Antal Jakovác

Marcell T. Kurbucz, Péter Pósfay, Antal Jakovác

The goal of the linear law-based feature space transformation (LLT) algorithm is to assist with the classification of univariate and multivariate time series. The presented R package, called LLT, implements this algorithm in a flexible yet user-friendly way. This package first splits the instances into training and test sets. It then utilizes time-delay embedding and spectral decomposition techniques to identify the governing patterns (called linear laws) of each input sequence (initial feature) within the training set. Finally, it applies the linear laws of the training set to transform the initial features of the test set. These steps are performed by three separate functions called trainTest, trainLaw, and testTrans. Their application requires a predefined data structure; however, for fast calculation, they use only built-in functions. The LLT R package and a sample dataset with the appropriate data structure are publicly available on GitHub.

Péter Pósfay, Marcell T. Kurbucz, Péter Kovács et al.

This paper introduces LLT-ECG, a novel method for electrocardiogram (ECG) signal classification that leverages concepts from theoretical physics to automatically generate features from time series data. Unlike traditional deep learning approaches, LLT-ECG operates in a forward manner, eliminating the need for backpropagation and hyperparameter tuning. By identifying linear laws that capture shared patterns within specific classes, the proposed method constructs a compact and verifiable representation, enhancing the effectiveness of downstream classifiers. We demonstrate LLT-ECG's state-of-the-art performance on real-world ECG datasets from PhysioNet, underscoring its potential for medical applications where speed and verifiability are crucial.

Marcell T. Kurbucz, Péter Pósfay, Antal Jakovác

The aim of this paper is to investigate the effect of a novel method called linear law-based feature space transformation (LLT) on the accuracy of intraday price movement prediction of cryptocurrencies. To do this, the 1-minute interval price data of Bitcoin, Ethereum, Binance Coin, and Ripple between 1 January 2019 and 22 October 2022 were collected from the Binance cryptocurrency exchange. Then, 14-hour nonoverlapping time windows were applied to sample the price data. The classification was based on the first 12 hours, and the two classes were determined based on whether the closing price rose or fell after the next 2 hours. These price data were first transformed with the LLT, then they were classified by traditional machine learning algorithms with 10-fold cross-validation. Based on the results, LLT greatly increased the accuracy for all cryptocurrencies, which emphasizes the potential of the LLT algorithm in predicting price movements.

Balázs P. Halmos, Balázs Hajós, Vince Á. Molnár et al.

We introduce ALT, an open-source Python package created for efficient and accurate time series classification (TSC). The package implements the adaptive law-based transformation (ALT) algorithm, which transforms raw time series data into a linearly separable feature space using variable-length shifted time windows. This adaptive approach enhances its predecessor, the linear law-based transformation (LLT), by effectively capturing patterns of varying temporal scales. The software is implemented for scalability, interpretability, and ease of use, achieving state-of-the-art performance with minimal computational overhead. Extensive benchmarking on real-world datasets demonstrates the utility of ALT for diverse TSC tasks in physics and related domains.

Marcell T. Kurbucz, Balázs Hajós, Balázs P. Halmos et al.

Time series classification (TSC) is fundamental in numerous domains, including finance, healthcare, and environmental monitoring. However, traditional TSC methods often struggle with the inherent complexity and variability of time series data. Building on our previous work with the linear law-based transformation (LLT) - which improved classification accuracy by transforming the feature space based on key data patterns - we introduce adaptive law-based transformation (ALT). ALT enhances LLT by incorporating variable-length shifted time windows, enabling it to capture distinguishing patterns of various lengths and thereby handle complex time series more effectively. By mapping features into a linearly separable space, ALT provides a fast, robust, and transparent solution that achieves state-of-the-art performance with only a few hyperparameters.

András Telcs, Marcell T. Kurbucz, Antal Jakovác

Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved hidden drivers on the observed dynamics. This paper presents a unified method capable of identifying fundamental causal relationships between pairs of systems, whether deterministic or stochastic. Notably, the method also uncovers hidden common causes beyond the observed variables. By analyzing the degrees of freedom in the system, our approach provides a more comprehensive understanding of both causal influence and hidden confounders. This unified framework is validated through theoretical models and simulations, demonstrating its robustness and potential for broader application.

Marcell T. Kurbucz, Péter Pósfay, Antal Jakovác

The goals of this paper are twofold: (1) to present a new method that is able to find linear laws governing the time evolution of Markov chains and (2) to apply this method for anomaly detection in Bitcoin prices. To accomplish these goals, first, the linear laws of Markov chains are derived by using the time embedding of their (categorical) autocorrelation function. Then, a binary series is generated from the first difference of Bitcoin exchange rate (against the United States Dollar). Finally, the minimum number of parameters describing the linear laws of this series is identified through stepped time windows. Based on the results, linear laws typically became more complex (containing an additional third parameter that indicates hidden Markov property) in two periods: before the crash of cryptocurrency markets inducted by the COVID-19 pandemic (12 March 2020), and before the record-breaking surge in the price of Bitcoin (Q4 2020 - Q1 2021). In addition, the locally high values of this third parameter are often related to short-term price peaks, which suggests price manipulation.