Familiar methods for knowledge derivation are based on statistical procedures, which are not accompanied by algorithms for updating of knowledge in real time. In this work, the algorithms are implemented successfully using both logical and statistical procedures whereby flexible arrays of experimental data is entered such that older data is removed and newer data is added. These data are packed together in groups and transformed into logical values of functions of multi-valued logic. The functions are accompanied by probability of occurrence of its values, which is evaluated in real time. In this way, a new construction is formed called multi-valued logical probability function (MLPF), which expresses simultaneously two mutually related correspondences-logical and probabilistic. The correspondences are updated in real time. MLPF is a system of production rules, which are updated in real time.
{"title":"Multi-valued logical method for knowledge extraction and updating in real time","authors":"E. Gegov, B. Vatchova, E. Gegov","doi":"10.1109/IS.2008.4670545","DOIUrl":"https://doi.org/10.1109/IS.2008.4670545","url":null,"abstract":"Familiar methods for knowledge derivation are based on statistical procedures, which are not accompanied by algorithms for updating of knowledge in real time. In this work, the algorithms are implemented successfully using both logical and statistical procedures whereby flexible arrays of experimental data is entered such that older data is removed and newer data is added. These data are packed together in groups and transformed into logical values of functions of multi-valued logic. The functions are accompanied by probability of occurrence of its values, which is evaluated in real time. In this way, a new construction is formed called multi-valued logical probability function (MLPF), which expresses simultaneously two mutually related correspondences-logical and probabilistic. The correspondences are updated in real time. MLPF is a system of production rules, which are updated in real time.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121816431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Video-based surveillance and security become extremely important in the new, 21st century for human safety, counter-terrorism, traffic control etc. Visual novelty detection and tracking are key elements of such activities. The current state-of-the-art approaches often suffer from high computational, memory storage costs and from not being fully automated (they usually require a human operator in the loop). This paper introduces a new approach to the problem of novelty detection in video streams that is based on recursive, and therefore, computationally efficient density estimation by a Cauchy type of kernel (as opposed to the usually used Gaussian one). The idea of the proposed approach stems from the recently introduced evolving clustering approach, eClustering and is suitable for online and real-time applications in fully autonomous and unsupervised systems as a stand-alone novelty detector or for priming a tracking algorithm. The approach proposed in this paper has evolving property - it can gradually update the background model and the criteria to detect novelty by unsupervised online learning. The proposed approach is faster by an order of magnitude than the well known kernel density estimation (KDE) method for background subtraction, while having has adaptive characteristics, and does not need any threshold to be pre-specified. Recursive expressions similar to the proposed approach in this paper can also be applied to image segmentation and landmark recognition used for self-localization in robotics. If combined with a real-time prediction using Kalman filter or evolving Takagi-Sugeno fuzzy models a fast and fully autonomous tracking system can be realized with potential applications in surveillance and robotic systems.
{"title":"A fast approach to novelty detection in video streams using recursive density estimation","authors":"R. Ramezani, P. Angelov, Xiaowei Zhou","doi":"10.1109/IS.2008.4670523","DOIUrl":"https://doi.org/10.1109/IS.2008.4670523","url":null,"abstract":"Video-based surveillance and security become extremely important in the new, 21st century for human safety, counter-terrorism, traffic control etc. Visual novelty detection and tracking are key elements of such activities. The current state-of-the-art approaches often suffer from high computational, memory storage costs and from not being fully automated (they usually require a human operator in the loop). This paper introduces a new approach to the problem of novelty detection in video streams that is based on recursive, and therefore, computationally efficient density estimation by a Cauchy type of kernel (as opposed to the usually used Gaussian one). The idea of the proposed approach stems from the recently introduced evolving clustering approach, eClustering and is suitable for online and real-time applications in fully autonomous and unsupervised systems as a stand-alone novelty detector or for priming a tracking algorithm. The approach proposed in this paper has evolving property - it can gradually update the background model and the criteria to detect novelty by unsupervised online learning. The proposed approach is faster by an order of magnitude than the well known kernel density estimation (KDE) method for background subtraction, while having has adaptive characteristics, and does not need any threshold to be pre-specified. Recursive expressions similar to the proposed approach in this paper can also be applied to image segmentation and landmark recognition used for self-localization in robotics. If combined with a real-time prediction using Kalman filter or evolving Takagi-Sugeno fuzzy models a fast and fully autonomous tracking system can be realized with potential applications in surveillance and robotic systems.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116525624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper focuses on neural networks with complex-valued (CV) neurons as well as on selected aspects of neural networks learning, pruning and rule extraction. CV neurons can be used as versatile substitutes in real-valued perceptron networks. Learning of CV layers is discussed in context of traditional multilayer feedforward architecture. Such learning is derivative-free and it usually requires networks of reduced size. Selected examples and applications of CV-networks in bioinformatics and pattern recognition are discussed. The paper also covers specialized learning techniques for logic rule extraction. Such techniques include learning with pruning, and can be used in expert systems, and other applications that rely on models developed to fit measured data.
{"title":"Learning in networks: Complex-valued neurons, pruning, and rule extraction","authors":"J. Zurada, I. Aizenberg, M. Mazurowski","doi":"10.1109/IS.2008.4670394","DOIUrl":"https://doi.org/10.1109/IS.2008.4670394","url":null,"abstract":"This paper focuses on neural networks with complex-valued (CV) neurons as well as on selected aspects of neural networks learning, pruning and rule extraction. CV neurons can be used as versatile substitutes in real-valued perceptron networks. Learning of CV layers is discussed in context of traditional multilayer feedforward architecture. Such learning is derivative-free and it usually requires networks of reduced size. Selected examples and applications of CV-networks in bioinformatics and pattern recognition are discussed. The paper also covers specialized learning techniques for logic rule extraction. Such techniques include learning with pruning, and can be used in expert systems, and other applications that rely on models developed to fit measured data.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131638539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Case-based planning which is an induction-based mechanism, has many practical applications in designing and planning of multi-agent systems, which has been recently known as a powerful processing tool in transactional and interactive environments. Intelligent tutoring systems, that have drawn the most attention in the computational mechanisms of concept transition in recent years, have successfully put into practice the concept of multi-agent interaction as well. This paper describes the advances applied in our intelligent tutoring multi-agent system architecture which facilitate meeting the requirements of intelligent tutoring systems and their users. In addition throughout this paper it is explained how case-based planning is utilized for designing and planning the proposed intelligent tutoring multi-agent system to attain an optimized final plan for current user or environment.
{"title":"A case-based planning approach to design and plan ITMAS","authors":"S. Saberi, Esfandiar Mohammad","doi":"10.1109/IS.2008.4670479","DOIUrl":"https://doi.org/10.1109/IS.2008.4670479","url":null,"abstract":"Case-based planning which is an induction-based mechanism, has many practical applications in designing and planning of multi-agent systems, which has been recently known as a powerful processing tool in transactional and interactive environments. Intelligent tutoring systems, that have drawn the most attention in the computational mechanisms of concept transition in recent years, have successfully put into practice the concept of multi-agent interaction as well. This paper describes the advances applied in our intelligent tutoring multi-agent system architecture which facilitate meeting the requirements of intelligent tutoring systems and their users. In addition throughout this paper it is explained how case-based planning is utilized for designing and planning the proposed intelligent tutoring multi-agent system to attain an optimized final plan for current user or environment.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132759932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a genetic algorithm (GA) based approach for solving the optimal power flow with FACTS devices to eliminate line over loads in the system following single line outages. The proposed approach introduces an index called the single contingency sensitivity (SCS) index to rank the system branches according to their suitability for installing thyristor controlled series capacitors(TCSCs). Once the locations are determined, the problem of identifying the optimal TCSC parameters is formulated as an optimization problem and a GA based approach is applied to solve the optimal power flow (OPF) problem. IEEE 30 bus system is considered to demonstrate the suitability of this algorithm. Case studies on IEEE test system show the effectiveness of this algorithm.
{"title":"Genetic Algorithm approach for Optimal Power Flow with FACTS devices","authors":"R. Banu, D. Devaraj","doi":"10.1109/IS.2008.4670477","DOIUrl":"https://doi.org/10.1109/IS.2008.4670477","url":null,"abstract":"This paper presents a genetic algorithm (GA) based approach for solving the optimal power flow with FACTS devices to eliminate line over loads in the system following single line outages. The proposed approach introduces an index called the single contingency sensitivity (SCS) index to rank the system branches according to their suitability for installing thyristor controlled series capacitors(TCSCs). Once the locations are determined, the problem of identifying the optimal TCSC parameters is formulated as an optimization problem and a GA based approach is applied to solve the optimal power flow (OPF) problem. IEEE 30 bus system is considered to demonstrate the suitability of this algorithm. Case studies on IEEE test system show the effectiveness of this algorithm.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134251840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
There is growing interest in modeling and processing nonlinear behavior in the biological systems. In this paper we applied such methods for detecting Functional Disorder in Gastric. Conventional tools for analyzing such data use information from the power spectral density of the time series, and hence are restricted to little information of data. This information does not provide a sufficient representation of a signal with strong nonlinear properties. In this work, we attempt to extract various nonlinear dynamical invariants of the underlying attractor from the signals. We show that these invariants can discriminate between normal and Functional Gastrointestinal Disorders (FGD) classes.
{"title":"Neural network application in strange attractor investigation to detect a FGD","authors":"Y. Z. Mehran, A. Nasrabadi","doi":"10.1109/IS.2008.4670470","DOIUrl":"https://doi.org/10.1109/IS.2008.4670470","url":null,"abstract":"There is growing interest in modeling and processing nonlinear behavior in the biological systems. In this paper we applied such methods for detecting Functional Disorder in Gastric. Conventional tools for analyzing such data use information from the power spectral density of the time series, and hence are restricted to little information of data. This information does not provide a sufficient representation of a signal with strong nonlinear properties. In this work, we attempt to extract various nonlinear dynamical invariants of the underlying attractor from the signals. We show that these invariants can discriminate between normal and Functional Gastrointestinal Disorders (FGD) classes.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116766638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work is focused on developing a more efficient computational scheme for estimation of process reaction rates based on NN models. In contrast to the traditional way of process reaction rates estimation by exhaustive and expensive search for the most appropriate parameterized structure, a neural network (NN) based procedure is proposed here to identify the reaction rates in the framework of an analytical process model. The reaction rates are not measured, therefore a special hybrid NN training structure and adaptation algorithm are proposed to make possible the supervised NN learning. The present contribution is focused on the general modelling of a class of nonlinear systems representing several industrial processes including crystallization and precipitation, polymerization reactors, distillation columns, biochemical fermentation and biological systems. The proposed algorithm is further applied for estimation of the sugar crystallization growth rate and compared with alternative solution.
{"title":"Neural network - based estimation of reaction rates with partly unknown states and completely known kinetics coefficients","authors":"P. Georgieva, S. de Azevedo","doi":"10.1109/IS.2008.4670443","DOIUrl":"https://doi.org/10.1109/IS.2008.4670443","url":null,"abstract":"This work is focused on developing a more efficient computational scheme for estimation of process reaction rates based on NN models. In contrast to the traditional way of process reaction rates estimation by exhaustive and expensive search for the most appropriate parameterized structure, a neural network (NN) based procedure is proposed here to identify the reaction rates in the framework of an analytical process model. The reaction rates are not measured, therefore a special hybrid NN training structure and adaptation algorithm are proposed to make possible the supervised NN learning. The present contribution is focused on the general modelling of a class of nonlinear systems representing several industrial processes including crystallization and precipitation, polymerization reactors, distillation columns, biochemical fermentation and biological systems. The proposed algorithm is further applied for estimation of the sugar crystallization growth rate and compared with alternative solution.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126096557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Olivier Couturier, Vincent Dubois, Tien-Ning Hsu, E. Nguifo
Providing efficient and easy-to-use graphical tools to users is a promising challenge for data mining (DM). Visual data mining (VDM) is a new and active research area which goal is to provide powerful and suitable tools for data miners. Some graphical tools have been developed to extract and visualize association rules (AR), among which a three dimension representation where the x-axis is the AR premise, the y-axis is the AR conclusion and the z-axis is a metric value of AR. The 3D approach is one standard representation that is often implemented in many DM tools. However this approach suffers from an overlapping between several objects in the 3D space making some objects unseen or partially truncated. This problem is known as the occlusion problem. In this paper, we propose to formalize it as an optimisation problem of occlusions. Then we define conditions to limit occlusions and finally we propose different heuristics based on ordering of axis-elements, to considerably reduce the number of generated occlusions.
为用户提供高效且易于使用的图形工具是数据挖掘(DM)面临的一个很有前途的挑战。可视化数据挖掘(Visual data mining, VDM)是一个新兴的、活跃的研究领域，其目标是为数据挖掘者提供强大的、合适的工具。已经开发了一些图形工具来提取和可视化关联规则(AR)，其中x轴是AR前提，y轴是AR结论，z轴是AR度量值的三维表示。3D方法是许多DM工具中经常实现的一种标准表示。然而，这种方法受到3D空间中多个对象之间重叠的影响，使得一些对象看不见或部分截断。这个问题被称为遮挡问题。在本文中，我们建议将其形式化为遮挡的优化问题。然后我们定义了限制遮挡的条件，最后我们提出了基于轴元素排序的不同启发式方法，以大大减少生成的遮挡数量。
{"title":"Optimizing occlusion appearances in 3D association rules visualization","authors":"Olivier Couturier, Vincent Dubois, Tien-Ning Hsu, E. Nguifo","doi":"10.1109/IS.2008.4670537","DOIUrl":"https://doi.org/10.1109/IS.2008.4670537","url":null,"abstract":"Providing efficient and easy-to-use graphical tools to users is a promising challenge for data mining (DM). Visual data mining (VDM) is a new and active research area which goal is to provide powerful and suitable tools for data miners. Some graphical tools have been developed to extract and visualize association rules (AR), among which a three dimension representation where the x-axis is the AR premise, the y-axis is the AR conclusion and the z-axis is a metric value of AR. The 3D approach is one standard representation that is often implemented in many DM tools. However this approach suffers from an overlapping between several objects in the 3D space making some objects unseen or partially truncated. This problem is known as the occlusion problem. In this paper, we propose to formalize it as an optimisation problem of occlusions. Then we define conditions to limit occlusions and finally we propose different heuristics based on ordering of axis-elements, to considerably reduce the number of generated occlusions.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126161521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes an intelligent component based approach for batch control based on ANSI/ISA S88 standard. Common intelligent software components have been built and reused for different application. The components are managed in a control recipe that describes their execution schedule. Furthermore, IEC 61499 standard is adopted as an application framework in which the functional components are implemented as IEC 61499 based function blocks (FB). The operation schedule of the controlled components is then implemented according IEC 61499, based on scheduler-selector-synchronizer (S3) architecture and SIPN models describing the sequence of control execution. An example of the proposed approach based on the real plant for distillation of sulphate turpentine located in Velingrad, Bulgaria is presented and discussed.
{"title":"Intelligent component based batch control using IEC61499 and ANSI/ISA S88","authors":"D. Ivanova, Georg Frey, I. Batchkova","doi":"10.1109/IS.2008.4670424","DOIUrl":"https://doi.org/10.1109/IS.2008.4670424","url":null,"abstract":"This paper proposes an intelligent component based approach for batch control based on ANSI/ISA S88 standard. Common intelligent software components have been built and reused for different application. The components are managed in a control recipe that describes their execution schedule. Furthermore, IEC 61499 standard is adopted as an application framework in which the functional components are implemented as IEC 61499 based function blocks (FB). The operation schedule of the controlled components is then implemented according IEC 61499, based on scheduler-selector-synchronizer (S3) architecture and SIPN models describing the sequence of control execution. An example of the proposed approach based on the real plant for distillation of sulphate turpentine located in Velingrad, Bulgaria is presented and discussed.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130242127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present theoretical results regarding decomposition of matrices with grades, i.e. matrices I with entries from a bounded ordered set L such as the real unit interval [0, 1]. If I is such an n times m matrix, we look for a decomposition of I into a product A omicron B of an ntimesk matrix A and a ktimesm matrix B with entries from L with k as small as possible. This problem generalizes the decomposition problem of Boolean factor analysis which is a particular case when L has just two elements 0 and 1. The product we consider is a supt-norm product of which the well known max-min product of Boolean matrices as well as max-min and max-min product of matrices with entries from [0, 1] are particular examples. I, A, and B can be interpreted as object times attribute, object times factor, and factor times attribute matrices describing degrees of expression of attributes on objects, factors on objects, and attributes on factors. In this interpretation, a decomposition I into A omicron B corresponds to discovery of k factors explaining the original data I. We propose to use formal concepts of I in the sense of formal concept analysis as factors. The formal concepts are fixed points of a particular closure operator and can be seen as particular submatrices of I. We prove several results regarding such a decomposition including a theorem which says that decompositions using formal concepts as factors are optimal in that they provide us with the least number of factors possible. Based on the geometrical insight provided by the theorem, we propose a greedy approximation algorithm for finding optimal decompositions. We provide examples illustrating the concepts and implications of the results.
{"title":"Optimal decompositions of matrices with grades","authors":"R. Belohlávek","doi":"10.1109/IS.2008.4670530","DOIUrl":"https://doi.org/10.1109/IS.2008.4670530","url":null,"abstract":"We present theoretical results regarding decomposition of matrices with grades, i.e. matrices I with entries from a bounded ordered set L such as the real unit interval [0, 1]. If I is such an n times m matrix, we look for a decomposition of I into a product A omicron B of an ntimesk matrix A and a ktimesm matrix B with entries from L with k as small as possible. This problem generalizes the decomposition problem of Boolean factor analysis which is a particular case when L has just two elements 0 and 1. The product we consider is a supt-norm product of which the well known max-min product of Boolean matrices as well as max-min and max-min product of matrices with entries from [0, 1] are particular examples. I, A, and B can be interpreted as object times attribute, object times factor, and factor times attribute matrices describing degrees of expression of attributes on objects, factors on objects, and attributes on factors. In this interpretation, a decomposition I into A omicron B corresponds to discovery of k factors explaining the original data I. We propose to use formal concepts of I in the sense of formal concept analysis as factors. The formal concepts are fixed points of a particular closure operator and can be seen as particular submatrices of I. We prove several results regarding such a decomposition including a theorem which says that decompositions using formal concepts as factors are optimal in that they provide us with the least number of factors possible. Based on the geometrical insight provided by the theorem, we propose a greedy approximation algorithm for finding optimal decompositions. We provide examples illustrating the concepts and implications of the results.","PeriodicalId":305750,"journal":{"name":"2008 4th International IEEE Conference Intelligent Systems","volume":"122 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121443737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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