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Using cantor sets for error detection.

ABSTRACT: Error detection is a fundamental need in most computer networks and communication systems in order to combat the effect of noise. Error detection techniques have also been incorporated with lossless data compression algorithms for transmission across communication networks. In this paper, we propose to incorporate a novel error detection scheme into a Shannon optimal lossless data compression algorithm known as Generalized Luröth Series (GLS) coding. GLS-coding is a generalization of the popular Arithmetic Coding which is an integral part of the JPEG2000 standard for still image compression. GLS-coding encodes the input message as a symbolic sequence on an appropriate 1D chaotic map Generalized Luröth Series (GLS) and the compressed file is obtained as the initial value by iterating backwards on the map. However, in the presence of noise, even small errors in the compressed file leads to catastrophic decoding errors owing to sensitive dependence on initial values, the hallmark of deterministic chaos. In this paper, we first show that repetition codes, the oldest and the most basic error correction and detection codes in literature, actually lie on a Cantor set with a fractal dimension of 1n , which is also the rate of the code. Inspired by this, we incorporate error detection capability to GLS-coding by ensuring that the compressed file (initial value on the chaotic map) lies on a Cantor set. Even a 1-bit error in the initial value will throw it outside the Cantor set, which can be detected while decoding. The rate of the code can be adjusted by the fractal dimension of the Cantor set, thereby controlling the error detection performance.

SUBMITTER: Nagaraj N

PROVIDER: S-EPMC7924470 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundOutliers, data points that significantly deviate from the norm, can have a substantial impact on statistical inference and provide valuable insights in data analysis. Multiple methods have been developed for outlier detection, however, almost all available approaches fail to consider the spatial dependence and heterogeneity in spatial data. Spatial data has diverse formats and semantics, requiring specialized outlier detection methodology to handle these unique properties. For now, there is limited research exists on robust spatial outlier detection methods designed specifically under the spatial error model (SEM) structure.MethodWe propose the Spatial-Θ-Iterative Procedure for Outlier Detection (Spatial-Θ-IPOD), which utilizes a mean-shift vector to identify outliers within the SEM. Our method enables an effective detection of spatial outliers while also providing robust coefficient estimates. To assess the performance of our approach, we conducted extensive simulations and applied it to a real-world empirical study using life expectancy data from multiple countries.ResultsSimulation results showed that the masking and JD (Joint Detection) indicators of our Spatial-Θ-IPOD method outperformed several commonly used methods, even in high-dimensional scenarios, demonstrating stable performance. Conversely, the Θ-IPOD method proved to be ineffective in detecting outliers when spatial correlation was present. Moreover, our model successfully provided reliable coefficient estimation alongside outlier detection. The proposed method consistently outperformed other models (both robust and non-robust) in most cases. In the empirical study, our proposed model successfully detected outliers and provided valuable insights in the modeling process.ConclusionsOur proposed Spatial-Θ-IPOD offers an effective solution for detecting spatial outliers for SEM while providing robust coefficient estimates. Notably, our approach showcases its relative superiority even in the presence of high leverage points. By successfully identifying outliers, our method enhances the overall understanding of the data and provides valuable insights for further analysis.

Project description:Error-related potentials (ErrPs) have been proposed as a means for improving brain-computer interface (BCI) performance by either correcting an incorrect action performed by the BCI or label data for continuous adaptation of the BCI to improve the performance. The latter approach could be relevant within stroke rehabilitation where BCI calibration time could be minimized by using a generalized classifier that is continuously being individualized throughout the rehabilitation session. This may be achieved if data are correctly labelled. Therefore, the aims of this study were: (1) classify single-trial ErrPs produced by individuals with stroke, (2) investigate test-retest reliability, and (3) compare different classifier calibration schemes with different classification methods (artificial neural network, ANN, and linear discriminant analysis, LDA) with waveform features as input for meaningful physiological interpretability. Twenty-five individuals with stroke operated a sham BCI on two separate days where they attempted to perform a movement after which they received feedback (error/correct) while continuous EEG was recorded. The EEG was divided into epochs: ErrPs and NonErrPs. The epochs were classified with a multi-layer perceptron ANN based on temporal features or the entire epoch. Additionally, the features were classified with shrinkage LDA. The features were waveforms of the ErrPs and NonErrPs from the sensorimotor cortex to improve the explainability and interpretation of the output of the classifiers. Three calibration schemes were tested: within-day, between-day, and across-participant. Using within-day calibration, 90% of the data were correctly classified with the entire epoch as input to the ANN; it decreased to 86% and 69% when using temporal features as input to ANN and LDA, respectively. There was poor test-retest reliability between the two days, and the other calibration schemes led to accuracies in the range of 63-72% with LDA performing the best. There was no association between the individuals' impairment level and classification accuracies. The results show that ErrPs can be classified in individuals with stroke, but that user- and session-specific calibration is needed for optimal ErrP decoding with this approach. The use of ErrP/NonErrP waveform features makes it possible to have a physiological meaningful interpretation of the output of the classifiers. The results may have implications for labelling data continuously in BCIs for stroke rehabilitation and thus potentially improve the BCI performance.

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Using cantor sets for error detection.

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