Category Archives: Mathematics

A clustering algorithm that claims to be simpler and faster than others

Yewang Chen, Yuanyuan Yang, Songwen Pei, Yi Chen, Jixiang Du, A simple rapid sample-based clustering for large-scale data, Engineering Applications of Artificial Intelligence, Volume 133, Part F, 2024 DOI: 10.1016/j.engappai.2024.108551.

Large-scale data clustering is a crucial task in addressing big data challenges. However, existing approaches often struggle to efficiently and effectively identify different types of big data, making it a significant challenge. In this paper, we propose a novel sample-based clustering algorithm, which is very simple but extremely efficient, and runs in about O(n×r) expected time, where n is the size of the dataset and r is the category number. The method is based on two key assumptions: (1) The data of each sufficient sample should have similar data distribution, as well as category distribution, to the entire data set; (2) the representative of each category in all sufficient samples conform to Gaussian distribution. It processes data in two stages, one is to classify data in each local sample independently, and the other is to globally classify data by assigning each point to the category of its nearest representative category center. The experimental results show that the proposed algorithm is effective, which outperforms other current variants of clustering algorithm.

Using fractal interpolation for time series prediction

Alexandra Băicoianu, Cristina Gabriela Gavrilă, Cristina Maria Păcurar, Victor Dan Păcurar, Fractal interpolation in the context of prediction accuracy optimization, Engineering Applications of Artificial Intelligence, Volume 133, Part D, 2024 DOI: 10.1016/j.engappai.2024.108380.

This paper focuses on the hypothesis of optimizing time series predictions using fractal interpolation techniques. In general, the accuracy of machine learning model predictions is closely related to the quality and quantitative aspects of the data used, following the principle of garbage-in, garbage-out. In order to quantitatively and qualitatively augment datasets, one of the most prevalent concerns of data scientists is to generate synthetic data, which should follow as closely as possible the actual pattern of the original data. This study proposes three different data augmentation strategies based on fractal interpolation, namely the Closest Hurst Strategy, Closest Values Strategy and Formula Strategy. To validate the strategies, we used four public datasets from the literature, as well as a private dataset obtained from meteorological records in the city of Braşov, Romania. The prediction results obtained with the LSTM model using the presented interpolation strategies showed a significant accuracy improvement compared to the raw datasets, thus providing a possible answer to practical problems in the field of remote sensing and sensor sensitivity. Moreover, our methodologies answer some optimization-related open questions for the fractal interpolation step using Optuna framework.

Change point detection through self-supervised learning

Xiangyu Bao, Liang Chen, Jingshu Zhong, Dianliang Wu, Yu Zheng, A self-supervised contrastive change point detection method for industrial time series, Engineering Applications of Artificial Intelligence, Volume 133, Part B, 2024, DOI: 10.1016/j.engappai.2024.108217.

Manufacturing process monitoring is crucial to ensure production quality. This paper formulates the detection problem of abnormal changes in the manufacturing process as the change point detection (CPD) problem for the industrial temporal data. The premise of known data property and sufficient data annotations in existing CPD methods limits their application in the complex manufacturing process. Therefore, a self-supervised and non-parametric CPD method based on temporal trend-seasonal feature decomposition and contrastive learning (CoCPD) is proposed. CoCPD aims to solve CPD problem in an online manner. By bringing the representations of time series segments with similar properties in the feature space closer, our model can sensitively distinguish the change points that do not conform to either historical data distribution or temporal continuity. The proposed CoCPD is validated by a real-world body-in-white production case and compared with 10 state-of-the-art CPD methods. Overall, CoCPD achieves promising results by Precision 70.6%, Recall 68.8%, and the mean absolute error (MAE) 8.27. With the ability to rival the best offline baselines, CoCPD outperforms online baseline methods with improvements in Precision, Recall and MAE by 14.90%, 11.93% and 43.93%, respectively. Experiment results demonstrate that CoCPD can detect abnormal changes timely and accurately.

See also: https://doi.org/10.1016/j.engappai.2024.108155

A survey on neurosymbolic RL and planning

K. Acharya, W. Raza, C. Dourado, A. Velasquez and H. H. Song, Neurosymbolic Reinforcement Learning and Planning: A Survey, IEEE Transactions on Artificial Intelligence, vol. 5, no. 5, pp. 1939-1953, May 2024 DOI: 10.1109/TAI.2023.3311428.

The area of neurosymbolic artificial intelligence (Neurosymbolic AI) is rapidly developing and has become a popular research topic, encompassing subfields, such as neurosymbolic deep learning and neurosymbolic reinforcement learning (Neurosymbolic RL). Compared with traditional learning methods, Neurosymbolic AI offers significant advantages by simplifying complexity and providing transparency and explainability. Reinforcement learning (RL), a long-standing artificial intelligence (AI) concept that mimics human behavior using rewards and punishment, is a fundamental component of Neurosymbolic RL, a recent integration of the two fields that has yielded promising results. The aim of this article is to contribute to the emerging field of Neurosymbolic RL by conducting a literature survey. Our evaluation focuses on the three components that constitute Neurosymbolic RL: neural, symbolic, and RL. We categorize works based on the role played by the neural and symbolic parts in RL, into three taxonomies: learning for reasoning, reasoning for learning, and learning–reasoning. These categories are further divided into subcategories based on their applications. Furthermore, we analyze the RL components of each research work, including the state space, action space, policy module, and RL algorithm. In addition, we identify research opportunities and challenges in various applications within this dynamic field.

Estimating speed from inertial data by dealing with noise and outliers

W. Xu, X. Peng and L. Kneip, Tight Fusion of Events and Inertial Measurements for Direct Velocity Estimation, IEEE Transactions on Robotics, vol. 40, pp. 240-256, 2024 DOI: 10.1109/TRO.2023.3333108.

Traditional visual-inertial state estimation targets absolute camera poses and spatial landmark locations while first-order kinematics are typically resolved as an implicitly estimated substate. However, this poses a risk in velocity-based control scenarios, as the quality of the estimation of kinematics depends on the stability of absolute camera and landmark coordinates estimation. To address this issue, we propose a novel solution to tight visual\u2013inertial fusion directly at the level of first-order kinematics by employing a dynamic vision sensor instead of a normal camera. More specifically, we leverage trifocal tensor geometry to establish an incidence relation that directly depends on events and camera velocity, and demonstrate how velocity estimates in highly dynamic situations can be obtained over short-time intervals. Noise and outliers are dealt with using a nested two-layer random sample consensus (RANSAC) scheme. In addition, smooth velocity signals are obtained from a tight fusion with preintegrated inertial signals using a sliding window optimizer. Experiments on both simulated and real data demonstrate that the proposed tight event-inertial fusion leads to continuous and reliable velocity estimation in highly dynamic scenarios independently of absolute coordinates. Furthermore, in extreme cases, it achieves more stable and more accurate estimation of kinematics than traditional, point-position-based visual-inertial odometry.

A PID-based global optimization algorithm

Yuansheng Gao, PID-based search algorithm: A novel metaheuristic algorithm based on PID algorithm, Expert Systems with Applications, Volume 232, 2023, DOI: 10.1016/j.eswa.2023.120886.

In this paper, a metaheuristic algorithm called PID-based search algorithm (PSA) is proposed for global optimization. The algorithm is based on an incremental PID algorithm that converges the entire population to an optimal state by continuously adjusting the system deviations. PSA is mathematically modeled and implemented to achieve optimization in a wide range of search spaces. PSA is used to solve CEC2017 benchmark test functions and six constrained problems. The optimization performance of PSA is verified by comparing it with seven metaheuristics proposed in recent years. The Kruskal-Wallis, Holm and Friedman tests verified the superiority of PSA in terms of statistical significance. The results show that PSA can be better balanced exploration and exploitation with strong optimization capability. Source codes�of PSA are publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/131534-pid-based-search-algorithm.

A brief summary of the state of the art in time series clustering

Hailin Li, Zechen Liu, Xiaoji Wan, Time series clustering based on complex network with synchronous matching states, Expert Systems with Applications, Volume 211, 2023 DOI: 10.1016/j.eswa.2022.118543.

Due to the extensive existence of time series in various fields, more and more research on time series data mining, especially time series clustering, has been done in recent years. Clustering technology can extract valuable information and potential patterns from time series data. This paper proposes a time series Clustering method based on Synchronous matching of Complex networks (CSC). This method uses density peak clustering algorithm to identify the state of each time point and obtains the state sequence according to the timeline of the original time series. State sequences is a new method to represent time series. By comparing two state sequences synchronously, the length of state sequence with step is calculated and the similarity is presented, which forms a new method to calculate the similarity of time series. Based on the obtained time series similarity, the relationship network of time series is constructed. Simultaneously, the community discovery technology is applied to cluster the relationship network and further achieve the complete time series clustering. The detailed process and simulation experiments of CSC method are given. Experimental results on different datasets show that CSC method is superior to other traditional time series clustering methods.

More robust KF through the use of skewed distributions

M. Bai, Y. Huang, B. Chen and Y. Zhang, A Novel Robust Kalman Filtering Framework Based on Normal-Skew Mixture Distribution, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 11, pp. 6789-6805, Nov. 2022 DOI: 10.1109/TSMC.2021.3098299.

In this article, a novel normal-skew mixture (NSM) distribution is presented to model the normal and/or heavy-tailed and/or skew nonstationary distributed noises. The NSM distribution can be formulated as a hierarchically Gaussian presentation by leveraging a Bernoulli distributed random variable. Based on this, a novel robust Kalman filtering framework can be developed utilizing the variational Bayesian method, where the one-step prediction and measurement-likelihood densities are modeled as NSM distributions. For implementation, several exemplary robust Kalman filters (KFs) are derived based on some specific cases of NSM distribution. The relationships between some existing robust KFs and the presented framework are also revealed. The superiority of the proposed robust Kalman filtering framework is validated by a target tracking simulation example.

Reducing outliers in time series with singular spectrum analysis and use of deep learning for change detection

Muktesh Gupta, Rajesh Wadhvani, Akhtar Rasool, Real-time Change-Point Detection: A deep neural network-based adaptive approach for detecting changes in multivariate time series data, Expert Systems with Applications, Volume 209, 2022 DOI: 10.1016/j.eswa.2022.118260.

The behavior of a time series may be affected by various factors. Changes in mean, variance, frequency, and auto-correlation are the most common. Change-Point Detection (CPD) aims to track down abrupt statistical characteristic changes in time series that can benefit many applications in different domains. As demonstrated in recently introduced CPD methodologies, deep learning approaches have the potential to identify more subtle changes. However, due to improper handling of data and insufficient training, these methodologies generate more false alarms and are not efficient enough in detecting change-points. In real-time CPD algorithms, preprocessed data plays a vital role in increasing the algorithm\u2019s efficiency and minimizing false alarm rates. Therefore, preprocessing of data should be a part of the algorithm, but in the existing methods, preprocessing of data is done initially, and then the whole dataset is passed to the CPD algorithm. A new three-phase architecture is proposed to address this issue, in which all phases, from preprocessing to CPD, work in an adaptive manner. The phases are integrated into a pipeline, allowing the algorithm to work in real-time. Our proposed strategy performs optimally and consistently based on performance metrics resulting from experiments on real-world datasets and artifacts. This work effectively addresses the issue of non-stationary data normalization using deep learning approaches. To reduce noise and outliers from the data, a recursive version of singular spectrum analysis is introduced. It is demonstrated that the method\u2019s performance has significantly improved by combining adaptive preprocessing with deep learning CPD techniques.

NOTE: See also C. Ma, L. Zhang, W. Pedrycz and W. Lu, “The Long-Term Prediction of Time Series: A Granular Computing-Based Design Approach,” in IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 10, pp. 6326-6338, Oct. 2022, doi: 10.1109/TSMC.2022.3144395.

See also https://babel.isa.uma.es/kipr/?p=1548

Non-parameterical detection of regimes in time series data (SODA), and its use in fuzzy forecasting

Shivani Pant, Sanjay Kumar, IFS and SODA based computational method for fuzzy time series forecasting, Expert Systems with Applications, Volume 209, 2022 DOI: 10.1016/j.eswa.2022.118213.

Time series forecasting has fascinated a great deal of interest from various research communities due to its wide applications in medicine, economics, finance, engineering and many other crucial fields. Various studies in past have shown that intuitionistic fuzzy sets (IFSs) not only handle non-stochastic non-determinism in time series forecasting but also enhance accuracy in forecasted outputs. Clustering is another one of the methods that improves accuracy of time series forecasting. The contribution of this research work is a novel computational fuzzy time series (FTS) forecasting method which relies on IFSs and self-organized direction aware (SODA) approach of clustering. The usage of SODA aids in making the proposed FTS forecasting method as autonomous as feasible, as it does not require human intervention or prior knowledge of the data. Forecasted outputs in proposed FTS forecasting method are computed using a weighted formula and weights are optimized using grey wolf optimization (GWO) method. Proposed FTS is applied to forecast enrolments of the University of Alabama and market price of State Bank of India (SBI) share at Bombay stock exchange (BSE), India and performance is compared in terms of root mean square error (RMSE), average forecasting error (AFE) and mean absolute deviation (MAD). Goodness of the proposed FTS forecasting method in forecasting enrolments of the University of Alabama and market price of SBI share is also tested using coefficient of correlation and determination, criteria of Akaike and Bayesian information.

See also https://babel.isa.uma.es/kipr/?p=1550