. Moreover, it is expected that the supply temperature of 0.87 °C can be reduced in the most inefficient sections.

Time-series classification with SAFE: Simple and fast segmented word embedding-based neural time series classifier

Dictionary-based classifiers are an essential group of approaches in the field of time series classification. Their distinctive characteristic is that they transform time series into segments made of symbols (words) and then classify time series using these words. Dictionary-based approaches are suitable for datasets containing time series of unequal length. The prevalence of dictionary-based methods inspired the research in this paper. We propose a new dictionary-based classifier called SAFE. The new approach transforms the raw numeric data into a symbolic representation using the Simple Symbolic Aggregate approXimation (SAX) method. We then partition the symbolic time series into a sequence of words. Then we employ the word embedding neural model known in Natural Language Processing to train the classifying mechanism. The proposed scheme was applied to classify 30 benchmark datasets and compared with a range of state-of-the-art time series classifiers. The name SAFE comes from our observation that this method is safe to use. Empirical experiments have shown that SAFE gives excellent results: it is always in the top 5%–10% when we rank the classification accuracy of state-of-the-art algorithms for various datasets. Our method ranks third in the list of state-of-the-art dictionary-based approaches (after the WEASEL and BOSS methods).

Charging Diagnosis of Power Battery Based on Adaptive STCKF and BLS for Electric Vehicles

This article proposes a BLS-STCKF estimation and diagnosis scheme of state of charge (SOC) and RUL prediction for power batteries in electric vehicles (EVs). First, the process of SOC estimation is considered as a time series problem. The walk-forward validation method has been applied in BLS (Broad Learning System) estimator training and validation. Then, a sliding window with variable width is used to help the time series SOC estimation improve. Meanwhile, STCKF (Strong Tracking Cubature Kalman Filter) is combined with BLS to help search for an optimal hyperparameter for BLS. Then, this article takes the SOC diagnosis as a problem of diagnosing abnormal time segments and uses HOT SAX(Heuristically Ordered Time series using Symbolic Aggregate ApproXimation) to detect SOC anomalies. Moreover, a prediction method of RUL (Remain Useful Life) has been designed by BLS-STCK. In light of result of RUL, the capacity degradation is considered to improve SOC estimation, and capacity retention coefficient is posed to adjust BLS-STCKF when battery aged. Finally, the proposed methods has also been evaluated by real driving data of EVs. Based on those critical experiments, rational analysis and conclusion have been illustrated that the proposed method has competitive accuracy.