Abstract The article presents new tools for investigating the statistical properties of the harmonic signal autocorrelation function (ACF). These tools enable identification of the ACF estimator errors in measurements in which the triggering of the measurements is non-synchronized. This is important because in many measurement situations the initial phase of the measured signal is random. The developed tools enable testing the ACF estimator of a harmonic signal in the presence of Gaussian noise. These are the formulas on the basis of which the statistical properties of the estimator can be determined, including the bias, the variance and the mean squared error (MSE). For comparison, the article also presents the ACF statistical analysis tools used in the conditions of synchronized measurement triggering, known from the literature. Operation of the new tools is verified by simulation and experimental studies. The conducted research shows that differences between the MSE results obtained with the use of the developed formulas and those attained from simulations and experimental tests are not greater than 1 dB.
{"title":"On the statistical analysis of the harmonic signal autocorrelation function","authors":"S. Sienkowski, M. Krajewski","doi":"10.34768/amcs-2021-0050","DOIUrl":"https://doi.org/10.34768/amcs-2021-0050","url":null,"abstract":"Abstract The article presents new tools for investigating the statistical properties of the harmonic signal autocorrelation function (ACF). These tools enable identification of the ACF estimator errors in measurements in which the triggering of the measurements is non-synchronized. This is important because in many measurement situations the initial phase of the measured signal is random. The developed tools enable testing the ACF estimator of a harmonic signal in the presence of Gaussian noise. These are the formulas on the basis of which the statistical properties of the estimator can be determined, including the bias, the variance and the mean squared error (MSE). For comparison, the article also presents the ACF statistical analysis tools used in the conditions of synchronized measurement triggering, known from the literature. Operation of the new tools is verified by simulation and experimental studies. The conducted research shows that differences between the MSE results obtained with the use of the developed formulas and those attained from simulations and experimental tests are not greater than 1 dB.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"6 1","pages":"729 - 744"},"PeriodicalIF":1.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91262144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Iaroslav Iaremko, R. Šenkeřík, R. Jašek, Petr Lukastik
Abstract This work presents an original model for detecting machine tool anomalies and emergency states through operation data processing. The paper is focused on an elastic hierarchical system for effective data reduction and classification, which encompasses several modules. Firstly, principal component analysis (PCA) is used to perform data reduction of many input signals from big data tree topology structures into two signals representing all of them. Then the technique for segmentation of operating machine data based on dynamic time distortion and hierarchical clustering is used to calculate signal accident characteristics using classifiers such as the maximum level change, a signal trend, the variance of residuals, and others. Data segmentation and analysis techniques enable effective and robust detection of operating machine tool anomalies and emergency states due to almost real-time data collection from strategically placed sensors and results collected from previous production cycles. The emergency state detection model described in this paper could be beneficial for improving the production process, increasing production efficiency by detecting and minimizing machine tool error conditions, as well as improving product quality and overall equipment productivity. The proposed model was tested on H-630 and H-50 machine tools in a real production environment of the Tajmac-ZPS company.
{"title":"An effective data reduction model for machine emergency state detection from big data tree topology structures","authors":"Iaroslav Iaremko, R. Šenkeřík, R. Jašek, Petr Lukastik","doi":"10.34768/amcs-2021-0041","DOIUrl":"https://doi.org/10.34768/amcs-2021-0041","url":null,"abstract":"Abstract This work presents an original model for detecting machine tool anomalies and emergency states through operation data processing. The paper is focused on an elastic hierarchical system for effective data reduction and classification, which encompasses several modules. Firstly, principal component analysis (PCA) is used to perform data reduction of many input signals from big data tree topology structures into two signals representing all of them. Then the technique for segmentation of operating machine data based on dynamic time distortion and hierarchical clustering is used to calculate signal accident characteristics using classifiers such as the maximum level change, a signal trend, the variance of residuals, and others. Data segmentation and analysis techniques enable effective and robust detection of operating machine tool anomalies and emergency states due to almost real-time data collection from strategically placed sensors and results collected from previous production cycles. The emergency state detection model described in this paper could be beneficial for improving the production process, increasing production efficiency by detecting and minimizing machine tool error conditions, as well as improving product quality and overall equipment productivity. The proposed model was tested on H-630 and H-50 machine tools in a real production environment of the Tajmac-ZPS company.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"30 1","pages":"601 - 611"},"PeriodicalIF":1.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89315760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Atanassov’s intuitionistic fuzzy sets and especially his intuitionistic fuzzy relations are tools that make it possible to model effectively imperfect information that we meet in many real-life situations. In this paper, we discuss the new concepts of the transitivity problem of Atanassov’s intuitionistic fuzzy relations in an epistemic aspect. The transitivity property reflects the consistency of a preference relation. Therefore, transitivity is important from the point of view of real problems appearing, e.g., in group decision making in preference procedures. We propose a new type of optimistic and pessimistic transitivity among the alternatives (options) considered and their use in the procedure of ranking the alternatives in a group decision making problem.
{"title":"New transitivity of Atanassov’s intuitionistic fuzzy sets in a decision making model","authors":"Barbara Pekala, Piotr Grochowalski, E. Szmidt","doi":"10.34768/amcs-2021-0038","DOIUrl":"https://doi.org/10.34768/amcs-2021-0038","url":null,"abstract":"Abstract Atanassov’s intuitionistic fuzzy sets and especially his intuitionistic fuzzy relations are tools that make it possible to model effectively imperfect information that we meet in many real-life situations. In this paper, we discuss the new concepts of the transitivity problem of Atanassov’s intuitionistic fuzzy relations in an epistemic aspect. The transitivity property reflects the consistency of a preference relation. Therefore, transitivity is important from the point of view of real problems appearing, e.g., in group decision making in preference procedures. We propose a new type of optimistic and pessimistic transitivity among the alternatives (options) considered and their use in the procedure of ranking the alternatives in a group decision making problem.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"327 1","pages":"563 - 576"},"PeriodicalIF":1.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76363282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper considers feature selection as a problem of an aggregation of three state-of-the-art filtration methods: Pearson’s linear correlation coefficient, the ReliefF algorithm and decision trees. A new wrapper method is proposed which, on the basis of a fusion of the above approaches and the performance of a classifier, is capable of creating a distinct, ordered subset of attributes that is optimal based on the criterion of the highest classification accuracy obtainable by a convolutional neural network. The introduced feature selection uses a weighted ranking criterion. In order to evaluate the effectiveness of the solution, the idea is compared with sequential feature selection methods that are widely known and used wrapper approaches. Additionally, to emphasize the need for dimensionality reduction, the results obtained on all attributes are shown. The verification of the outcomes is presented in the classification tasks of repository data sets that are characterized by a high dimensionality. The presented conclusions confirm that it is worth seeking new solutions that are able to provide a better classification result while reducing the number of input features.
{"title":"A weighted wrapper approach to feature selection","authors":"Maciej Kusy, R. Zajdel","doi":"10.34768/amcs-2021-0047","DOIUrl":"https://doi.org/10.34768/amcs-2021-0047","url":null,"abstract":"Abstract This paper considers feature selection as a problem of an aggregation of three state-of-the-art filtration methods: Pearson’s linear correlation coefficient, the ReliefF algorithm and decision trees. A new wrapper method is proposed which, on the basis of a fusion of the above approaches and the performance of a classifier, is capable of creating a distinct, ordered subset of attributes that is optimal based on the criterion of the highest classification accuracy obtainable by a convolutional neural network. The introduced feature selection uses a weighted ranking criterion. In order to evaluate the effectiveness of the solution, the idea is compared with sequential feature selection methods that are widely known and used wrapper approaches. Additionally, to emphasize the need for dimensionality reduction, the results obtained on all attributes are shown. The verification of the outcomes is presented in the classification tasks of repository data sets that are characterized by a high dimensionality. The presented conclusions confirm that it is worth seeking new solutions that are able to provide a better classification result while reducing the number of input features.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"47 3 1","pages":"685 - 696"},"PeriodicalIF":1.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87455596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Big data, artificial intelligence and the Internet of things (IoT) are still very popular areas in current research and industrial applications. Processing massive amounts of data generated by the IoT and stored in distributed space is not a straightforward task and may cause many problems. During the last few decades, scientists have proposed many interesting approaches to extract information and discover knowledge from data collected in database systems or other sources. We observe a permanent development of machine learning algorithms that support each phase of the data mining process, ensuring achievement of better results than before. Rough set theory (RST) delivers a formal insight into information, knowledge, data reduction, uncertainty, and missing values. This formalism, formulated in the 1980s and developed by several researches, can serve as a theoretical basis and practical background for dealing with ambiguities, data reduction, building ontologies, etc. Moreover, as a mature theory, it has evolved into numerous extensions and has been transformed through various incarnations, which have enriched expressiveness and applicability of the related tools. The main aim of this article is to present an overview of selected applications of RST in big data analysis and processing. Thousands of publications on rough sets have been contributed; therefore, we focus on papers published in the last few years. The applications of RST are considered from two main perspectives: direct use of the RST concepts and tools, and jointly with other approaches, i.e., fuzzy sets, probabilistic concepts, and deep learning. The latter hybrid idea seems to be very promising for developing new methods and related tools as well as extensions of the application area.
{"title":"Applications of rough sets in big data analysis: An overview","authors":"P. Pięta, T. Szmuc","doi":"10.34768/amcs-2021-0046","DOIUrl":"https://doi.org/10.34768/amcs-2021-0046","url":null,"abstract":"Abstract Big data, artificial intelligence and the Internet of things (IoT) are still very popular areas in current research and industrial applications. Processing massive amounts of data generated by the IoT and stored in distributed space is not a straightforward task and may cause many problems. During the last few decades, scientists have proposed many interesting approaches to extract information and discover knowledge from data collected in database systems or other sources. We observe a permanent development of machine learning algorithms that support each phase of the data mining process, ensuring achievement of better results than before. Rough set theory (RST) delivers a formal insight into information, knowledge, data reduction, uncertainty, and missing values. This formalism, formulated in the 1980s and developed by several researches, can serve as a theoretical basis and practical background for dealing with ambiguities, data reduction, building ontologies, etc. Moreover, as a mature theory, it has evolved into numerous extensions and has been transformed through various incarnations, which have enriched expressiveness and applicability of the related tools. The main aim of this article is to present an overview of selected applications of RST in big data analysis and processing. Thousands of publications on rough sets have been contributed; therefore, we focus on papers published in the last few years. The applications of RST are considered from two main perspectives: direct use of the RST concepts and tools, and jointly with other approaches, i.e., fuzzy sets, probabilistic concepts, and deep learning. The latter hybrid idea seems to be very promising for developing new methods and related tools as well as extensions of the application area.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"30 1","pages":"659 - 683"},"PeriodicalIF":1.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85548435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper is concerned with clustering with respect to the shape and size of 2D contours that are boundaries of cross-sections of 3D objects of revolution. We propose a number of similarity measures based on combined disparate Procrustes analysis (PA) and dynamic time warping (DTW) distances. A motivation and the main application for this study comes from archaeology. The computational experiments performed refer to the clustering of archaeological pottery.
{"title":"A Comprehensive Study of Clustering a Class of 2D Shapes","authors":"A. Kaliszewska, M. Syga","doi":"10.34768/amcs-2022-0008","DOIUrl":"https://doi.org/10.34768/amcs-2022-0008","url":null,"abstract":"Abstract The paper is concerned with clustering with respect to the shape and size of 2D contours that are boundaries of cross-sections of 3D objects of revolution. We propose a number of similarity measures based on combined disparate Procrustes analysis (PA) and dynamic time warping (DTW) distances. A motivation and the main application for this study comes from archaeology. The computational experiments performed refer to the clustering of archaeological pottery.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"451 1","pages":"95 - 109"},"PeriodicalIF":1.9,"publicationDate":"2021-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76060694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mingheng Zhang, Xingyi Wan, L. Gang, Xin Lv, Zengwen Wu, Zhaoyang Liu
Abstract Reliability, efficiency and generalization are basic evaluation criteria for a vehicle automated driving system. This paper proposes an automated driving decision-making method based on the Wasserstein generative adversarial imitation learning–deep deterministic policy gradient (WGAIL–DDPG(λ)). Here the exact reward function is designed based on the requirements of a vehicle’s driving performance, i.e., safety, dynamic and ride comfort performance. The model’s training efficiency is improved through the proposed imitation learning strategy, and a gain regulator is designed to smooth the transition from imitation to reinforcement phases. Test results show that the proposed decision-making model can generate actions quickly and accurately according to the surrounding environment. Meanwhile, the imitation learning strategy based on expert experience and the gain regulator can effectively improve the training efficiency for the reinforcement learning model. Additionally, an extended test also proves its good adaptability for different driving conditions.
{"title":"An Automated Driving Strategy Generating Method Based on WGAIL–DDPG","authors":"Mingheng Zhang, Xingyi Wan, L. Gang, Xin Lv, Zengwen Wu, Zhaoyang Liu","doi":"10.34768/amcs-2021-0031","DOIUrl":"https://doi.org/10.34768/amcs-2021-0031","url":null,"abstract":"Abstract Reliability, efficiency and generalization are basic evaluation criteria for a vehicle automated driving system. This paper proposes an automated driving decision-making method based on the Wasserstein generative adversarial imitation learning–deep deterministic policy gradient (WGAIL–DDPG(λ)). Here the exact reward function is designed based on the requirements of a vehicle’s driving performance, i.e., safety, dynamic and ride comfort performance. The model’s training efficiency is improved through the proposed imitation learning strategy, and a gain regulator is designed to smooth the transition from imitation to reinforcement phases. Test results show that the proposed decision-making model can generate actions quickly and accurately according to the surrounding environment. Meanwhile, the imitation learning strategy based on expert experience and the gain regulator can effectively improve the training efficiency for the reinforcement learning model. Additionally, an extended test also proves its good adaptability for different driving conditions.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"42 1","pages":"461 - 470"},"PeriodicalIF":1.9,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73630303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper proposes novel forecasting models for fractional-order chaotic oscillators, such as Duffing’s, Van der Pol’s, Tamaševičius’s and Chua’s, using feedforward neural networks. The models predict a change in the state values which bears a weighted relationship with the oscillator states. Such an arrangement is a suitable candidate model for out-of-sample forecasting of system states. The proposed neural network-assisted weighted model is applied to the above oscillators. The improved out-of-sample forecasting results of the proposed modeling strategy compared with the literature are comprehensively analyzed. The proposed models corresponding to the optimal weights result in the least mean square error (MSE) for all the system states. Further, the MSE for the proposed model is less in most of the oscillators compared with the one reported in the literature. The proposed prediction model’s out-of-sample forecasting plots show the best tracking ability to approximate future state values.
本文提出了一种基于前馈神经网络的分数阶混沌振子Duffing’s、Van der Pol’s、Tamaševičius’s和Chua’s预测模型。该模型预测状态值的变化与振子状态有加权关系。这种排列是一种适合于系统状态的样本外预测的候选模型。将所提出的神经网络辅助加权模型应用于上述振子。并将改进后的模型预测结果与文献进行了比较。所提出的模型与最优权重相对应，使系统所有状态的均方误差(MSE)最小。此外，与文献中报道的模型相比，所提出模型的MSE在大多数振荡器中都较小。所提出的预测模型的样本外预测图显示出最好的跟踪能力，以近似未来的状态值。
{"title":"Forecasting Models for Chaotic Fractional–Order Oscillators Using Neural Networks","authors":"Kishore Bingi, B. Prusty","doi":"10.34768/amcs-2021-0026","DOIUrl":"https://doi.org/10.34768/amcs-2021-0026","url":null,"abstract":"Abstract This paper proposes novel forecasting models for fractional-order chaotic oscillators, such as Duffing’s, Van der Pol’s, Tamaševičius’s and Chua’s, using feedforward neural networks. The models predict a change in the state values which bears a weighted relationship with the oscillator states. Such an arrangement is a suitable candidate model for out-of-sample forecasting of system states. The proposed neural network-assisted weighted model is applied to the above oscillators. The improved out-of-sample forecasting results of the proposed modeling strategy compared with the literature are comprehensively analyzed. The proposed models corresponding to the optimal weights result in the least mean square error (MSE) for all the system states. Further, the MSE for the proposed model is less in most of the oscillators compared with the one reported in the literature. The proposed prediction model’s out-of-sample forecasting plots show the best tracking ability to approximate future state values.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"42 1","pages":"387 - 398"},"PeriodicalIF":1.9,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74583125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector’s indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers’ sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace–Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer’s length (understood as the sum of the volume vector’s indications). Moreover, we present some numerical computations illustrating theoretical results.
{"title":"Queueing Systems with Random Volume Customers and a Sectorized Unlimited Memory Buffer","authors":"O. Tikhonenko, M. Ziółkowski, W. Kempa","doi":"10.34768/amcs-2021-0032","DOIUrl":"https://doi.org/10.34768/amcs-2021-0032","url":null,"abstract":"Abstract In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector’s indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers’ sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace–Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer’s length (understood as the sum of the volume vector’s indications). Moreover, we present some numerical computations illustrating theoretical results.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"64 1","pages":"471 - 486"},"PeriodicalIF":1.9,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78936111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A linear combination of Gaussian components is known as a Gaussian mixture model. It is widely used in data mining and pattern recognition. In this paper, we propose a method to estimate the parameters of the density function given by a Gaussian mixture model. Our proposal is based on the Gini index, a methodology to measure the inequality degree between two probability distributions, and consists in minimizing the Gini index between an empirical distribution for the data and a Gaussian mixture model. We will show several simulated examples and real data examples, observing some of the properties of the proposed method.
{"title":"Fitting a Gaussian Mixture Model Through the Gini Index","authors":"A. López-Lobato, M. L. Avendaño-Garrido","doi":"10.34768/amcs-2021-0033","DOIUrl":"https://doi.org/10.34768/amcs-2021-0033","url":null,"abstract":"Abstract A linear combination of Gaussian components is known as a Gaussian mixture model. It is widely used in data mining and pattern recognition. In this paper, we propose a method to estimate the parameters of the density function given by a Gaussian mixture model. Our proposal is based on the Gini index, a methodology to measure the inequality degree between two probability distributions, and consists in minimizing the Gini index between an empirical distribution for the data and a Gaussian mixture model. We will show several simulated examples and real data examples, observing some of the properties of the proposed method.","PeriodicalId":50339,"journal":{"name":"International Journal of Applied Mathematics and Computer Science","volume":"479 1","pages":"487 - 500"},"PeriodicalIF":1.9,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77473772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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